Independent Columns Research Articles

Use of Falling-Head Infiltration to Estimate Hydraulic Conductivity at Various Depths

Most infiltration methods measure the saturated hydraulic conductivity (Ks) of the unsaturated zone at only one depth at or near the surface. The purpose of this study was to extend the falling-head infiltration theory to a multistep falling-head infiltration test (MSFIT) for estimating Ks at various depths in a one-dimensional saturated vertical flow domain. A general analytical solution for Ks is derived for the wetted region of each step in the MSFIT. The Ks values for individual wetted sub-regions are calculated sequentially from the top down based on the fact that the Ks value of the whole wetted region is the depth-weighted harmonic mean of sub-regions for flow perpendicular to the wetted layers. The resolution of the wetted sub-region is determined by the number of steps and the change of the ponded water head. The MSFIT is performed in three independent laboratory two-layer sand columns. The mean value of Ks for the upper coarse sand is 2.13 × 10 cm/sec, and that for the lower fine sand is 3.63 × 10 cm/sec. Similar Ks results are obtained from 12 core sample measurements. In a field study with the MSFIT, the mean values of Ks estimated from top down are 8.37 × 10, 2.73 × 10, and 3.21 × 10 cm/sec, respectively. The decreasing Ks with depth is similar to the result of small core samples and is consistent with field observations of the soil texture. The proposed MSFIT is simple, flexible, and versatile for obtaining hydraulic conductivity at various depths for one-dimensional saturated vertical flow domains.

Innovative modelling of 3D unsaturated flow in porous media by coupling independent models for vertical and lateral flows

Unsaturated groundwater flows are mathematically represented by the Richards equation. Hitherto, in Hydrology, solutions of this equation mainly serve as an alimentation of the source term for the surface runoff modelling. Therefore, the complete resolution of the 3D model looks surplus to requirements and the infiltration is dealt either thanks to 1D vertical modelling of the Richards equation or through derivate models (like e.g. the Green–Ampt infiltration model or the Horton law), thus ignoring eventual horizontal transfers.Nowadays, the request for more detailed information is real, and the physics of groundwater unsaturated flow needs to be represented more reliably. This information could be furnished by the resolution of the complete 3D model, but, although numerically mastered and well documented, it is very costly for large scale–both in time and space–real applications (climate change adaptation of watersheds).The authors propose an original solution decoupling the 3D equations into 1D vertical equations and a 2D depth-integrated horizontal equation. The aim is to consider independent vertical columns of infiltration coupled with lateral transfer of mass through the boundary conditions. On this basis, they postulate that the mass transfers in the three dimensions are correctly represented. This way problematic like the supply of the aquifers, the re-emergence of groundwater to surface water or especially the capability of memorization of past rainy events …could be reliably depicted.The two coupled models are solved on a unique numerical frame. A cell-centred Finite Volume method is used to solve the parabolic partial differential equations. The spatial derivatives are approximate by a second order central difference scheme, while the time splitting follows an implicit backward Euler scheme coupled with Picard iteration.The method has been tested and its reliability assessed on different theoretical two-dimensional cross-sectional test cases representing infiltration phenomena.

Inference with Transposable Data: Modeling the Effects of Row and Column Correlations.

We consider the problem of large-scale inference on the row or column variables of data in the form of a matrix. Many of these data matrices are transposable meaning that neither the row variables nor the column variables can be considered independent instances. An example of this scenario is detecting significant genes in microarrays when the samples may be dependent due to latent variables or unknown batch effects. By modeling this matrix data using the matrix-variate normal distribution, we study and quantify the effects of row and column correlations on procedures for large-scale inference. We then propose a simple solution to the myriad of problems presented by unanticipated correlations: We simultaneously estimate row and column covariances and use these to sphere or de-correlate the noise in the underlying data before conducting inference. This procedure yields data with approximately independent rows and columns so that test statistics more closely follow null distributions and multiple testing procedures correctly control the desired error rates. Results on simulated models and real microarray data demonstrate major advantages of this approach: (1) increased statistical power, (2) less bias in estimating the false discovery rate, and (3) reduced variance of the false discovery rate estimators.

