Abstract: This introduction to the R package rgenoud is a modied version of Mebane and Sekhon (2011), published in the Journal of Statistical Software. That version of the introduction contains higher resolution gures. genoud is an R function that combines evolutionary algorithm methods with a derivativebased (quasi-Newton) method to solve dicult optimization problems. genoud may also be used for optimization problems for which derivatives do not exist. genoud solves problems that are nonlinear or perhaps even discontinuous in the parameters of the function to be optimized. When the function to be optimized (for example, a log-likelihood) is nonlinear in the model’s parameters, the function will generally not be globally concave and may have irregularities such as saddlepoints or discontinuities. Optimization methods that rely on derivatives of the objective function may be unable to nd any optimum at all. Multiple local optima may exist, so that there is no guarantee that a derivative-based method will converge to the global optimum. On the other hand, algorithms that do not use derivative information (such as pure genetic algorithms) are for many problems needlessly poor at local hill climbing. Most statistical problems are regular in a neighborhood of the solution. Therefore, for some portion of the search space, derivative information is useful. The function supports parallel processing on multiple CPUs on a single machine or a cluster of computers.

Abstract: We present a current catalog of 21 cm HI line sources extracted from the Arecibo Legacy Fast Arecibo L-band Feed Array (ALFALFA) survey over ~2800 square degrees of sky: the alpha.40 catalog. Covering 40% of the final survey area, the alpha.40 catalog contains 15855 sources in the regions 07h30m < R.A. < 16h30m, +04 deg < Dec. < +16 deg and +24 deg < Dec. < +28 deg and 22h < R.A. < 03h, +14 deg < Dec. < +16 deg and +24 deg < Dec. < +32 deg. Of those, 15041 are certainly extragalactic, yielding a source density of 5.3 galaxies per square degree, a factor of 29 improvement over the catalog extracted from the HI Parkes All Sky Survey. In addition to the source centroid positions, HI line flux densities, recessional velocities and line widths, the catalog includes the coordinates of the most probable optical counterpart of each HI line detection, and a separate compilation provides a crossmatch to identifications given in the photometric and spectroscopic catalogs associated with the Sloan Digital Sky Survey Data Release 7. Fewer than 2% of the extragalactic HI line sources cannot be identified with a feasible optical counterpart; some of those may be rare OH megamasers at 0.16 < z < 0.25. A detailed analysis is presented of the completeness, width dependent sensitivity function and bias inherent in the current alpha.40 catalog. The impact of survey selection, distance errors, current volume coverage and local large scale structure on the derivation of the HI mass function is assessed. While alpha.40 does not yet provide a completely representative sampling of cosmological volume, derivations of the HI mass function using future data releases from ALFALFA will further improve both statistical and systematic uncertainties.

Abstract: For 3-dimensional field theories with $ \mathcal{N} = 2 $ supersymmetry the Euclidean path integrals on the three-sphere can be calculated using the method of localization; they reduce to certain matrix integrals that depend on the R-charges of the matter fields. We solve a number ofsuch large N matrix models and calculate the free energy F as a function of the trial R-charges consistent with the marginality of the super potential. In all our $ \mathcal{N} = 2 $ superconformal examples, the local maximization of F yields answers that scale as N 3/2 and agree with the dual M-theory backgrounds AdS 4 × Y, where Y are 7-dimensional Sasaki-Einstein spaces. We also find in toric examples that local F-maximization is equivalent to the minimization of the volume of Y over the space of Sasakian metrics, a procedure also referred to as Z-minimization. Moreover, we find that the functions F and Z are related for any trial R-charges. In the models we study F is positive and decreases along RG flows. We therefore propose the “F-theorem” that we hope applies to all 3-d field theories: the finite part of the free energy on the three-sphere decreases along RG trajectories and is stationary at RG fixed points. We also show that in an infinite class of Chern-Simons-matter gauge theories where the Chern-Simons levels do not sum to zero, the free energy grows as N 5/3 at large N. This non-trivial scaling matches that of the free energy of the gravity duals in type IIA string theory with Romans mass.

