Consecutive Columns Research Articles

A shaping two-stage anomaly data recovery method based on multi-norm joint optimization under energy internet

With the deep integration of energy networks and information communication technology, the involvement of hardware and environmental factors intensifies the challenges to data security. Prior research focuses predominantly on interpolating random missing data under the assumption of no data damage, without providing strategies for addressing continuous data loss. To overcome, we proposes a novel two-stage data recovery method, that includes three-fold ideas: (1) it introduces the matrix shaping differentiation strategy to realize the differentiated recovery of random and continuous missing data; (2) it designs a two-stage data recovery approach, in which the first stage constructs a random missing data recovery objective function by eliminating the consecutive missing data columns, and the second stage performs temporal pre-interpolation backfilling on the eliminated columns and introduces the temporal correlation to construct the temporal smoothing objective function; and (3) it develops an alternating direction method of multipliers-based iterative solution algorithm. Experimental results on four public datasets demonstrate that our model is superior to five state-of-the-art and classical methods in terms of random missing error rate, random column missing error rate, root mean square error, and mean absolute error.

The maximum 2D subarray polytope: Facet-inducing inequalities and polyhedral computations

Given a matrix with real-valued entries, the maximum 2D subarray problem consists in finding a rectangular submatrix with consecutive rows and columns maximizing the sum of its entries. In this work we start a polyhedral study of an integer programming formulation for this problem. We thus define the 2D subarray polytope , explore conditions ensuring the validity of linear inequalities, and provide several families of facet-inducing inequalities. We also report computational experiments assessing the reduction of the dual bound for the linear relaxation achieved by these families of inequalities.

PlasmaCap EBA: An innovative method of isolating plasma proteins from human plasma.

The growing demand for immunoglobulin (IG) requires development of improved plasma fractionation methods to provide higher yields in a cost effective, scalable manner without compromising product purity and efficacy. A novel protein extraction method, utilizing expanded bed adsorption (EBA) chromatography, has been developed. PlasmaCap IG (10% liquid formulation intravenous IG [IVIG]) is the first plasma-derived product manufactured using PlasmaCap EBA technology. The PlasmaCap EBA platform consists of a series of consecutive columns which bind a target protein, or group of proteins, in their native state directly from cryo-poor plasma. EBA chromatography includes five key steps: (1) expand, (2) sanitize and equilibrate, (3) load, (4) wash and (5) elute. These steps are made possible using high-density tungsten-carbide agarose beads, suspended by upward flow. The PlasmaCap EBA process was evaluated during Evolve's clinical campaign for scalability, product quality and yield. PlasmaCap EBA technology can be predictably scaled by maintaining the minimum residence time and residence time distribution for EBA columns of different diameters. Scalability of the manufacturing process was demonstrated by the 50-fold volumetric increase from laboratory-scale lots to clinical-scale lots. The process is also associated with enhanced product purity, such as lower aggregates. The PlasmaCap EBA process is expected to have the same or better yield and purity at commercial scale production compared to the clinical campaign. The PlasmaCap EBA platform was used to successfully develop PlasmaCap IG (10% liquid formulation IVIG) with proven scalability, product quality and yield.

The reconstruction of 4QWords of Ezekiel: Re-assessing 4Q385, 4Q386, and 4Q385b

This article re-examines the material reconstruction of the copies of 4QWords of Ezekiel olim 4QPseudo Ezekiel (4Q385 and 4Q386) via the use of digital tools and the Stegemann method. The findings evince that 4Q385 frgs. 2, 3, and 6 share the same deterioration patterns, suggesting that they originated in consecutive columns. The new sequence of the visions that emerge is as follows: “accelerating time” (4Q385 4), the divine merkabah (4Q385 6), and the resurrection of the dry bones (4Q385 2 + 3). 4Q385b is tentatively identified a replacement sheet. In light of the material differences in the parchment, top-margin height, and orthography, 4Q385b most likely belonged to the beginning of the composition—as per Qimron, although on different grounds. This material proposal establishes the name of the composition as 4QWords of Ezekiel. The reconstruction is followed by a transcription of the discussed fragments.