Safety analysis of independent columns mounted on isolated bearing system

This paper explores the safety performance of independent column mounted on isolated bearing. Considering large displacement of the isolator bearing under earthquake, the accumulated permanent deformations in the independent column may render gravity forces the dominant forces and make the system collapse by lateral instability. By means of dynamic response simulation of the system under seismic excitations, the safety of system is derived by optimality method and expert systems. The results show that the safety of system mainly depends on the lateral force, irrespective of the axial force. The lateral force is largely influenced by the displacement of the system. The absolute value of the constraint moment has significant effect on the safety of column. The more the absolute value of the constraint moment is, the worse the safety of system is. The independent column is impossible to be instability with an adequate section of column employed.

Dynamic collapse test on eccentric reinforced concrete structures with and without seismic retrofit

Reconnaissance reports on structures damaged or collapsed by severe earthquakes have revealed several common characteristics in their structural members and systems, such as insufficient reinforcement details in beam-column joints and transverse confinements, low aspect ratios, soft and or weak stories, and eccentric plans. Dynamic tests were carried out to investigate the collapse process of reinforced concrete structures that had seismically deficient reinforcement details (light transverse reinforcement) and seismic systems (soft/weak stories and eccentric plans). A comparison of collapse behaviors with and without seismic retrofits also verified the effectiveness of the SRF (super reinforced with flexibility) strengthening method, which was developed to prevent the loss of axial load carrying capacity even at excessive lateral deformation. The columns of one specimen were strengthened with polyester fiber belts and its shear walls with polyester fiber sheets, while the members of the other were not. Each specimen was designed following old (1970s) reinforcement detail practice in Japan, and is a one-third-scale reinforced concrete structure with considerable stiffness and strength eccentricity in the first story. The specimens were composed of independent column frame and shear wall frame. Torsional response resulting from the eccentricity in the 1st story induced a displacement concentration on the weak frame, and eventually the independent columns of the RC specimen failed in shear and lost their axial load carrying capacity. On the other hand, the SRF specimen survived not only an identical earthquake load to the one that caused the RC specimen to fail, but also three additional earthquake loads, although significant strength deterioration and considerable lateral and vertical deformation were generated at the end of the test. The following conclusions were drawn from the comparison of the two specimens’ responses: axial column collapse cannot be predicted from vertical responses since the vertical behavior of bare RC columns was not discernibly different from that of SRF columns until axial collapse was initiated, and the SRF strengthening method is effective in confining the column and preventing the cracking progress, thus modifying the failure mode of the RC columns from brittle shear failure after flexural yield to flexural dominant behavior.

The Whitney embedding theorem for tropical torsion modules: Classification of tropical modules

We prove here a tropical version of the well-known Whitney embedding theorem [32] stating that a smooth connected m-dimensional compact differential manifold can be embedded into R 2 m + 1 . The tropical version of this theorem states that a tropical torsion module with m generators can always be embedded into the free tropical module R ̲ p , where p (equals to 2 for m = 2 , and 3 ⩽ p ⩽ m ( m - 1 ) otherwise) is the number of rows supporting the torsion, when the generators are given by the (independent) columns of a matrix of size n × m . As a corollary, we get that tropical m-dimensional torsion modules are classified by a ( m - 1 ) m ( m - 1 ) - 1 -parameter family.

Chang's Theorem on Betti Numbers of Exponent-Two Modules over Regular Local Rings

Let (R, 𝔪, k) be a regular local ring of dimension n and let M be a finite length R-module. Horrock's conjecture [2] says that the ith Betti number of M must be at least . The article “Betti Numbers of Modules of Exponent Two over Regular Local Rings,” by Shou-Te Chang [1], addresses the case that 𝔪2 M = 0. The purpose of the present article is to correct a few problems in the arguments in [1]. In particular, we will be analyzing certain Koszul matrices and systematically finding a maximal set of linearly independent columns of these matrices.

