Browsing by Subject "MATRIX"

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  • Li, Xiaodong; Meng, Shuo; Puhakka, Eini; Ikonen, Jussi; Liu, Longcheng; Siitari-Kauppi, Marja (2020)
    To determine the diffusion and sorption properties of radionuclides in intact crystalline rocks, a new electromigration device was built and tested by running with I- and Se(IV) ions. By introducing a potentiostat to impose a constant voltage over the studied rock sample, the electromigration device can give more stable and accurate experimental results than those from the traditional electromigration devices. In addition, the variation in the pH of the background electrolytes was minimised by adding a small amount of NaHCO3 as buffers. To interpret the experimental results with more confidence, an advection-dispersion model was also developed in this study, which accounts for the most important mechanisms governing ionic transport in the electromigration experiments. Data analysis of the breakthrough curves by the advection-dispersion model, instead of the traditional ideal plug-flow model, suggest that the effective diffusivities of I- and Se(IV) are (1.15 +/- 0.06) x 10(-13) m(2)/s and (3.50 +/- 0.86) x 10(-14) m(2)/s, respectively. The results also show that I- is more mobile than Se(IV) ions when migrating through the same intact rock sample and that their sorption properties are almost identical.
  • Stape, Thiago Henrique Scarabello; Seseogullari-Dirihan, Roda; Tjäderhane, Leo; Abunas, Gabriel; Marcondes Martins, Luis Roberto; Tezvergil-Mutluay, Arzu (2018)
    In dentistry, the wet-bonding approach relies on water to maintain demineralized collagen expanded for proper resin infiltration; nevertheless, hydrolytic instability of the resin-dentin interface is inevitable with current bonding techniques. Considering dimethyl sulfoxide's (DMSO) ability to "biomodify" collagen and precipitate enzymes, the aim was to test whether the use of DMSO would permit adequate resin bonding to H3PO4-etched dehydrated dentin and assess its impact on collagen degradation by host-derived enzymes. Etched dentin surfaces from extracted sound human molars were randomly bonded in wet or dry conditions using aqueous or ethanolic DMSO solutions as pretreatments and bonding resins with or without DMSO. Bonded teeth were sectioned into resin-dentin slabs for confocal in situ zymography and beams for microtensile bond strength test. Demineralized powdered dentin was incubated in the tested DMSO -media and a hydroxyproline assay evaluated dissolution of collagen peptides. Zymography was performed on protein extracts obtained from dry and wet H3PO4-ecthed dentin powder treated with the DMSO- media. The correlative biochemical analysis demonstrated that reduction of water content during dentin hybridization by the innovative dry-bonding approaches with DMSO is effective to inactivate host-derived MMP-2 and MMP-9 and thus reduce collagen degradation while simultaneously optimizing resin-dentin bonding.
  • Koskela, Antti; Mena, Hermann (2020)
    We consider a Krylov subspace approximation method for the symmetric differential Riccati equation (X)over dot = AX XA(T) +Q - XSX, X(0) = X-0. The method we consider is based on projecting the large-scale equation onto a Krylov subspace spanned by the matrix A and the low-rank factors of X-0 and Q. We prove that the method is structure preserving in the sense that it preserves two important properties of the exact flow, namely the positivity of the exact flow and also the property of monotonicity. We provide a theoretical a priori error analysis that shows superlinear convergence of the method. Moreover, we derive an a posteriori error estimate that is shown to be effective in numerical examples.