Investigating the performance of stone columns in an extremely soft clay—A case study

SummaryStone columns are used to improve soft soils; however, they fail through bulging, punching, and lateral expansion when the soil is extremely soft. The present study investigated the performance of stone columns in an extremely soft clay (ESC) through the addition of the appropriate geosynthetic materials. Field test was conducted for the foremost purpose of obtaining the optimal spacing between the consecutive stone columns and therefore prevents the failures of stone columns in ESC soils. The study further examined the failure modes of stone columns for the case of ESC soils. The computer programming software FLAC 3D was used for modeling and simulation, while Auto CAD was used to draw needed geometries of the case study. The results revealed that the full encasement of the stone column with suitable geogrids, optimal spacing, and proper design of cushion will enable the efficient use of stone columns as a composite foundation in ESC. The considered appropriate thickness of the cushion was found to be 30 cm, and this cushion helps the embedded soft clay soils to work together with the installed encased stone columns in ESC soils. The center‐to‐center (optimal) spacing between two consecutive stone columns showed optimal performance at distance S ≤ 5d of the diameter of the stone column. These findings show that stone column encased with suitable geogrids and optimal spacing will improve the bearing capacity, reduce settlement, and decrease the lateral deflection as well as hoop strain of the foundation.

Characterizing total positivity: Single vector tests via linear complementarity, sign non‐reversal and variation diminution

A matrix A $A$ is called totally positive (or totally non-negative) of order k $k$ , denoted by T P k $TP_k$ (or T N k $TN_k$ ), if all minors of size at most k $k$ are positive (or non-negative). These matrices have featured in diverse areas in mathematics, including algebra, analysis, combinatorics, differential equations and probability theory. The goal of this article is to provide a novel connection between total positivity and optimization/game theory. Specifically, we draw a relationship between totally positive matrices and the linear complementarity problem (LCP), which generalizes and unifies linear and quadratic programming problems and bimatrix games — this connection is unexplored, to the best of our knowledge. We show that A $A$ is T P k $TP_k$ if and only if for every submatrix A r $A_r$ of A $A$ formed from r $r$ consecutive rows and r $r$ consecutive columns (with r ⩽ k $r\leqslant k$ ), LCP ( A r , q ) $\mathrm{LCP}(A_r,q)$ has a unique solution for each vector q < 0 $q<0$ . In fact this can be strengthened to check the solution set of the LCP at a single vector for each such square submatrix. These novel characterizations are in the spirit of classical results characterizing T P $TP$ matrices by Gantmacher–Krein [Compos. Math. 1937] and P $P$ -matrices by Ingleton [Proc. London Math. Soc. 1966]. Our work contains two other contributions, both of which characterize total positivity using single test vectors whose coordinates have alternating signs — that is, lie in a certain open bi-orthant. First, we improve on one of the main results in recent joint work [Bull. London Math. Soc., 2021], which provided a novel characterization of T P k $TP_k$ matrices using sign non-reversal phenomena. We further improve on a classical characterization of total positivity by Brown–Johnstone–MacGibbon [J. Amer. Statist. Assoc. 1981] (following Gantmacher–Krein, 1950) involving the variation diminishing property. Finally, we use a Pólya frequency function of Karlin [Trans. Amer. Math. Soc. 1964] to show that our aforementioned characterizations of total positivity, involving (single) test-vectors drawn from the ‘alternating’ bi-orthant, do not work if these vectors are drawn from any other open orthant.

Simultaneous carbon dioxide reduction and methane generation in biogas for rural household use via anaerobic digestion of wetland grass with cow dung

In the present study, wetland grass (common reed) and cow manure were used as substrates for biogas production during 45-days hydraulic retention reaction. The fermenter has a total volume of 200 L and a working volume of 150 L. Following biogas generation, methane enhancement processes were combined with a chemical process. The solvents including H2O, NaOH, and Ca(OH)2 were taken in two consecutive columns for 3 h, and variation of components was measured after every 15 min. The results showed 2,254 L of biogas as 343.08 ml CH4g-1VSremoved of yields, with concomitant removal of H2S by H2O, NaOH, and Ca(OH)2 absorbers. The total removal of H2S using H2O, NaOH, and Ca(OH)2 was observed to be were 55.56, 98.89, and 98.75 %, respectively. A total enhancement of methane production using NaOH and Ca(OH)2 was observed to be 88.04 and 85.9%, respectively. As a result, H2S and CO2 emissions are significantly decreased, while low-cost chemical treatments improve bio-methane generation. This study also highlights the environmental implications of co-digesting wetland grass with cow dung, and the findings indicated that the strategy is highly effective in increasing biogas production and methane contents.