Abstract: For 3-dimensional field theories with {\cal N}=2 supersymmetry the Euclidean path integrals on the three-sphere can be calculated using the method of localization; they reduce to certain matrix integrals that depend on the R-charges of the matter fields. We solve a number of such large N matrix models and calculate the free energy F as a function of the trial R-charges consistent with the marginality of the superpotential. In all our {\cal N}=2 superconformal examples, the local maximization of F yields answers that scale as N^{3/2} and agree with the dual M-theory backgrounds AdS_4 x Y, where Y are 7-dimensional Sasaki-Einstein spaces. We also find in toric examples that local F-maximization is equivalent to the minimization of the volume of Y over the space of Sasakian metrics, a procedure also referred to as Z-minimization. Moreover, we find that the functions F and Z are related for any trial R-charges. In the models we study F is positive and decreases along RG flows. We therefore propose the "F-theorem" that we hope applies to all 3-d field theories: the finite part of the free energy on the three-sphere decreases along RG trajectories and is stationary at RG fixed points. We also show that in an infinite class of Chern-Simons-matter gauge theories where the Chern-Simons levels do not sum to zero, the free energy grows as N^{5/3} at large N. This non-trivial scaling matches that of the free energy of the gravity duals in type IIA string theory with Romans mass.

Abstract: In the efficient global optimization problem, we minimize an unknown function f, using as few observations f(x) as possible. It can be considered a continuum-armed-bandit problem, with noiseless data, and simple regret. Expected-improvement algorithms are perhaps the most popular methods for solving the problem; in this paper, we provide theoretical results on their asymptotic behaviour. Implementing these algorithms requires a choice of Gaussian-process prior, which determines an associated space of functions, its reproducing-kernel Hilbert space (RKHS). When the prior is fixed, expected improvement is known to converge on the minimum of any function in its RKHS. We provide convergence rates for this procedure, optimal for functions of low smoothness, and describe a modified algorithm attaining optimal rates for smoother functions. In practice, however, priors are typically estimated sequentially from the data. For standard estimators, we show this procedure may never find the minimum of f. We then propose alternative estimators, chosen to minimize the constants in the rate of convergence, and show these estimators retain the convergence rates of a fixed prior.

Abstract: This paper addresses the problem of establishing correspondences between two sets of visual features using higher order constraints instead of the unary or pairwise ones used in classical methods. Concretely, the corresponding hypergraph matching problem is formulated as the maximization of a multilinear objective function over all permutations of the features. This function is defined by a tensor representing the affinity between feature tuples. It is maximized using a generalization of spectral techniques where a relaxed problem is first solved by a multidimensional power method and the solution is then projected onto the closest assignment matrix. The proposed approach has been implemented, and it is compared to state-of-the-art algorithms on both synthetic and real data.

Abstract: Given a set F of n positive functions over a ground set X, we consider the problem of computing x* that minimizes the expression ∑f ∈ Ff(x), over x ∈ X. A typical application is shape fitting, where we wish to approximate a set P of n elements (say, points) by a shape x from a (possibly infinite) family X of shapes. Here, each point p ∈ P corresponds to a function f such that f(x) is the distance from p to x, and we seek a shape x that minimizes the sum of distances from each point in P. In the k-clustering variant, each x\in X is a tuple of k shapes, and f(x) is the distance from p to its closest shape in x.Our main result is a unified framework for constructing coresets and approximate clustering for such general sets of functions. To achieve our results, we forge a link between the classic and well defined notion of e-approximations from the theory of PAC Learning and VC dimension, to the relatively new (and not so consistent) paradigm of coresets, which are some kind of "compressed representation" of the input set F. Using traditional techniques, a coreset usually implies an LTAS (linear time approximation scheme) for the corresponding optimization problem, which can be computed in parallel, via one pass over the data, and using only polylogarithmic space (i.e, in the streaming model). For several function families F for which coresets are known not to exist, or the corresponding (approximate) optimization problems are hard, our framework yields bicriteria approximations, or coresets that are large, but contained in a low-dimensional space.We demonstrate our unified framework by applying it on projective clustering problems. We obtain new coreset constructions and significantly smaller coresets, over the ones that appeared in the literature during the past years, for problems such as: k-Median [Har-Peled and Mazumdar,STOC'04], [Chen, SODA'06], [Langberg and Schulman, SODA'10]; k-Line median [Feldman, Fiat and Sharir, FOCS'06], [Deshpande and Varadarajan, STOC'07]; Projective clustering [Deshpande et al., SODA'06] [Deshpande and Varadarajan, STOC'07]; Linear lp regression [Clarkson, Woodruff, STOC'09 ]; Low-rank approximation [Sarlos, FOCS'06]; Subspace approximation [Shyamalkumar and Varadarajan, SODA'07], [Feldman, Monemizadeh, Sohler and Woodruff, SODA'10], [Deshpande, Tulsiani, and Vishnoi, SODA'11].The running times of the corresponding optimization problems are also significantly improved. We show how to generalize the results of our framework for squared distances (as in k-mean), distances to the qth power, and deterministic constructions.

