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See detailInverse analysis in geotechnics: soil parameter identification by genetic algorithm
Levasseur, Séverine ULg; Malécot, Yann; Boulon, Marc et al

in 8th. World Congress on Computational Mechanics (WCCM8) & 5th. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) (2008)

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See detailInverse analysis on in situ geotechnical measurement using a genetic algorithm
Malécot, Yann; Levasseur, Séverine ULg; Boulon, Marc et al

in Pande, G. N.; Pietruszczak, S. (Eds.) Numerical Models in Geomechanics (2004)

This paper is dedicated to the identification of constitutive parameters of the Mohr-Coulomb constitutive model from in situ measurements. A general definition of an objective function is proposed. A ... [more ▼]

This paper is dedicated to the identification of constitutive parameters of the Mohr-Coulomb constitutive model from in situ measurements. A general definition of an objective function is proposed. A direct approach of inverse analysis is used to identify the shear modulus and the friction angle in four different situations. The first two examples deal with a “numerical” and with a real pressuremeter curve. A difficult convergence and a strong non unicity of solution is observed, which is classical in inverse analysis (ill posed problems). In a second stage, the horizontal displacements related to two excavation problems are used for identifying the two mechanical parameters. A clear minimum of the objective function is detected, giving a unique solution. The reasons of these differences are discussed and some ways of improving the interpretation of the pressuremeter test results are proposed. [less ▲]

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See detailInverse analysis techniques for parameter identification in simulation of excavation support systems
Rechea, Cecilia; Levasseur, Séverine ULg; Finno, Richard J

in Computers & Geotechnics (2008), 35(3), 331-345

Two numerical procedures are described that quantitatively identify a set of constitutive parameters that best represents observed ground movement data associated with deep excavations in urban ... [more ▼]

Two numerical procedures are described that quantitatively identify a set of constitutive parameters that best represents observed ground movement data associated with deep excavations in urban environments. This inverse problem is solved by minimizing an objective (or error) function of the weighted least-squares type that contains the difference between observed and calculated ground displacements. The problem is solved with two different minimization algorithms, one based on a gradient method and the other on a genetic algorithm. The objective function is shown to be smooth with a unique solution. Both methods are applied to lateral movements from synthetic and real excavations to illustrate various aspects of the implementation of the methods. The advantages and disadvantages of each method applied to excavation problems are discussed. [less ▲]

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See detailInverse control of prolactin and growth hormone gene expression: effect of thyroliberin on transcription and RNA stabilization
Laverriere, J. N.; Morin, A.; Tixier-Vidal, A. et al

in EMBO Journal (1983), 2(9), 1493-9

The hypothalamic tripeptide thyroliberin (TRH) regulates prolactin (PRL) and growth hormone (GH) synthesis inversely by modulating the levels of their specific mRNA. Changes in mRNA levels could involve ... [more ▼]

The hypothalamic tripeptide thyroliberin (TRH) regulates prolactin (PRL) and growth hormone (GH) synthesis inversely by modulating the levels of their specific mRNA. Changes in mRNA levels could involve both transcriptional and posttranscriptional events. To examine further these possibilities, we have investigated the effect of TRH on the biosynthesis and degradation of PRL and GH RNA in a rat pituitary tumor cell line. Newly synthesized PRL and GH RNA sequences were quantified in nuclear and cytoplasmic fractions by hybridization of 3H-labelled RNA to immobilized plasmid DNA containing either PRL or GH cDNA sequences. Steady-state levels of specific RNA were estimated by RNA blot hybridization. The results indicate that TRH increases in a rapid but transient manner the transcription of the PRL gene, and suggest that it does not alter the processing and the transport to the cytoplasm. In contrast, after a lag-time, TRH seems to induce a long-lasting inhibition on GH, as well as on overall gene transcription. Furthermore, we observed an effect of TRH on mRNA stability. TRH significantly increases the half-life of PRL mRNA. Our results also support the hypothesis that TRH decreases the half-life of GH mRNA. Such post-transcriptional action of TRH amplifies and prolongs the regulations exerted at the transcriptional level. [less ▲]

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See detailInverse Design of Compressor and Turbine Blades at Transonic Flow Conditions
Léonard, Olivier ULg; Van den Braembussche, René

in Proceedings of the ASME Turbo Expo 1992 (1992, June)

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See detailInverse dynamics of parallel kinematic manipulators with flexible links
Guimaraes Bastos Junior, Guaraci ULg; Seifried, Robert; Bruls, Olivier ULg