Safety analysis of independent columns mounted on isolated bearing system

This paper explores the safety performance of independent column mounted on isolated bearing. Considering large displacement of the isolator bearing under earthquake, the accumulated permanent deformations in the independent column may render gravity forces the dominant forces and make the system collapse by lateral instability. By means of dynamic response simulation of the system under seismic excitations, the safety of system is derived by optimality method and expert systems. The results show that the safety of system mainly depends on the lateral force, irrespective of the axial force. The lateral force is largely influenced by the displacement of the system. The absolute value of the constraint moment has significant effect on the safety of column. The more the absolute value of the constraint moment is, the worse the safety of system is. The independent column is impossible to be instability with an adequate section of column employed.

Sparse Jacobian Computation Using ADIC2 and ColPack

Many scientific applications benefit from the accurate and e cient computation of derivatives. Automatically generating these derivative computations from an applications source code o ers a competitive alternative to other approaches, such as less accurate numerical approximations or labor-intensive analytical implementations. ADIC2 is a source transformation tool for generating code for computing the derivatives (e.g., Jacobian or Hessian) of a function given the C or C++ implementation of that function. Often the Jacobian or Hessian is sparse and presents the opportunity to greatly reduce storage and computational requirements in the automatically generated derivative computation. ColPack is a tool that compresses structurally independent columns of the Jacobian and Hessian matrices through graph coloring approaches. In this paper, we describe the integration of ColPack coloring capabilities into ADIC2, enabling accurate and e cient sparse Jacobian computations. We present performance results for a case study of a simulated moving bed chromatography application. Overall, the computation of the Jacobian by integrating ADIC2 and ColPack is approximately 40% faster than a comparable implementation that integrates ADOL-C and ColPack when the Jacobian is computed multiple times.

Hydrogen fluoride total and partial column time series above the Jungfraujoch from long‐term FTIR measurements: Impact of the line‐shape model, characterization of the error budget and seasonal cycle, and comparison with satellite and model data

Time series of hydrogen fluoride (HF) total columns have been derived from ground‐based Fourier transform infrared (FTIR) solar spectra recorded between March 1984 and December 2009 at the International Scientific Station of the Jungfraujoch (Swiss Alps, 46.5°N, 8.0°E, 3580 m asl) with two high‐resolution spectrometers (one homemade and one Bruker 120‐HR). Solar spectra have been inverted with the PROFFIT 9.5 algorithm, using the optimal estimation method. An intercomparison of HF total columns retrieved with PROFFIT and SFIT‐2–the other reference algorithm in the FTIR community–is performed for the first time. The effect of a Galatry line shape model on HF retrieved total columns and vertical profiles, on the residuals of the fits and on the error budget is also quantified. Information content analysis indicates that in addition to HF total vertical abundance, three independent stratospheric HF partial columns can be derived from our Bruker spectra. A complete error budget has been established and indicates that the main source of systematic error is linked to HF spectroscopy and that the random error affecting our HF total columns does not exceed 2.5%. Ground‐based middle and upper stratospheric HF amounts have been compared to satellite data collected by the HALOE or ACE‐FTS instruments. Comparisons of our FTIR HF total and partial columns with runs performed by two three‐dimensional numerical models (SLIMCAT and KASIMA) are also included. Finally, FTIR and model HF total and partial columns time series have been analyzed to derive the main characteristics of their seasonal cycles.

Restricted Isometry Property of Matrices with Independent Columns and Neighborly Polytopes by Random Sampling

This paper considers compressed sensing matrices and neighborliness of a centrally symmetric convex polytope generated by vectors ±X 1,…,±X N ∈ℝ n , (N≥n). We introduce a class of random sampling matrices and show that they satisfy a restricted isometry property with overwhelming probability. In particular, we prove that matrices with i.i.d. centered and variance 1 entries that satisfy uniformly a subexponential tail inequality possess the restricted isometry property with overwhelming probability. We show that such “sensing” matrices are valid for the exact reconstruction process of m-sparse vectors via l 1 minimization with m≤Cn/log 2(cN/n). The class of sampling matrices we study includes the case of matrices with columns that are independent isotropic vectors with log-concave densities. We deduce that if K⊂ℝ n is a convex body and X 1,…,X N ∈K are i.i.d. random vectors uniformly distributed on K, then, with overwhelming probability, the symmetric convex hull of these points is an m-centrally-neighborly polytope with m∼n/log 2(cN/n).