Abstract: Given a large number of basis functions that can be potentially more than the number of samples, we consider the problem of learning a sparse target function that can be expressed as a linear combination of a small number of these basis functions. We are interested in two closely related themes: · feature selection, or identifying the basis functions with nonzero coefficients; · estimation accuracy, or reconstructing the target function from noisy observations. Two heuristics that are widely used in practice are forward and backward greedy algorithms. First, we show that neither idea is adequate. Second, we propose a novel combination that is based on the forward greedy algorithm but takes backward steps adaptively whenever beneficial. For least squares regression, we develop strong theoretical results for the new procedure showing that it can effectively solve this problem under some assumptions. Experimental results support our theory.

Abstract: Given a static array of $n$ totally ordered objects, the range minimum query problem is to build a data structure that allows us to answer efficiently subsequent on-line queries of the form “what is the position of a minimum element in the subarray ranging from $i$ to $j$?”. We focus on two settings, where (1) the input array is available at query time, and (2) the input array is available only at construction time. In setting (1), we show new data structures (a) of size $\frac{2n}{c(n)}-\Theta\bigl(\frac{n\lg\lg n}{c(n)\lg n}\bigr)$ bits and query time $O(c(n))$ for any positive integer function $c(n)\in O\bigl(n^\varepsilon\bigr)$ for an arbitrary constant $0<\varepsilon<1$, or (b) with $O(nH_k)+o(n)$ bits and $O(1)$ query time, where $H_k$ denotes the empirical entropy of $k$th order of the input array. In setting (2), we give a data structure of size $2n+o(n)$ bits and query time $O(1)$. All data structures can be constructed in linear time and almost in-place.

Abstract: In this paper, new synchronization and state estimation problems are considered for an array of coupled discrete time-varying stochastic complex networks over a finite horizon. A novel concept of bounded H∞ synchronization is proposed to handle the time-varying nature of the complex networks. Such a concept captures the transient behavior of the time-varying complex network over a finite horizon, where the degree of bounded synchronization is quantified in terms of the H∞-norm. A general sector-like nonlinear function is employed to describe the nonlinearities existing in the network. By utilizing a timevarying real-valued function and the Kronecker product, criteria are established that ensure the bounded H∞ synchronization in terms of a set of recursive linear matrix inequalities (RLMIs), where the RLMIs can be computed recursively by employing available MATLAB toolboxes. The bounded H∞ state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that, over a finite horizon, the dynamics of the estimation error is guaranteed to be bounded with a given disturbance attenuation level. Again, an RLMI approach is developed for the state estimation problem. Finally, two simulation examples are exploited to show the effectiveness of the results derived in this paper.

Abstract: Given a set $F$ of $n$ positive functions over a ground set $X$, we consider the problem of computing $x^*$ that minimizes the expression $\sum_{f\in F}f(x)$, over $x\in X$. A typical application is \emph{shape fitting}, where we wish to approximate a set $P$ of $n$ elements (say, points) by a shape $x$ from a (possibly infinite) family $X$ of shapes. Here, each point $p\in P$ corresponds to a function $f$ such that $f(x)$ is the distance from $p$ to $x$, and we seek a shape $x$ that minimizes the sum of distances from each point in $P$. In the $k$-clustering variant, each $x\in X$ is a tuple of $k$ shapes, and $f(x)$ is the distance from $p$ to its closest shape in $x$. Our main result is a unified framework for constructing {\em coresets} and {\em approximate clustering} for such general sets of functions. To achieve our results, we forge a link between the classic and well defined notion of $\varepsilon$-approximations from the theory of PAC Learning and VC dimension, to the relatively new (and not so consistent) paradigm of coresets, which are some kind of "compressed representation" of the input set $F$. Using traditional techniques, a coreset usually implies an LTAS (linear time approximation scheme) for the corresponding optimization problem, which can be computed in parallel, via one pass over the data, and using only polylogarithmic space (i.e, in the streaming model). We show how to generalize the results of our framework for squared distances (as in $k$-mean), distances to the $q$th power, and deterministic constructions.