Conference (2012, May)

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See detailInverse dynamics of serial and parallel underactuated multibody systems using a DAE optimal control approach
Guimaraes Bastos Junior, Guaraci ULg; Seifried, Robert; Bruls, Olivier ULg

in Multibody System Dynamics (2013)

The inverse dynamics analysis of underactuated multibody systems aims at determining the control inputs in order to track a prescribed trajectory. This paper studies the inverse dynamics of non-minimum ... [more ▼]

The inverse dynamics analysis of underactuated multibody systems aims at determining the control inputs in order to track a prescribed trajectory. This paper studies the inverse dynamics of non-minimum phase underactuated multibody systems with serial and parallel planar topology, e.g. for end-effector control of flexible manipulators or manipulators with passive joints. Unlike for minimum phase systems, the inverse dynamics of non-minimum phase systems cannot be solved by adding trajectory constraints (servoconstraints) to the equations of motion and applying a forward time integration. Indeed, the inverse dynamics of a non-minimum phase system is known to be non-causal, which means that the control forces and torques should start before the beginning of the trajectory (preactuation phase) and continue after the end-point is reached (post-actuation phase). The existing stable inversion method roposed for general nonlinear non-minimum phase systems requires to derive explicitly the equations of the internal dynamics and to solve a boundary value problem. This paper proposes an alternative solution strategy which is based on an optimal control approach using a direct transcription method. The method is illustrated for the inverse dynamics of an underactuated serial manipulator with rigid links and four degrees-of-freedom and an underactuated parallel machine. An important advantage of the proposed approach is that it can be applied directly to the standard equations of motion of multibody systems either in ODE or in DAE form. Therefore, it is easier to implement this method in a general purpose simulation software. [less ▲]

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See detailINVERSE DYNAMICS OF UNDERACTUATED MULTIBODY SYSTEMS USING A DAE OPTIMAL CONTROL APPROACH
Guimaraes Bastos Junior, Guaraci ULg; Seifried, Robert; Bruls, Olivier ULg

in Proceedings of the ECCOMAS Thematic Conference (MULTIBODY DYNAMICS) 2011 (2011, July)

The inverse dynamics analysis of underactuated multibody systems aims at determining the control inputs in order to track a prescribed trajectory. This paper studies the inverse dynamics of non-minimum ... [more ▼]

The inverse dynamics analysis of underactuated multibody systems aims at determining the control inputs in order to track a prescribed trajectory. This paper studies the inverse dynamics of non-minimum phase underactuated multibody systems, e.g. for end-effector control of flexible manipulators or manipulators with passive joints. Unlike for minimum phase systems, the inverse dynamics of non-minimum phase systems cannot be solved by adding trajectory constraints to the equations of motion and by applying a forward time integration. Indeed, the inverse dynamics of a non-minimum phase system is known to be non-causal, which means that the control forces and torques should start before the beginning of the trajectory (pre-actuation phase) and continue after the end-point is reached (post-actuation phase). The existing stable inversion method proposed for general nonlinear non-minimum phase systems requires to derive explicitly the equations of the internal dynamics and to solve a boundary value problem. This paper proposes an alternative solution strategy which is based on an optimal control approach. The method is illustrated for the inverse dynamics of a planar underactuated manipulator with rigid links and four degrees-of-freedom. An important advantage of the proposed approach is that it can be applied directly to the standard equations of motion of multibody systems either in ODE or in DAE form. Therefore, it is easier to implement this method in a general purpose simulation software. [less ▲]

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See detailInverse Estimates of Anthropogenic Carbon Dioxide From Ocean Interior Carbon Measurements and Ocean General Circulation Models
Mikaloff Fletcher, S. E.; Gruber, N. P.; Jacobson, A. R. et al

Conference (2003, December)

The ocean is an important sink for atmospheric carbon dioxide, and the exchange of carbon dioxide between the atmosphere and ocean plays a critical role in determining the spatial distribution of ... [more ▼]

