Efficient learning of decomposable models with a bounded clique size

The learning of probability distributions from data is a ubiquitous problem in the fields of Statistics and Artificial Intelligence. During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models due to their advantageous theoretical properties. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k, which controls the complexity of the model. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for k > 2. In this work, we propose a family of algorithms which approximates this problem with a computational complexity of O(k · n^2 log n) in the worst case, where n is the number of implied random variables. The structures of the decomposable models that solve the maximum likelihood problem are called maximal k-order decomposable graphs. Our proposals, called fractal trees, construct a sequence of maximal i-order decomposable graphs, for i = 2, ..., k, in k − 1 steps. At each step, the algorithms follow a divide-and-conquer strategy based on the particular features of this type of structures. Additionally, we propose a prune-and-graft procedure which transforms a maximal k-order decomposable graph into another one, increasing its likelihood. We have implemented two particular fractal tree algorithms called parallel fractal tree and sequential fractal tree. These algorithms can be considered a natural extension of Chow and Liu’s algorithm, from k = 2 to arbitrary values of k. Both algorithms have been compared against other efficient approaches in artificial and real domains, and they have shown a competitive behavior to deal with the maximum likelihood problem. Due to their low computational complexity they are especially recommended to deal with high dimensional domains.

Influence of Contact Angle and Tube Size on Capillary-Driven Flow Under Microgravity

The influence of contact angle and tube radius on the capillary-driven flow for circular cylindrical tubes is studied systematically by microgravity experiments using the drop tower. Experimental results show that the velocity of the capillary flow decreases monotonically with an increase in the contact angle. However, the time-evolution of the velocity of the capillary flow is different for different sized tubes. At the beginning of the microgravity period, the capillary flow in a thinner tube moves faster than that in a thicker tube, and then the latter overtakes the former. Therefore, there is an intersection between the curves of meniscus velocity vs microgravity time for two differently sized tubes. In addition, for two given sized tubes this intersection is delayed when the contact angle increases. The experimental results are analyzed theoretically and also supported by numerical computations.

Report on estimating the size of dolphin schools, based on data obtained during a charter cruise of the M/V Gina Anne, October 11 -November 25, 1979

Estimates of dolphin school sizes made by observers and crew members aboard tuna seiners or by observers on ship or aerial surveys are important components of population estimates of dolphins which are involved in the yellowfin tuna fishery in the eastern Pacific. Differences in past estimates made from tuna seiners and research ships and aircraft have been noted by Brazier (1978). To compare various methods of estimating dolphin school sizes a research cruise was undertaken with the following major objectives: 1) compare estimates made by observers aboard a tuna seiner and in the ship's helicopter, from aerial photographs, and from counts made at the backdown channel, 2) compare estimates of observers who are told the count of the school size after making their estimate to the observer who is not aware of the count to determine if observers can learn to estimate more accurately, and 3) obtain movie and still photographs of dolphin schools of known size at various stages of chase, capture and release to be used for observer training. The secondary objectives of the cruise were to: 1) obtain life history specimens and data from any dolphins that were killed incidental to purse seining. These specimens and data were to be analyzed by the U.S. National Marine Fisheries Service ( NMFS ) , 2) record evasion tactics of dolphin schools by observing them from the helicopter while the seiner approached the school, 3) examine alternative methods for estimating the distance and bearing of schools where they were first sighted, 4) collect the Commission's standard cetacean sighting, set log and daily activity data and expendable bathythermograph data. (PDF contains 31 pages.)

Sexual maturity, fecundity and egg size of wild and cultured samples of Bagrus bayad macropterus

Twenty four matured samples of Bagrus bayad macropterus from the wild (Shiroro Lake, Nigeria) and under captivity, size ranging from 412.69-3300.00 g total body weight, were analysed for sexual maturity,fecundity and egg size. The average fecundity obtained were 53352.59 and 21028.32 eggs for the wild and cultured fish respectively.Positive relationship was observed between fecundity, body size and gonad weight. Fecundity increased as body size increased. A more positive and linear relationship was observed between fecundity and gonad weight than fecundity and total body weight. Egg diameter,length and weight were determined from the egg samples. The mean size range of eggs for cultured fish was 0.74-1.05 mm of diameter; 1.01-1.20 mm of length and 0.25-0.40 mg of weight. Wild samples had mean size range of 0.68-l.09 mm of diameter, 0.85-1.38 mm of length and egg mean weight range was 0.15- 0.40 mg. Sexual maturity is dependent on size (1 kg and above). The egg diameter, egg length and weight bear no relationship with each other. Gonad development study indicated that gonad development was faster under captivity than in wild

The Effects of Grain Size Distribution and Structure on Mechanical Behavior of Silt

Abstract: In order to investigate the effects of the grain size distribution and the micro-structure of soils on the mechani- cal characteristics, some static triaxial compression tests were carried out, and then the relationship of stress-strain and the strength behavior of silty sand were compared among undisturbed samples with different grain size distribution, undis- turbed and remolded samples with the same grain size distribution, and reconstituted samples (or called mixed samples) with different grain size distribution. The effects of grain size distribution and structure on the mechanic behavior of silty sands were mainly analyzed. It is shown that the obvious differences of the mechanical characteristics between undis- turbed soils and remolded soils are caused by the differences of soil structures. Although the grain size distribution are different between two soil samples, their mechanical characteristics may be close to each other, or may have obvious differences because of the effects of micro-structure.