Abstract: In this paper, we introduce a two-point boundary value problem for a finite fractional difference equation. We invert the problem and construct and analyse the corresponding Green's function. We then provide an application and obtain sufficient conditions for the existence of positive solutions for a two-point boundary value problem for a nonlinear finite fractional difference equation.

Abstract: SUMMARY Seismic interferometry, also known as Green’s function retrieval by crosscorrelation, has a wide range of applications, ranging from surface wave tomography using ambient noise, to creating virtual sources for improved reflection seismology. Despite its successful applications, the crosscorrelation approach also has its limitations. The main underlying assumptions are that the medium is lossless and that the wave field is equipartitioned. These assumptions are in practice often violated: the medium of interest is often illuminated from one side only, the sources may be irregularly distributed, and, particularly for EM applications, losses may be significant. These limitations may partly be overcome by reformulating seismic interferometry as a multidimensional deconvolution (MDD) process. We present a systematic analysis of seismic interferometry by crosscorrelation and by MDD. We show that for the non-ideal situations mentioned above, the correlation function is proportional to a Green’s function with a blurred source. The source blurring is quantified by a so-called point-spread function which, like the correlation function, can be derived from the observed data (i.e., without the need to know the sources and the medium). The source of the Green’s function obtained by the correlation method can be deblurred by deconvolving the correlation function for the point-spread function. This is the essence of seismic interferometry by MDD. We illustrate the crosscorrelation and MDD methods for controlled-source and passive data applications with numerical examples and discuss the advantages and limitations of both methods.

Abstract: A new parameter-free approximation for the exchange-correlation kernel fxc of time-dependent densityfunctional theory is proposed. This kernel is expressed as an algorithm in which the exact Dyson equation for the response, as well as an approximate expression for fxc in terms of the dielectric function, are solved together self-consistently, leading to a simple parameter-free kernel. We apply this to the calculation of optical spectra for various small band gap (Ge, Si, GaAs, AlN, TiO2, SiC), large band gap (C, LiF, Ar, Ne), and magnetic (NiO) insulators. The calculated spectra are in very good agreement with the experiment for this diverse set of materials, highlighting the universal applicability of the new kernel. The ab initio calculation of optical absorption spectra of nanostructures and solids is a formidable task. The current state-of-the-art is based on many-body perturbation theory. A typical calculation involves two distinct steps: First, the quasiparticle spectral density function is calculated using the GW approximation, yielding accurate electron removal and addition energies, and is therefore a good prediction for the fundamental gap. In the second step, the BetheSalpeter equation (BSE) is solved using the one-body Green’s function obtained in the GW step. Resonances, corresponding to bound electron-hole pairs called excitons, which have energies inside the gap, can then appear in the spectrum. The two-step procedure described above is a well-established method for yielding macroscopic dielectric tensors which are generally in good agreement with the experiment [1–6]. Unfortunately, solving the BSE involves diagonalizing a large matrix which couples different Bloch state k points. As a consequence, the method is computationally expensive. Time-dependent density-functional theory (TDDFT) [7], which extends density-functional theory into the time

Abstract: In this chapter we consider the Particle Swarm Optimization (PSO) algorithm, which is another biologically inspired optimization algorithm. Consider again the problem in which we want to find the minimum of a function J(x), \(x \in {\mathbb R}^{n}\). Assume that measurements or an analytical expression of the gradient \( abla J(x)\) are not available. Moreover, even if they are available, assume the function is very non-uniform or noisy so that this information is not useful. The PSO algorithm is another population based optimization algorithm which can be used to solve such problems. It is a direct search (non-gradient) algorithm where a population of particles “search” in parallel for the minimum of a given function in a multi-dimensional (n-dimensional) space (or region/domain) without using gradient information. Below we describe the basic PSO iteration. Then we discuss a modified decentralized and asynchronous version better suited for parallel and distributed implementations. Moreover, we discuss various neighborhood strategies including static and dynamic (i.e., time-varying) neighborhoods.