The ocean is an important sink for atmospheric carbon dioxide, and the exchange of carbon dioxide between the atmosphere and ocean plays a critical role in determining the spatial distribution of atmospheric carbon dioxide. However, there is still a great deal of uncertainty in both magnitude and regional patterns of anthropogenic uptake associated with estimates of oceanic carbon fluxes. Using a recently developed technique, exchange of anthropogenic carbon dioxide across the air-sea interface have been estimated from observations of dissolved inorganic carbon and nutrient concentrations and an Ocean General Circulation Model (OGCM) using a Green's function inverse modeling technique. Previous sensitivity studies have shown that model circulation error is an important source of error in the ocean inversion. In order to address the role of ocean circulation biases, inverse estimates of anthropogenic carbon air-sea gas exchange are presented using basis functions from a suite of seven different OGCM's. The robustness of the ocean inversion will be quantified and the effects of differences between approaches to modeling ocean circulation on the ocean carbon cycle will be explored. These results will be discussed in the context of recent atmospheric inverse estimates. [less ▲]

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See detailInverse estimates of anthropogenic CO2 uptake, transport, and storage by the ocean
Mikaloff Fletcher, S. E.; Gruber, N.; Jacobson, A. R. et al

in Global Biogeochemical Cycles (2006), 20(2),

[1] Regional air-sea fluxes of anthropogenic CO2 are estimated using a Green's function inversion method that combines data-based estimates of anthropogenic CO2 in the ocean with information about ocean ... [more ▼]

[1] Regional air-sea fluxes of anthropogenic CO2 are estimated using a Green's function inversion method that combines data-based estimates of anthropogenic CO2 in the ocean with information about ocean transport and mixing from a suite of Ocean General Circulation Models (OGCMs). In order to quantify the uncertainty associated with the estimated fluxes owing to modeled transport and errors in the data, we employ 10 OGCMs and three scenarios representing biases in the data-based anthropogenic CO2 estimates. On the basis of the prescribed anthropogenic CO2 storage, we find a global uptake of 2.2 +/- 0.25 Pg C yr(-1), scaled to 1995. This error estimate represents the standard deviation of the models weighted by a CFC-based model skill score, which reduces the error range and emphasizes those models that have been shown to reproduce observed tracer concentrations most accurately. The greatest anthropogenic CO2 uptake occurs in the Southern Ocean and in the tropics. The flux estimates imply vigorous northward transport in the Southern Hemisphere, northward cross-equatorial transport, and equatorward transport at high northern latitudes. Compared with forward simulations, we find substantially more uptake in the Southern Ocean, less uptake in the Pacific Ocean, and less global uptake. The large-scale spatial pattern of the estimated flux is generally insensitive to possible biases in the data and the models employed. However, the global uptake scales approximately linearly with changes in the global anthropogenic CO2 inventory. Considerable uncertainties remain in some regions, particularly the Southern Ocean. [less ▲]

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See detailInverse estimates of the oceanic sources and sinks of natural CO2 and the implied oceanic carbon transport
Mikaloff Fletcher, S. E.; Gruber, N.; Jacobson, A. R. et al

in Global Biogeochemical Cycles (2007), 21(1),

We use an inverse method to estimate the global-scale pattern of the air-sea flux of natural CO2, i.e., the component of the CO2 flux due to the natural carbon cycle that already existed in preindustrial ... [more ▼]

We use an inverse method to estimate the global-scale pattern of the air-sea flux of natural CO2, i.e., the component of the CO2 flux due to the natural carbon cycle that already existed in preindustrial times, on the basis of ocean interior observations of dissolved inorganic carbon (DIC) and other tracers, from which we estimate Delta C-gasex, i.e., the component of the observed DIC that is due to the gas exchange of natural CO2. We employ a suite of 10 different Ocean General Circulation Models (OGCMs) to quantify the error arising from uncertainties in the modeled transport required to link the interior ocean observations to the surface fluxes. The results from the contributing OGCMs are weighted using a model skill score based on a comparison of each model's simulated natural radiocarbon with observations. We find a pattern of air-sea flux of natural CO2 characterized by outgassing in the Southern Ocean between 44 degrees S and 59 degrees S, vigorous uptake at midlatitudes of both hemispheres, and strong outgassing in the tropics. In the Northern Hemisphere and the tropics, the inverse estimates generally agree closely with the natural CO2 flux results from forward simulations of coupled OGCM-biogeochemistry models undertaken as part of the second phase of the Ocean Carbon Model Intercomparison Project (OCMIP-2). The OCMIP-2 simulations find far less air-sea exchange than the inversion south of 20 degrees S, but more recent forward OGCM studies are in better agreement with the inverse estimates in the Southern Hemisphere. The strong source and sink pattern south of 20 degrees S was not apparent in an earlier inversion study, because the choice of region boundaries led to a partial cancellation of the sources and sinks. We show that the inversely estimated flux pattern is clearly traceable to gradients in the observed Delta C-gasex, and that it is relatively insensitive to the choice of OGCM or potential biases in Delta C-gasex. Our inverse estimates imply a southward interhemispheric transport of 0.31 +/- 0.02 Pg C yr(-1), most of which occurs in the Atlantic. This is considerably smaller than the 1 Pg C yr(-1) of Northern Hemisphere uptake that has been inferred from atmospheric CO2 observations during the 1980s and 1990s, which supports the hypothesis of a Northern Hemisphere terrestrial sink. [less ▲]