Determination of fluoroquinolone antibiotics in wastewater using ultra high‐performance liquid chromatography with mass spectrometry and fluorescence detection

A new ultra HPLC (UHPLC) method using both MS and fluorescence detection (FD) was developed for the determination of five fluoroquinolones in wastewaters. Systematic method development approach was compared with a conventional one. During the systematic approach, a possibility of automatic switching among four independent analytical columns of different chemistries has been used. Acidic as well as basic pH using ACN and methanol as organic modifiers was tested. The best separation of fluoroquinolones was obtained on phenyl analytical column at pH 10.5, which is a completely novel approach for separation of fluoroquinolones. Further, a new SPE procedure was developed for the sample preparation using basic pH as well. The sensitivity and selectivity of FD and MS detection were compared. FD at basic pH 10.5 demonstrated lower sensitivity than at acidic pH, which is conventionally performed. At basic pH, UHPLC-MS/MS was found about two orders of magnitude more sensitive than FD. Both methods were validated and subsequently UHPLC-FD method was used for the evaluation of stability of fluoroquinolones. UHPLC-MS/MS method was used for the analysis of wastewater samples. Norfloxacin and ciprofloxacin were detected in samples of influent and effluent from wastewater treatment plant. Ofloxacin was detected only in influent from wastewater treatment plant.

Calculation of limit probabilities of the distribution of permanent of a random matrix over the field GF(p)

of the distribution of the permanent of a random matrix Amn = ‖αij‖ with m rows and n independent columns over the field GF(p).

Decoupling Zeros of Positive Discrete-Time Linear Sys-tems

The notions of decoupling zeros of positive discrete-time linear systems are introduced. The relationships between the decoupling zeros of standard and positive discrete-time linear systems are analyzed. It is shown that: 1) if the positive system has decoupling zeros then the corresponding standard system has also decoupling zeros, 2) the positive system may not have decoupling zeros when the corresponding standard system has decoupling zeros, 3) the positive and standard systems have the same decoupling zeros if the rank of reachability (observability) matrix is equal to the number of linearly independent monomial columns (rows) and some additional assumptions are satisfied.

An autonomous assessment system based on combined latent semantic kernels

In this paper, we develop an autonomous assessment system based on the kernel combinations which are mixed by two kernel matrices from the WordNet and corpus. Many researchers have tried to integrate these two resources in many applications, to utilize diverse information extracted from each resource. However, since two resources have been represented in quite different ways, one resource has been secondary to another. To fully integrate two resources at the same level, we first transform the WordNet, which has a hierarchical structure, into a matrix structure. Concurrently, another matrix, which represents a co-occurrence of words in the collection of text documents, is constructed. We then build two initial latent semantic kernels from both matrices and merge them into a new single kernel matrix. When we merge two matrices, we split each initial matrix into independent columns and mix the columns with various methods. We acquire a few combined kernel matrices which show various performances in experiments. Compared to the basic vector space model, original kernel matrices, and the BLEU based method, the combined matrices improve the accuracy of assessment.

The impact of IBM Cell technology on the programming paradigm in the context of computer systems for climate and weather models

AbstractThe call for ever‐increasing model resolutions and physical processes in climate and weather models demands a continual increase in computing power. The IBM Cell processor's order‐of‐magnitude peak performance increase over conventional processors makes it very attractive to fulfill this requirement. However, the Cell's characteristics, 256 kB local memory per SPE and the new low‐level communication mechanism, make it very challenging to port an application. As a trial, we selected the solar radiation component of the NASA GEOS‐5 climate model, which: (1) is representative of column‐physics components (half of the total computational time), (2) has an extremely high computational intensity: the ratio of computational load to main memory transfers, and (3) exhibits embarrassingly parallel column computations. In this paper, we converted the baseline code (single‐precision Fortran) to C and ported it to an IBM BladeCenter QS20. For performance, we manually SIMDize four independent columns and include several unrolling optimizations. Our results show that when compared with the baseline implementation running on one core of Intel's Xeon Woodcrest, Dempsey, and Itanium2, the Cell is approximately 8.8x, 11.6x, and 12.8x faster, respectively. Our preliminary analysis shows that the Cell can also accelerate the dynamics component (∼25% total computational time). We believe these dramatic performance improvements make the Cell processor very competitive as an accelerator. Copyright © 2009 John Wiley & Sons, Ltd.