Sign non‐reversal property for totally non‐negative and totally positive matrices, and testing total positivity of their interval hull

A matrix $A$ is totally positive (or non-negative) of order $k$, denoted $TP_k$ (or $TN_k$), if all minors of size $\leq k$ are positive (or non-negative). It is well-known that such matrices are characterized by the variation diminishing property together with the sign non-reversal property. We do away with the former, and show that $A$ is $TP_k$ if and only if every submatrix formed from at most $k$ consecutive rows and columns has the sign non-reversal property. In fact this can be strengthened to only consider test vectors in $\mathbb{R}^k$ with alternating signs. We also show a similar characterization for all $TN_k$ matrices - more strongly, both of these characterizations use a single vector (with alternating signs) for each square submatrix. These characterizations are novel, and similar in spirit to the fundamental results characterizing $TP$ matrices by Gantmacher-Krein [Compos. Math. 1937] and $P$-matrices by Gale-Nikaido [Math. Ann. 1965]. As an application, we study the interval hull $\mathbb{I}(A,B)$ of two $m \times n$ matrices $A=(a_{ij})$ and $B = (b_{ij})$. This is the collection of $C \in \mathbb{R}^{m \times n}$ such that each $c_{ij}$ is between $a_{ij}$ and $b_{ij}$. Using the sign non-reversal property, we identify a two-element subset of $\mathbb{I}(A,B)$ that detects the $TP_k$ property for all of $\mathbb{I}(A,B)$ for arbitrary $k \geq 1$. In particular, this provides a test for total positivity (of any order), simultaneously for an entire class of rectangular matrices. In parallel, we also provide a finite set to test the total non-negativity (of any order) of an interval hull $\mathbb{I}(A,B)$.

A new reconstruction of the “Wisdom of the Hands” unit in 4QInstructiond (4Q418)

This study presents the material reconstruction of the unit on חכמת ידים‎—“Wisdom of the Hands,” in copy d of the wisdom composition Instruction (4Q418), followed by a complete transcription and an English translation. The study presents the location of nine fragments of 4Q418, placed on three consecutive columns, along with new joins and new readings. The reconstruction is based on the principles of the Stegemann method for the reconstruction of fragmentary scrolls, alongside new digital tools and software, as elaborated below. The new findings allow for a better understanding of the practical wisdom of Instruction, and provide new valuable data for future reconstruction of the entire composition.

High-Throughput Fractionation Coupled to Mass Spectrometry for Improved Quantitation in Metabolomics.

Metabolomics is emerging as an important field in life sciences. However, a weakness of current mass spectrometry (MS) based metabolomics platforms is the time-consuming analysis and the occurrence of severe matrix effects in complex mixtures. To overcome this problem, we have developed an automated and fast fractionation module coupled online to MS. The fractionation is realized by the implementation of three consecutive high performance solid-phase extraction columns consisting of a reversed phase, mixed-mode anion exchange, and mixed-mode cation exchange sorbent chemistry. The different chemistries resulted in an efficient interaction with a wide range of metabolites based on polarity, charge, and allocation of important matrix interferences like salts and phospholipids. The use of short columns and direct solvent switches allowed for fast screening (3 min per polarity). In total, 50 commonly reported diagnostic or explorative biomarkers were validated with a limit of quantification that was comparable with conventional LC–MS(/MS). In comparison with a flow injection analysis without fractionation, ion suppression decreased from 89% to 25%, and the sensitivity was 21 times higher. The validated method was used to investigate the effects of circadian rhythm and food intake on several metabolite classes. The significant diurnal changes that were observed stress the importance of standardized sampling times and fasting states when metabolite biomarkers are used. Our method demonstrates a fast approach for global profiling of the metabolome. This brings metabolomics one step closer to implementation into the clinic.