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See detailInverse Expression of Two Laminin Binding Proteins, 67lr and Galectin-3, Correlates with the Invasive Phenotype of Trophoblastic Tissue
van den Brule, F. A.; Price, J.; Sobel, M. E. et al

in Biochemical and Biophysical Research Communications (1994), 201(1), 388-93

Tumor invasion of host tissues and trophoblastic penetration of the endometrium share common biological features. Both processes involve the invasion of basement membranes, an event that is initiated by ... [more ▼]

Tumor invasion of host tissues and trophoblastic penetration of the endometrium share common biological features. Both processes involve the invasion of basement membranes, an event that is initiated by adhesion of cancer or trophoblast cells to basement membrane components and particularly to laminin. Adhesion to this latter glycoprotein is mediated through a variety of cell surface receptors. We have previously shown that the 67 kD Laminin Receptor (67LR) and a 31 kD Human Laminin Binding Protein, recently renamed galectin-3, are inversely modulated as the invasive phenotype of cancer cells progresses, with up regulation of the former, and down regulation of the latter, respectively. In this study, we examined the expression of these two proteins in 27 human trophoblastic specimens at different gestational ages using Northern and Western blot techniques. Expression of the 67LR increased from 7 weeks to a maximum at 12 weeks, when invasion is maximal, and then decreased. Expression of galectin-3 was inversely modulated by the gestational age, with a minimum expression at 12 weeks. Our data demonstrate that invasive trophoblast displays the same pattern of laminin binding proteins expression than invasive cancer cells, and further demonstrates that invasion of the extracellular matrix by trophoblast and cancer cells share common molecular mechanisms. [less ▲]

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See detailAn inverse modelling approach to estimate the hygric parameters of clay-based masonry during a Moisture Buffer Value test
Dubois, Samuel ULg; McGregor, Fionn; Evrard, Arnaud et al

in Building & Environment (2014), 81

This paper presents an inverse modelling approach for parameter estimation of a model dedicated to the description of moisture mass transfer in porous hygroscopic building materials. The hygric behaviour ... [more ▼]

This paper presents an inverse modelling approach for parameter estimation of a model dedicated to the description of moisture mass transfer in porous hygroscopic building materials. The hygric behaviour of unfired clay-based masonry samples is specifically studied here and the Moisture Buffer Value (MBV) protocol is proposed as a data source from which it is possible to estimate several parameters at once. Those include materials properties and experimental parameters. For this purpose, the mass of two clay samples with different compositions is continuously monitored during several consecutive humidity cycles in isothermal conditions. Independently of these dynamic experimental tests, their moisture storage and transport parameters are measured with standard steady-state methods. A simple moisture transfer model developed in COMSOL Multiphysics is used to predict the moisture uptake/release behaviour during the MBV tests. The set of model parameters values that minimizes the difference between simulated and experimental results is then automatically estimated using an inverse modelling algorithm based on Bayesian techniques. For materials properties, the optimized parameters values are compared to values that were experimentally measured in steady state. And because a precise understanding of parameters is needed to assess the confidence in the inverse modelling results, a sensitivity analysis of the model is also provided. [less ▲]

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See detailInverse modelling of nanoindentation tests to identify Ti-555 behaviour
Gerday, Anne-Françoise ULg; Clement, N.; Jacques, P. J. et al

in Proceedings of the 11th world conference on titanium (2007)

Nanoindentation is commonly used to probe local plastic properties of materials [1-4]. From these nanoindentation tests, finite element (FE) modeling is currently used to identify material data. The ... [more ▼]