TT-cross approximation for multidimensional arrays

As is well known, a rank-r matrix can be recovered from a cross of r linearly independent columns and rows, and an arbitrary matrix can be interpolated on the cross entries. Other entries by this cross or pseudo-skeleton approximation are given with errors depending on the closeness of the matrix to a rank-r matrix and as well on the choice of cross. In this paper we extend this construction to d-dimensional arrays (tensors) and suggest a new interpolation formula in which a d-dimensional array is interpolated on the entries of some TT-cross (tensor train-cross). The total number of entries and the complexity of our interpolation algorithm depend on d linearly, so the approach does not suffer from the curse of dimensionality.We also propose a TT-cross method for computation of d-dimensional integrals and apply it to some examples with dimensionality in the range from d=100 up to d=4000 and the relative accuracy of order 10-10. In all constructions we capitalize on the new tensor decomposition in the form of tensor trains (TT-decomposition).

A Seismic Isolated Long-Span Overhanging Urban Infrastructure

The design and construction of a long-span, seismic isolated office building located in Tokyo and completed in October 2003, meets the needs of a sustainable urban environment. The 6-story building is 20 m × 80 m and uses a large-scale “trussed cage” structure, the upper part of which is supported on six base isolators on independent columns, creating an expansive area at ground level. The building’s seismic design uses artificial earthquake input movement taking into account the soft soil of the site and the frequency of Japan’s earthquakes. We detail the structural system and design concept, construction process, and health monitoring in the section that follow.

Determinants of Water Permeability through Nanoscopic Hydrophilic Channels

Naturally occurring pores show a variety of polarities and sizes that are presumably directly linked to their biological function. Many biological channels are selective toward permeants similar or smaller in size than water molecules, and therefore their pores operate in the regime of single-file water pores. Intrinsic factors affecting water permeability through such pores include the channel-membrane match, the structural stability of the channel, the channel geometry and channel-water affinity. We present an extensive molecular dynamics study on the role of the channel geometry and polarity on the water osmotic and diffusive permeability coefficients. We show that the polarity of the naturally occurring peptidic channels is close to optimal for water permeation, and that the water mobility for a wide range of channel polarities is essentially length independent. By systematically varying the geometry and polarity of model hydrophilic pores, based on the fold of gramicidin A, the water density, occupancy, and permeability are studied. Our focus is on the characterization of the transition between different permeation regimes in terms of the structure of water in the pores, the average pore occupancy and the dynamics of the permeating water molecules. We show that a general relationship between osmotic and diffusive water permeability coefficients in the single-file regime accounts for the time averaged pore occupancy, and that the dynamics of the permeating water molecules through narrow non single file channels effectively behaves like independent single-file columns.

A power sparse approximate inverse preconditioning procedure for large sparse linear systems

AbstractMotivated by the Cayley–Hamilton theorem, a novel adaptive procedure, called a Power Sparse Approximate Inverse (PSAI) procedure, is proposed that uses a different adaptive sparsity pattern selection approach to constructing a right preconditioner M for the large sparse linear system Ax=b. It determines the sparsity pattern of M dynamically and computes the n independent columns of M that is optimal in the Frobenius norm minimization, subject to the sparsity pattern of M. The PSAI procedure needs a matrix–vector product at each step and updates the solution of a small least squares problem cheaply. To control the sparsity of M and develop a practical PSAI algorithm, two dropping strategies are proposed. The PSAI algorithm can capture an effective approximate sparsity pattern of A−1 and compute a good sparse approximate inverse M efficiently. Numerical experiments are reported to verify the effectiveness of the PSAI algorithm. Numerical comparisons are made for the PSAI algorithm and the adaptive SPAI algorithm proposed by Grote and Huckle as well as for the PSAI algorithm and three static Sparse Approximate Inverse (SAI) algorithms. The results indicate that the PSAI algorithm is at least comparable to and can be much more effective than the adaptive SPAI algorithm and it often outperforms the static SAI algorithms very considerably and is more robust and practical than the static ones for general problems. Copyright © 2008 John Wiley & Sons, Ltd.