Abstract: We propose an efficient bottom-up power-line communication (PLC) channel simulator that exploits transmission-line theory concepts and that is able to generate statistically representative in-home channels. We first derive from norms and practices a statistical model of European in-home topologies. The model describes how outlets are arranged in a topology and are interconnected via intermediate nodes referred to as derivation boxes. Then, we present an efficient method to compute the channel transfer function between any pair of outlets belonging to a topology realization. The method is based on a systematic remapping technique that leads to the subdivision of the network in elementary units, and on an efficient way to compute the unit transfer function referred to as the voltage ratio approach. The difference from the more conventional and complex ABCD matrix approach is also discussed. We finally show that the simulator can be configured with a small set of parameters and that it offers a theoretical framework to study the statistical PLC channel properties as a function of the topology characteristics, which is discussed in Part II of this work.

Abstract: The context is sensor control for multi-object Bayes filtering in the framework of partially observed Markov decision processes (POMDPs). The current information state is represented by the multi-object probability density function (pdf), while the reward function associated with each sensor control (action) is the information gain measured by the alpha or Renyi divergence. Assuming that both the predicted and updated state can be represented by independent identically distributed (IID) cluster random finite sets (RFSs) or, as a special case, the Poisson RFSs, this work derives the analytic expressions of the corresponding Renyi divergence based information gains. The implementation of Renyi divergence via the sequential Monte Carlo method is presented. The performance of the proposed reward function is demonstrated by a numerical example, where a moving range-only sensor is controlled to estimate the number and the states of several moving objects using the PHD filter.

Abstract: A system and method of controlling a vehicle with a trailer comprises determining the presence of a trailer, generating an oscillation signal indicative of trailer swaying relative to the vehicle, generating an initial weighted dynamic control signal for a vehicle dynamic control system in response to the oscillation signal, operating at least one vehicle dynamic system according to the dynamic control signal, and thereafter, iteratively generating a penalty function for the weighted dynamic control signal as a function of the oscillation signal response. A neural network with an associated trainer modifies the dynamic control signal as a function of trailer sway response.

Abstract: We present three formulas for calculating intersystem crossing rates in the Condon approximation to the golden rule by means of a time-dependent approach: an expression using the full time correlation function which is exact for harmonic oscillators, a second-order cumulant expansion, and a short-time approximation of this expression. While the exact expression and the cumulant expansion require numerical integration of the time correlation function, the integration of the short-time expansion can be performed analytically. To ensure convergence in the presence of large oscillations of the correlation function, we use a Gaussian damping function. The strengths and weaknesses of these approaches as well as the dependence of the results on the choice of the technical parameters of the time integration are assessed on four test examples, i.e., the nonradiative S1 ⇝ T1 transitions in thymine, phenalenone, flavone, and porphyrin. The obtained rate constants are compared with previous results of a time-independent approach. Very good agreement between the literature values and the integrals over the full time correlation functions are observed. Furthermore, the comparison suggests that the cumulant expansion approximates the exact expression very well while allowing the interval of the time integration to be significantly shorter. In cases with sufficiently high vibrational density of states also the short-time approximation yields rates in good agreement with the results of the exact formula. A great advantage of the time-dependent approach over the time-independent approach is its excellent computational efficiency making it the method of choice in cases of large energy gaps, large numbers of normal modes, and high densities of final vibrational states.

Abstract: For revenue and welfare maximization in single-dimensional Bayesian settings, Chawla et al. (STOC10) recently showed that sequential posted-price mechanisms (SPMs), though simple in form, can perform surprisingly well compared to the optimal mechanisms. In this paper, we give a theoretical explanation of this fact, based on a connection to the notion of correlation gap.Loosely speaking, for auction environments with matroid constraints, we can relate the performance of a mechanism to the expectation of a monotone submodular function over a random set. This random set corresponds to the winner set for the optimal mechanism, which is highly correlated, and corresponds to certain demand set for SPMs, which is independent. The notion of correlation gap of Agrawal et al. (SODA10) quantifies how much we "lose" in the expectation of the function by ignoring correlation in the random set, and hence bounds our loss in using certain SPM instead of the optimal mechanism. Furthermore, the correlation gap of a monotone and submodular function is known to be small, and it follows that certain SPM can approximate the optimal mechanism by a good constant factor.Exploiting this connection, we give tight analysis of a greedy-based SPM of Chawla et al. for several environments. In particular, we show that it gives an e/(e − 1)-approximation for matroid environments, gives asymptotically a 1/(1--1/√2πk)-approximation for the important sub-case of k-unit auctions, and gives a (p + 1)-approximation for environments with p-independent set system constraints.