Nanoindentation is commonly used to probe local plastic properties of materials [1-4]. From these nanoindentation tests, finite element (FE) modeling is currently used to identify material data. The general ambition of this research is to extract the material parameters representative of the response of a new generation of Ti alloy, called Ti-555, in order to perform simulations on representative microscopic cells and guide the optimization of the alloy. In this paper, the identification of the flow parameters of the -phase of this alloy, using a microscopic crystal plasticity-based constitutive law is described. The nanoindentation tests are performed using a pyramidal Berkovich diamond indenter and the different slip systems of the b.c.c. -phase are supposed to be activated with identical critical shear stresses. The FE nanoindentation force-displacement curves obtained with the microscopic constitutive law are compared to the experimental ones. The influence of the orientation of the grains is also analysed. A previous sensivity analysis on different parameters with different constitutive laws and materials has shown a great influence of different parameters on the nanoindentation results but almost no influence of other parameters [5-6]. [less ▲]

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See detailInverse Modulation of Il-10 and Il-12 in the Blood of Women with Preneoplastic Lesions of the Uterine Cervix
Jacobs, Nathalie ULg; Giannini, Sandra L; Doyen, Jean ULg et al

in Clinical & Experimental Immunology (1998), 111(1), 219-24

It has been postulated that an impaired immune response may contribute to the progression of human papillomavirus (HPV)-associated preneoplastic lesions. Based on this hypothesis, we evaluated the ... [more ▼]

It has been postulated that an impaired immune response may contribute to the progression of human papillomavirus (HPV)-associated preneoplastic lesions. Based on this hypothesis, we evaluated the cytokine production in the blood of patients with squamous intraepithelial lesions (SIL) of the uterine cervix. The levels of type-1 (interferon-gamma (IFN-gamma) and IL-12) and type-2(IL-4 and IL-10) cytokines were measured in whole blood culture supernatants of patients with low- and high-grade SIL and control women. There was no difference in IL-4 and IFN-gamma levels between patients with SIL and the control group. In contrast, the ratio of IL-12/IL-10 levels was significantly lower in patients with SIL compared with the control group. A lower IL-12/IL-10 ratio in women with SIL was also observed when peripheral blood mononuclear cell (PBMC) culture supernatants and plasma samples were analysed. In patients, neither the lower expression of the CD3epsilon chain nor the higher frequency of HLA-DRB1*1501 expression could be correlated with abnormal cytokine production. These results suggest that a part of the cytokine network, namely IL-10 and IL-12, is perturbed in patients with SIL. A better knowledge of the role of these cytokines in regulating the growth of HPV-associated SIL might have practical implications for the development of vaccines or immunomodulatory strategies in the treatment of cervical cancers. [less ▲]

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See detailInverse Modulation of Intraepithelial Langerhans' Cells and Stromal Macrophage/Dendrocyte Populations in Human Papillomavirus-Associated Squamous Intraepithelial Lesions of the Cervix
Al-Saleh, Walid; Delvenne, Philippe ULg; Arrese Estrada, Jorge ULg et al

in Virchows Archiv : An International Journal of Pathology (1995), 427(1), 41-8

Ninety-four cervical biopsies from normal tissue to high-grade squamous intraepithelial lesion (SILs) were examined for the presence of intraepithelial Langerhans' cells and subpopulations of stromal ... [more ▼]

Ninety-four cervical biopsies from normal tissue to high-grade squamous intraepithelial lesion (SILs) were examined for the presence of intraepithelial Langerhans' cells and subpopulations of stromal macrophages/dendrocytes by immunohistochemistry using anti-S100, -L1, -CD68 and -factor XIIIa antibodies. Human papillomavirus (HPV) detection was performed in all cases by using first a mixture of DNA probes for 14 HPV types commonly found in anogenital biopsies at low stringency conditions (Tm -40 degrees C) and by reanalyzing the tissues at high stringency (Tm -10 degrees C) with HPV 6/11, 16/18 and 31/33/35 biotinylated probe cocktails and individual digoxigenin-labelled probes. SILs and metaplastic tissues were significantly associated with a depletion of S100-positive intraepithelial Langerhans' cells when compared with normal epithelium. In contrast, there was a significant increase in L1-positive stromal macrophages in SIL biopsies compared with normal or metaplastic cervix. A significantly higher density of CD68-positive macrophages was also observed in high-grade SILs compared with normal or metaplastic biopsies and with low-grade SILs. The density of factor XIIIa-positive dendrocytes was found to be higher in SILs compared with metaplastic tissues and in high-grade SILs when compared with normal cervical biopsies. No specific relationship was found between the densities of these cells and the HPV type detected in SILs separated into low grade and high grade. The significance of this inverse modulation of intraepithelial Langerhans' cells and stromal macrophages/dendrocytes in normal and SIL biopsies is discussed in relation to HPV infection and malignant transformation. [less ▲]