Influence of growth defects on the running-in behavior of an a-C:H:W coating under pure sliding contact conditions

The mechanical and tribological behaviors of coated surfaces are affected by the presence of local variations on coating composition, morphology and microstructure. During the deposition process, irregular surface topography and/or process instabilities can produce regions with macroscale defects, including voids and macroparticles. The interface between those regions and other portions of the coating presents an irregular columnar structure, identified by discrepancies between two consecutive columns, which may lead to local lower mechanical properties. In this work, numerical and experimental analyses were conducted to explore the effect of growth defects with irregular columnar boundaries (GDICB) on the mechanical and tribological behavior of a Tungsten Carbide/Carbon (a-C:H:W) multilayer coating subjected to multiscale tribological tests, including macroscale reciprocating tests and microscale scratch tests. Samples consisted of a commercial a-C:H:W coating deposited onto polished AISI H13 discs and AISI 52100 steel balls. Mechanical properties and microscale surface topography were evaluated using a triboindenter capable of carring out instrumented indentation tests and scanning probe microscopy techniques, while the microstructure was observed by scanning electron microscopy analyses. Macroscale reciprocating tests revealed a variable GDICB mechanical behavior, including deformation and detachment of those regions inside the wear track in the beginning of the test. Microscale scratch test results indicated a load-dependent mechanical behavior of the GDICB, showing a transition from deformation to detachment mechanism with the increase in the normal load. The digital tribology package TriboCODE was applied to model a realistic representation of the microscale scratch test, allowing the identification of individual GDICB behavior dependence on the applied normal load and the local mechanical properties.

Recognition method research on rough handling of express parcels based on acceleration features and CNN

Abstract Rough Handling of Express Parcels (RHEP) increases the risk of courier cargo damage and hurts the reputation of the express industry. Meanwhile, RHEP indirectly caused excessive use of packaging materials and cushioning materials, thereby aggravating environmental and social problems, such as waste disposal pressure and waste of resources. The prerequisite to prevent RHEP is recognition of it. Three typical types of RHEP (dropping, kicking fast and throwing) are discussed in this paper. For these types of RHEP, an intelligent recognition method is proposed. The main idea is to window the acceleration data of the package and extract the features in the window, then arrange these feature data into a three-dimensional matrix as the input of the CNN, and finally obtain the recognition result. In the study, mean, variance, kurtosis, skewness, dynamic range, short-term energy, and zero-crossing rate were considered to be good features in the issues dealt with in this paper. The feature data are organized in a way that different features occupy different channels. Within the uniform channel, three rows correspond to three axes, and the time window order corresponds to consecutive columns. This arrangement of feature data can take full advantage of convolution operations to mine the potential information of acceleration signals with time series characteristics and spatial characteristics. Experimental results show that the recognition accuracy of this method can reach 93.2% -96.12% steadily, which is better than the performance of directly arranging features into vectors and sending it to the fully connected network (recognition accuracy is 85% -95% and fluctuates greatly). Combining the recognition results of this method with the time and place of RHEP can more clearly analyze the causes of RHEP and propose targeted preventive measures.

Progressive collapse assessment of gravity-load designed European RC buildings under multi-column loss scenarios

Natural and man-made disasters often produce the collapse of multiple structural members at the ground floor of buildings, which may trigger a progressive collapse of the structure. Nonetheless, only a few experimental tests and numerical studies have been carried out to assess the effects of multiple column loss.In this paper, the progressive collapse capacity of gravity-load designed, reinforced concrete (RC) buildings complying with Eurocode 2 is numerically investigated, considering both simultaneous and sequential removal of ground-floor columns. The study focuses on a benchmark RC frame used in previous investigations on single-column loss scenarios, using nonlinear fibre-based capacity modelling and incremental dynamic analysis. Progressive collapse capacity was evaluated at multiple structural scales, in terms of axial strains, beam drifts and gravity load resisted by the structure after column loss. Analysis results allowed the quantification of both load and drift capacities under varying relative location and deactivation times of removed columns, as well as the control point. A comparison with numerical/experimental data highlighted that the sudden loss of two consecutive columns can drastically reduce the load capacity, resulting in a progressive collapse of the RC framed structure. A sequential loss of columns induced either positive or negative variations in load capacity, depending on the ratio between removal times, whereas drift capacity significantly reduced in almost all cases.

