Fast Hierarchical Clustering and Other Applications of Dynamic Closest Pairs

We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean closest pairs, we show how to insert and delete objects from an n-object set, maintaining the closest pair, in O(n log^2 n) time per update and O(n) space. With quadratic space, we can instead use a quadtree-like structure to achieve an optimal time bound, O(n) per update. We apply these data structures to hierarchical clustering, greedy matching, and TSP heuristics, and discuss other potential applications in machine learning, Groebner bases, and local improvement algorithms for partition and placement problems. Experiments show our new methods to be faster in practice than previously used heuristics.Comment: 20 pages, 9 figures. A preliminary version of this paper appeared at the 9th ACM-SIAM Symp. on Discrete Algorithms, San Francisco, 1998, pp. 619-628. For source code and experimental results, see http://www.ics.uci.edu/~eppstein/projects/pairs

Towards an Optimal Reconstruction of Baryon Oscillations

The Baryon Acoustic Oscillations (BAO) in the large-scale structure of the universe leave a distinct peak in the two-point correlation function of the matter distribution. That acoustic peak is smeared and shifted by bulk flows and non-linear evolution. However, it has been shown that it is still possible to sharpen the peak and remove its shift by undoing the effects of the bulk flows. We propose an improvement to the standard acoustic peak reconstruction. Contrary to the standard approach, the new scheme has no free parameters, treats the large-scale modes consistently, and uses optimal filters to extract the BAO information. At redshift of zero, the reconstructed linear matter power spectrum leads to a markedly improved sharpening of the reconstructed acoustic peak compared to standard reconstruction.Comment: 20 pages, 5 figures; footnote adde

Estimating CDM Particle Trajectories in the Mildly Non-Linear Regime of Structure Formation. Implications for the Density Field in Real and Redshift Space

We obtain approximations for the CDM particle trajectories starting from Lagrangian Perturbation Theory. These estimates for the CDM trajectories result in approximations for the density in real and redshift space, as well as for the momentum density that are better than what standard Eulerian and Lagrangian perturbation theory give. For the real space density, we find that our proposed approximation gives a good cross-correlation (>95%) with the non-linear density down to scales almost twice smaller than the non-linear scale, and six times smaller than the corresponding scale obtained using linear theory. This allows for a speed-up of an order of magnitude or more in the scanning of the cosmological parameter space with N-body simulations for the scales relevant for the baryon acoustic oscillations. Possible future applications of our method include baryon acoustic peak reconstruction, building mock galaxy catalogs, momentum field reconstruction.Comment: 25 pages, 11 figures; reference adde

Bayesian stochastic blockmodeling

This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data, based on the stochastic blockmodel (SBM), as well as its degree-corrected and overlapping generalizations. We focus on nonparametric formulations that allow their inference in a manner that prevents overfitting, and enables model selection. We discuss aspects of the choice of priors, in particular how to avoid underfitting via increased Bayesian hierarchies, and we contrast the task of sampling network partitions from the posterior distribution with finding the single point estimate that maximizes it, while describing efficient algorithms to perform either one. We also show how inferring the SBM can be used to predict missing and spurious links, and shed light on the fundamental limitations of the detectability of modular structures in networks.Comment: 44 pages, 16 figures. Code is freely available as part of graph-tool at https://graph-tool.skewed.de . See also the HOWTO at https://graph-tool.skewed.de/static/doc/demos/inference/inference.htm

Designing peptide nanoparticles for efficient brain delivery

The targeted delivery of therapeutic compounds to the brain is arguably the most significant open problem in drug delivery today. Nanoparticles (NPs) based on peptides and designed using the emerging principles of molecular engineering show enormous promise in overcoming many of the barriers to brain delivery faced by NPs made of more traditional materials. However, shortcomings in our understanding of peptide self-assembly and blood–brain barrier (BBB) transport mechanisms pose significant obstacles to progress in this area. In this review, we discuss recent work in engineering peptide nanocarriers for the delivery of therapeutic compounds to the brain, from synthesis, to self-assembly, to in vivo studies, as well as discussing in detail the biological hurdles that a nanoparticle must overcome to reach the brain

On the dynamics of crystalline motions

Solids can exist in polygonal shapes with boundaries unions of flat -pieces· called· facets. Analyzing the- growth -of such crystalline shapes is an important problem in materials science. In this paper we derive equa­tions that govern the evolution of such shapes; we formulate the correspon­ding initial-value problem variationally; and we use this formulation to establish a comparison principle for crystalline evolutions. This principle as­serts that two evolving crystals one initially inside the other will remain in that configuration for all time

Advantageous grain boundaries in iron pnictide superconductors

High critical temperature superconductors have zero power consumption and could be used to produce ideal electric power lines. The principal obstacle in fabricating superconducting wires and tapes is grain boundaries-the misalignment of crystalline orientations at grain boundaries, which is unavoidable for polycrystals, largely deteriorates critical current density. Here, we report that High critical temperature iron pnictide superconductors have advantages over cuprates with respect to these grain boundary issues. The transport properties through well-defined bicrystal grain boundary junctions with various misorientation angles (thetaGB) were systematically investigated for cobalt-doped BaFe2As2 (BaFe2As2:Co) epitaxial films fabricated on bicrystal substrates. The critical current density through bicrystal grain boundary (JcBGB) remained high (> 1 MA/cm2) and nearly constant up to a critical angle thetac of ~9o, which is substantially larger than the thetac of ~5o for YBCO. Even at thetaGB > thetac, the decay of JcBGB was much smaller than that of YBCO.Comment: to appear in Nature Communication

Strategic Voting in Sequential Committees ∗

We consider strategic voting in sequential committees in a common value setting with incomplete information. A proposal is considered against the status quo in one committee, and only upon its approval advances for consideration in a second committee. Committee members (i) are privately and imperfectly informed about an unobservable state of nature which is relevant to their payoffs, and (ii) have a publicly observable bias with which they evaluate information. We show that the tally of votes in the originating committee can aggregate and transmit relevant information for members of the second committee in equilibrium, provide conditions for the composition and size of committees under which this occurs, and characterize all three classes of voting equilibria with relevant informative voting

On Loops in Inflation II: IR Effects in Single Clock Inflation

In single clock models of inflation the coupling between modes of very different scales does not have any significant dynamical effect during inflation. It leads to interesting projection effects. Larger and smaller modes change the relation between the scale a mode of interest will appear in the post-inflationary universe and will also change the time of horizon crossing of that mode. We argue that there are no infrared projection effects in physical questions, that there are no effects from modes of longer wavelength than the one of interest. These potential effects cancel when computing fluctuations as a function of physically measurable scales. Modes on scales smaller than the one of interest change the mapping between horizon crossing time and scale. The correction to the mapping computed in the absence of fluctuations is enhanced by a factor N_e, the number of e-folds of inflation between horizon crossing and reheating. The new mapping is stochastic in nature but its variance is not enhanced by N_e.Comment: 13 pages, 1 figure; v2: JHEP published version, added minor comments and reference