Unilateral vs. Bilateral link-formation: Bridging the gap

We provide a model that bridges the gap between two benchmark models of strategic network formation: Jackson and Wolinsky' s model based on bilateral formation of links, and Bala and Goyal's two-way fl ow model, where links can be unilaterally formed. In the model introduced and studied here a link can be created unilaterally. When it is only supported by one of the two players the fl ow through the link suffers a certain decay, but when it is supported by both the fl ow runs without friction. When the decay in links supported by only one player is maximal (i.e. there is no flow) we have Jackson and Wolinsky 's connections model without decay, while when flow in such links is perfect we have Bala and Goyal' s two-way flow model. We study Nash, strict Nash and pairwise stability for the intermediate models. Efficiency and dynamics are also examined.

Movement of a Spherical Brownian Particle Between Infinite Parallel Plates: Hindered Dispersion and Sedimentation

The dispersion of an isolated, spherical, Brownian particle immersed in a Newtonian fluid between infinite parallel plates is investigated. Expressions are developed for both a 'molecular' contribution to dispersion, which arises from random thermal fluctuations, and a 'convective' contribution, arising when a shear flow is applied between the plates. These expressions are evaluated numerically for all sizes of the particle relative to the bounding plates, and the method of matched asymptotic expansions is used to develop analytical expressions for the dispersion coefficients as a function of particle size to plate spacing ratio for small values of this parameter.

It is shown that both the molecular and convective dispersion coefficients decrease as the size of the particle relative to the bounding plates increase. When the particle is small compared to the plate spacing, the coefficients decrease roughly proportional to the particle size to plate spacing ratio. When the particle closely fills the space between the plates, the molecular dispersion coefficient approaches zero slowly as an inverse logarithmic function of the particle size to plate spacing ratio, and the convective dispersion coefficent approaches zero approximately proportional to the width of the gap between the edges of the sphere and the bounding plates.

Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

Scanning tunneling spectroscopic studies on high-temperature superconductors and Dirac materials

This thesis details the investigations of the unconventional low-energy quasiparticle excitations in electron-type cuprate superconductors and electron-type ferrous superconductors as well as the electronic properties of Dirac fermions in graphene and three-dimensional strong topological insulators through experimental studies using spatially resolved scanning tunneling spectroscopy (STS) experiments.

Magnetic-field- and temperature-dependent evolution of the spatially resolved quasiparticle spectra in the electron-type cuprate La_0.1Sr_0.9CuO₂ (La-112) T_C = 43 K, are investigated experimentally. For temperature (T) less than the superconducting transition temperature (TC), and in zero field, the quasiparticle spectra of La-112 exhibits gapped behavior with two coherence peaks and no satellite features. For magnetic field measurements at T < TC, first ever observation of vortices in La-112 are reported. Moreover, pseudogap-like spectra are revealed inside the core of vortices, where superconductivity is suppressed. The intra-vortex pseudogap-like spectra are characterized by an energy gap of V_PG = 8.5 ± 0.6 meV, while the inter-vortex quasiparticle spectra shows larger peak-to-peak gap values characterized by Δ_pk-pk(H) >V_PG, and Δ_pk-pk (0)=12.2 ± 0.8 meV > Δ_pk-pk (H > 0). The quasiparticle spectra are found to be gapped at all locations up to the highest magnetic field examined (H = 6T) and reveal an apparent low-energy cutoff at the V_PG energy scale.

Magnetic-field- and temperature-dependent evolution of the spatially resolved quasiparticle spectra in the electron-type "122" iron-based Ba(Fe_1-xCo_x)₂A_s2 are investigated for multiple doping levels (x = 0.06, 0.08, 0.12 with T_C= 14 K, 24 K, and 20 K). For all doping levels and the T < T_C, two-gap superconductivity is observed. Both superconducting gaps decrease monotonically in size with increasing temperature and disappear for temperatures above the superconducting transition temperature, T_C. Magnetic resonant modes that follow the temperature dependence of the superconducting gaps have been identified in the tunneling quasiparticle spectra. Together with quasiparticle interference (QPI) analysis and magnetic field studies, this provides strong evidence for two-gap sign-changing s-wave superconductivity.

Additionally spatial scanning tunneling spectroscopic studies are performed on mechanically exfoliated graphene and chemical vapor deposition grown graphene. In all cases lattice strain exerts a strong influence on the electronic properties of the sample. In particular topological defects give rise to pseudomagnetic fields (B ~ 50 Tesla) and charging effects resulting in quantized conductance peaks associated with the integer and fractional Quantum Hall States.

Finally, spectroscopic studies on the 3D-STI, Bi₂Se₃ found evidence of impurity resonance in the surface state. The impurities are in the unitary limit and the spectral resonances are localized spatially to within ~ 0.2 nm of the impurity. The spectral weight of the impurity resonance diverges as the Fermi energy approaches the Dirac point and the rapid recovery of the surface state suggests robust topological protection against perturbations that preserve time reversal symmetry.

Wetlands and coastal water quality: Should wetland size matter?

Generally, wetlands are thought to perform water purification functions, removing contaminants as water flows through sediment and vegetation. This paradigm was challenged when Grant et al. (2001) reported that Talbert Salt Marsh (Figure 1.) increased fecal indicator bacteria (FIB) output to coastal waters, contributing to poor coastal water quality. Like most southern California wetlands, Talbert Salt Marsh has been severely degraded. It is a small (10 ha), restored wetland, only 1/100th its original size, and located at the base of a highly urbanized watershed. Is it reasonable to expect that this or any severely altered wetland will perform the same water purification benefits as a natural wetland? To determine how a more pristine southern California coastal wetland attenuated bacterial contaminants, we investigated FIB concentrations entering and exiting Carpinteria Salt Marsh (Figure 2.), a 93 ha, moderate-sized, relatively natural wetland.(PDF contains 4 pages)