Design of High‐Productivity Mixed Tocopherol Purification from Deodorized Distillates by Tandem Reverse Phase Chromatography

AbstractCurrently, there is a great demand for high‐purity natural tocopherols in food supplements due to their antioxidant and Vitamin E activity. Deodorized distillate (DOD), a by‐product of the vegetable oil refining process, is a major source of these natural tocopherols. Isolation of pure tocopherols from DOD is challenging due to their lower concentration and presence of large quantities of polar and hydrophobic components. Several multistep methods are known in the art for the purification of tocopherols from DOD and crude feed stocks. This work presents a single‐step tandem reverse phase chromatography method for high‐purity tocopherols from DOD containing 4–8% of tocopherols (mixture of α, β, γ, and δ isomers). Tandem chromatography involved two consecutive chromatography columns, in which the first column is operated in frontal adsorption mode for maximum loading with partial removal of impurities and the second column operated in step wise separation mode causing high purity. The Developed tandem two‐column process produces 60% and 95% purity tocopherol grades at a high loading of 381 (g of DOD) per (L of resin). The developed method recovers up to 77% of loaded tocopherols in purified form with a productivity of 3.4 g L−1 hour−1.

Pullusurfactans A–E, new biosurfactants produced by Aureobasidium pullulans A11211-4-57 from a fleabane, Erigeron annus (L.) pers.

Yeast biosurfactants have potent applications in medical, cosmeceutical, and food industries due to their specific modes of action, low toxicity, and applicability. In this study, biosurfactant-producing yeasts were screened for various industrial applications. Among them, Aureobasidium pullulans strain A11211-4-57 with potent surfactant activity from fleabane flower, Erigeron annus (L.) pers., was selected. From culture supernatant of strain A11211-4-57, five new low-surface-tension chemicals designated as pullusurfactans A-E were identified through consecutive chromatography steps, involving ODS, silica gel, Sephadex LH-20, and ODS Sep-pak cartridge columns. Based on mass and NMR measurements, structures of pullusurfactans A-E were determined as myo-inositol lipids with molecular formulae of C20H35O9, C18H32O8, C20H35O9, C24H42O9, and C18H32O8, respectively. These compounds exhibited potent biosurfactant activities (22.90, 22.40, 32.28, 25.28, and 22.44 mN/m, respectively). These results suggest that these novel biosurfactants have potential use as biosurfactants in industrial aspect.

Adding Value to Bioethanol through a Purification Process Revamp

A comprehensive technical feasibility study was conducted of a bioethanol demonstration plant with the aim of converting parts of an existing fuel-grade bioethanol production into a more valuable solvent-grade ethanol. The study focuses on the separation unit, which consists of three consecutive distillation columns and a dehydration step using molecular sieves. This separation unit did not permit sufficient removal of crotonaldehyde and methanol for obtaining solvent-grade ethanol. Therefore, an additional distillation column after the dehydration step was investigated by simulation. It is operated at subatmospheric pressure and enables simultaneous removal of methanol, crotonaldehyde, and water in the distillate. The distillate meets the fuel-grade ethanol specifications, while the bottom product meets the solvent-grade specifications. It enables around 70% solvent-grade ethanol production and employs a vacuum pump that is already used in the considered plant. A stationary operating point is characteriz...

Recycling givens rotations for the efficient approximation of pseudospectra of band-dominated operators

We study spectra and pseudospectra of certain bounded linear operators on $\ell^2({\mathbb Z})$. The operators are generally non-normal, and their matrix representation has a characteristic off-diagonal decay. Based on a result of Chandler-Wilde, Chonchaiya and Lindner for tridiagonal infinite matrices, we demonstrate an efficient algorithm for the computation of upper and lower bounds on the pseudospectrum of operators that are merely norm limits of band matrices -- the so-called band-dominated operators. After approximation by a band matrix and fixing a parameter $n\in{\mathbb N}$, one looks at $n$ consecutive columns $\{k+1,...,k+n\}$, $k\in{\mathbb Z}$, of the corresponding matrix and computes the smallest singular value of that section via QR factorization. We here propose a QR factorization by a sequence of Givens rotations in such a way that a large part of the computation can be reused for the factorization of the next submatrix -- when $k$ is replaced by $k+1$. The computational cost for the next factorization(s) is ${\mathcal O}(nd)$ as opposed to a naive implementation with ${\mathcal O}(nd^2)$, where $d$ is the bandwidth. So our algorithm pays off for large bands, which is attractive when approximating band-dominated operators with a full (i.e. not banded) matrix.

The impact of citrate concentration on adhesion of platelets and leukocytes to adsorbents in whole blood lipoprotein apheresis.