Abstract: This paper deals with iterative gradient and subgradient methods with random feasibility steps for solving constrained convex minimization problems, where the constraint set is specified as the intersection of possibly infinitely many constraint sets. Each constraint set is assumed to be given as a level set of a convex but not necessarily differentiable function. The proposed algorithms are applicable to the situation where the whole constraint set of the problem is not known in advance, but it is rather learned in time through observations. Also, the algorithms are of interest for constrained optimization problems where the constraints are known but the number of constraints is either large or not finite. We analyze the proposed algorithm for the case when the objective function is differentiable with Lipschitz gradients and the case when the objective function is not necessarily differentiable. The behavior of the algorithm is investigated both for diminishing and non-diminishing stepsize values. The almost sure convergence to an optimal solution is established for diminishing stepsize. For non-diminishing stepsize, the error bounds are established for the expected distances of the weighted averages of the iterates from the constraint set, as well as for the expected sub-optimality of the function values along the weighted averages.

Abstract: This paper addresses the problem of minimizing a convex, Lipschitz function $f$ over a convex, compact set $\xset$ under a stochastic bandit feedback model. In this model, the algorithm is allowed to observe noisy realizations of the function value $f(x)$ at any query point $x \in \xset$. The quantity of interest is the regret of the algorithm, which is the sum of the function values at algorithm's query points minus the optimal function value. We demonstrate a generalization of the ellipsoid algorithm that incurs $\otil(\poly(d)\sqrt{T})$ regret. Since any algorithm has regret at least $\Omega(\sqrt{T})$ on this problem, our algorithm is optimal in terms of the scaling with $T$.

Abstract: By a modification of the method that was applied in (Korolev and Shevtsova, 2010), here the inequalities $\Delta_n\leq0.3328(\beta_3+0.429)/\sqrt{n}$ and $\Delta_n\leq0.33554(\beta_3+0.415)/\sqrt{n}$ are proved for the uniform distance $\Delta_n$ between the standard normal distribution function and the distribution function of the normalized sum of an arbitrary number $n\geq1$ of independent identically distributed random variables with zero mean, unit variance and finite third absolute moment $\beta_3$. The first of these two inequalities improves one that was proved in (Korolev and Shevtsova, 2010), and as well sharpens the best known upper estimate for the absolute constant $C_0$ in the classical Berry--Esseen inequality to be $C_0<0.4756$, since $0.3328(\beta_3+0.429)\leq0.3328\cdot1.429\beta_3<0.4756\beta_3$ by virtue of the condition $\beta_3\geq1$. The second of these inequalities is also a structural improvement of the classical Berry--Esseen inequality, and as well sharpens the upper estimate for $C_0$ still more to be $C_0<0.4748$.

Abstract: In this work, we introduce multiplicative drift analysis as a suitable way to analyze the runtime of randomized search heuristics such as evolutionary algorithms. We give a multiplicative version of the classical drift theorem. This allows easier analyses in those settings where the optimization progress is roughly proportional to the current distance to the optimum. To display the strength of this tool, we regard the classical problem how the (1+1) Evolutionary Algorithm optimizes an arbitrary linear pseudo-Boolean function. Here, we first give a relatively simple proof for the fact that any linear function is optimized in expected time $O(n \log n)$, where $n$ is the length of the bit string. Afterwards, we show that in fact any such function is optimized in expected time at most ${(1+o(1)) 1.39 \euler n\ln (n)}$, again using multiplicative drift analysis. We also prove a corresponding lower bound of ${(1-o(1))e n\ln(n)}$ which actually holds for all functions with a unique global optimum. We further demonstrate how our drift theorem immediately gives natural proofs (with better constants) for the best known runtime bounds for the (1+1) Evolutionary Algorithm on combinatorial problems like finding minimum spanning trees, shortest paths, or Euler tours.