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See detailInverse modulation of steady-state messenger RNA levels of two non-integrin laminin-binding proteins in human colon carcinoma.
Castronovo, Vincenzo ULg; Campo, E.; van den Brule, F. A. et al

in Journal of the National Cancer Institute (1992), 84(15), 1161-9

BACKGROUND: Interactions between cells and the basement membrane glycoprotein laminin are altered during colon cancer progression. Colon carcinoma and normal mucosa cells express a variety of laminin ... [more ▼]

BACKGROUND: Interactions between cells and the basement membrane glycoprotein laminin are altered during colon cancer progression. Colon carcinoma and normal mucosa cells express a variety of laminin-binding proteins, including the 67-kd laminin receptor (67 LR) and a 31-kd human laminin-binding protein (HLBP31) homologous to the 31-kd human IgE-binding protein/galactoside-binding lectin. PURPOSE: To investigate whether various laminin-binding proteins are differentially expressed in human colon carcinoma, we studied messenger RNA (mRNA) levels of the 67 LR and HLBP31 in matched tumor and adjacent normal mucosa samples from a series of 21 patients. METHODS: Total cellular RNA from tumor and normal mucosa was isolated and analyzed by Northern and slot blot hybridization. In addition, HLBP31 protein levels were assessed by the immunoblot technique. Quantitative laminin affinity chromatography was also used to measure the synthesis of HLBP31 protein in five human cancer cell lines. RESULTS: The steady-state mRNA level of HLBP31 was downregulated (i.e., decreased) in 18 of 21 human colon carcinomas compared with the level in their corresponding normal colonic mucosa. On average, the level of HLBP31 mRNA was decreased 50% +/- 30% (+/- SD) in the colon cancers. The mean ratio of colon cancer HLBP31 mRNA to adjacent normal mucosa HLBP31 mRNA was twofold lower in primary tumors of patients with metastases (0.3 +/- 0.2 SD) than in primary tumors of patients free of metastatic lesions (0.6 +/- 0.2 SD). The differences between the two groups of patients were statistically significant (P less than .05, Wilcoxon-Mann-Whitney test). We have previously shown that the ratio of colon cancer 67 LR mRNA to corresponding normal mucosa 67 LR mRNA was increased in the same patient population. When the two ratios (ratio of cancer to normal HLBP31 mRNA and ratio of cancer to normal 67 LR mRNA) were compared, HLBP31 mRNA/67 LR mRNA was significantly lower (P less than .05) in primary tumors with metastases (mean +/- SD, 0.3 +/- 0.2) than in primary cancers without metastases (mean +/- SD, 0.7 +/- 0.5). The steady-state level of HLBP31 mRNA was directly correlated with the amount of HLBP31 protein in both colon tissue samples and human cancer cell lines. CONCLUSION: HLBP31 mRNA expression in colon cancer tissues is modulated inversely to that of 67 LR mRNA expression. The down-regulation of HLBP31 appears to be associated with the metastatic capabilities of colon cancer cells. IMPLICATIONS: Prospective studies on a large cohort should determine if the systematic detection of HLBP31 and 67 LR protein and/or mRNA can be a valuable adjunct in the prognostic evaluation of primary colon cancers. [less ▲]

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See detailInverse soil parameter identification of an earth and rockfill dam by genetic algorithm optimization
Vahdati, Pooya; Levasseur, Séverine ULg; Mattsson, Hans et al

in Sharing Experience for Safe and Sustainable Water Storage (2013)

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See detailInverse star, borders, and palstars
Rampersad, Narad ULg; Shallit, Jeffrey; Wang, Ming-wei

in Information Processing Letters (2011), 111

A language L is closed if L = L*. We consider an operation on closed languages, L-*, that is an inverse to Kleene closure. It is known that if L is closed and regular, then L-* is also regular. We show ... [more ▼]

A language L is closed if L = L*. We consider an operation on closed languages, L-*, that is an inverse to Kleene closure. It is known that if L is closed and regular, then L-* is also regular. We show that the analogous result fails to hold for the context-free languages. Along the way we find a new relationship between the unbordered words and the prime palstars of Knuth, Morris, and Pratt. We use this relationship to enumerate the prime palstars, and we prove that neither the language of all unbordered words nor the language of all prime palstars is context-free. [less ▲]

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