Lipoprotein apheresis is applied to deplete low density lipoprotein and other apolipoprotein B containing lipoproteins in patients with severe familial hypercholesterolemia, hypertriglyceridemia associated pancreatitis, or lipoprotein (a)-hyperlipoproteinemia. Anticoagulation of the extracorporeal circuit may influence cellular activation, as evidenced by a reduction of inflammatory parameters during regional citrate anticoagulation with acid citrate dextrose A (ACD-A) commonly used in whole blood lipid apheresis. While the citrate concentration in the extracorporeal circuit has to ensure efficient anticoagulation, citrate infusion into the patient should be limited to avoid citrate overload. We assessed the influence of citrate concentration on cellular activation during in vitro circulation of whole blood containing 2.8 mM citrate (ACD-A 1:40), 5.6 mM citrate (ACD-A 1:20), or 13 mM citrate over polyacrylate-based adsorbents for lipoprotein apheresis. We found increased platelet adhesion for anticoagulation with 2.8 mM citrate as compared to 5.6 or 13 mM citrate, as shown by cell counting and confirmed by scanning electron microscopy of adsorbent beads as well as by elevated levels of platelet activation markers and of platelet-derived microvesicles. Leukocytes showed an equivalent adhesion pattern, while red blood cells remained unaffected at all citrate concentrations. Passage of blood over two consecutive columns resulted in enhanced platelet adhesion to the second column, presumably due to upstream preactivation. In conclusion, citrate influences activation and adhesion of platelets and leukocytes in a concentration-dependent manner, and ACD-A 1:20, equivalent to a citrate concentration of 5.6 mM in whole blood, ensures minimal cellular activation during passage of whole blood over polyacrylate-based adsorbents.

Copyright Protection for Digital Images using Singular Value Decomposition and Integer Wavelet Transform

This paper presents a new technique for copyright protection of images using integer wavelet transform (IWT), singular value decomposition (SVD) and Arnold transform. We divide the cover image into four sub-images by picking alternate pixels from consecutive rows and columns and embed the copyright mark into the sub-image having the largest sum of singular values. The embedding is done by modifying singular values of the IWT coefficients of the selected sub-image. The use of Arnold transform and SVD increases security and robustness against geometric and several signals processing attacks, while IWT provides computational efficiency. We compare the performance of our technique with state-of-the-art-methods. The experimental results show that the proposed technique is more imperceptible and achieves higher security and robustness against various signal processing (filtering, compression, noise addition, histogram equalization and motion blur) and geometrical (cropping, resizing, rotation) attacks.

Removal of metal ions from a petrochemical wastewater using brown macro-algae as natural cation-exchangers

Four brown macro-algae, Ascophyllum nodosum, Fucus spiralis, Laminaria hyperborea and Pelvetia canaliculata, were investigated as natural cation exchangers for the removal of transition metals from a petrochemical wastewater. The wastewater presents a high conductivity due to chloride, sulfate, sodium, calcium and residual concentrations of copper, zinc and nickel species. According to all-inorganic species evaluated, the molar fraction of Zn2+, Cu2+ and Ni2+ is near 92% and the remaining species are ZnCl+, ZnSO4, CuSO4, NiCl+ and NiSO4. A Langmuir multicomponent model was able to predict the ion-exchange equilibrium data for Cu, Ni, Zn and Ca species present in the petrochemical wastewater. L. hyperborea showed a higher uptake capacity than the other brown algae tested. The equilibrium affinity constants for the functional groups decreased in the following order: Cu>Zn>Ni≈Ca, except for L. hyperborea, which presents a lesser affinity for Ca. Ion-exchange breakthrough curves obtained from a fixed-bed column packed with raw L.hyperborea, led to an operating capacity of 0.22, 0.10 and 0.05mEq/g for Cu, Zn and Ni, corresponding to 1558, 515, 528BV (7.2BV/h), respectively. The treatment strategy consisted in the operation of two consecutive columns, the first one for copper ions removal (operating capacity of 1558 BV – 7.2 BV/h) and the second one for zinc and nickel removal (operating capacity of 163BV–7.3BV/h). The elution of Cu, Zn and Ni from the natural resin was achieved with 10 and 6BV of HCl (0.4M, 1.2%) (150 and 90g HCl/L of resin), using a flow rate of 3.6BV/h, respectively for the first and second columns.