  • Pfeifer, Marion; Lefebvre, Veronique; Gardner, Toby A.; Arroyo-Rodriguez, Victor; Baeten, Lander; Banks-Leite, Cristina; Barlow, Jos; Betts, Matthew G.; Brunet, Joerg; Cerezo, Alexis; Cisneros, Laura M.; Collard, Stuart; D'Cruze, Neil; da Silva Motta, Catarina; Duguay, Stephanie; Eggermont, Hilde; Eigenbrod, Felix; Hadley, Adam S.; Hanson, Thor R.; Hawes, Joseph E.; Scalley, Tamara Heartsill; Klingbeil, Brian T.; Kolb, Annette; Kormann, Urs; Kumar, Sunil; Lachat, Thibault; Lakeman Fraser, Poppy; Lantschner, Victoria; Laurance, William F.; Leal, Inara R.; Lens, Luc; Marsh, Charles J.; Medina-Rangel, Guido F.; Melles, Stephanie; Mezger, Dirk; Oldekop, Johan A.; Overal, William L.; Owen, Charlotte; Peres, Carlos A.; Phalan, Ben; Pidgeon, Anna M.; Pilia, Oriana; Possingham, Hugh P.; Possingham, Max L.; Raheem, Dinarzarde C.; Ribeiro, Danilo B.; Ribeiro Neto, Jose D.; Robinson, W. Douglas; Robinson, Richard; Rytwinski, Trina; Scherber, Christoph; Slade, Eleanor M.; Somarriba, Eduardo; Stouffer, Philip C.; Struebig, Matthew J.; Tylianakis, Jason M.; Tscharntke, Teja; Tyre, Andrew J.; Urbina Cardona, Jose N.; Vasconcelos, Heraldo L.; Wearn, Oliver; Wells, Konstans; Willig, Michael R.; Wood, Eric; Young, Richard P.; Bradley, Andrew V.; Ewers, Robert M. (2014)
  • Bitu, Carolina C.; Kauppila, Joonas H.; Bufalino, Andreia; Nurmenniemi, Sini; Teppo, Susanna; Keinanen, Meeri; Vilen, Suvi-Tuuli; Lehenkari, Petri; Nyberg, Pia; Coletta, Ricardo D.; Salo, Tuula (2013)
  • Delayre, C.; Sammaljärvi, J.; Billon, S.; Muuri, E.; Sardini, P.; Siitari-Kauppi, M. (2020)
    This study aims to further develop the C-14-PMMA porosity calculation method with a novel autoradiography technique, the Micro-pattern gas detector autoradiography (MPGDA). In this study, the MPGDA is compared with phosphor screen autoradiography (SPA). A set of rock samples from Martinique Island exhibiting a large range of connected porosities was used to validate the MPGDA method. Calculated porosities were found to be in agreement with ones from the SPA and the triple-weight method (TW). The filmless nature of MPGDA as well as straightforward determination of C-14 radioactivity from the source rock makes the porosity calculation less uncertain. The real-time visualization of radioactivity from C-14 beta emissions by MPGDA is a noticeable improvement in comparison to SPA.
  • Bonnet, M.; Sardini, P.; Billon, S.; Siitari-Kauppi, M.; Kuva, J.; Fonteneau, L.; Caner, L. (2020)
    Because cracks control the global mechanical and transport properties of crystalline rocks, it is of a crucial importance to suitably determine their aperture distribution, which evolves through alteration processes and rock weathering. Due to the high variability of crack networks in rocks, a multiscale approach is needed. The C-14-PMMA (polymethylmethacrylate) method was developed to determine crack apertures using a set of artificial crack samples with different controlled apertures and tilt angles and also using Monte Carlo simulations. The experiments and simulations show the same result: the estimation of apparent aperture w(A) was successful regardless of tilt angle, even if the estimates are less accurate for low tilt angles (
  • Mehtala, P.; Pashley, D. H.; Tjaderhane, L. (2017)
    Objectives. Infiltration of adhesive on dentin matrix depends on interaction of surface and adhesive. Interaction depends on dentin wettability, which can be enhanced either by increasing dentin surface energy or lowering the surface energy of adhesive. The objective was to examine the effect of dimethyl sulfoxide (DMSO) on demineralized dentin wettability and dentin organic matrix expansion. Methods. Acid-etched human dentin was used for sessile drop contact angle measurement to test surface wetting on 1-5% DMSO-treated demineralized dentin surface, and linear variable differential transformer (LVDT) to measure expansion/shrinkage of dentinal matrix. DMSO-water binary liquids were examined for surface tension changes through concentrations from 0 to 100% DMSO. Kruskal-Wallis and Mann-Whitney tests were used to test the differences in dentin wettability, expansion and shrinkage, and Spearman test to test the correlation between DMSO concentration and water surface tension. The level of significance was p <0.05. Results. Pretreatment with 1-5% DMSO caused statistically significant concentration dependent increase in wetting: the immediate contact angles decreased by 11.8% and 46.6% and 60 s contact angles by 9.5% and 47.4% with 1% and 5% DMSO, respectively. DMSOwater mixtures concentration-dependently expanded demineralized dentin samples less than pure water, except with high (>80%) DMSO concentrations which expanded demineralized dentin more than water. Drying times of LVDT samples increased significantly with the use of DMSO. Significance. Increased dentin wettability may explain the previously demonstrated increase in adhesive penetration with DMSO-treated dentin, and together with the expansion of collagen matrix after drying may also explain previously observed increase in dentin adhesive bonding. (C) 2017 The Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
  • Ding, Yaping; Li, Wei; Correia, Alexandra; Yang, Yuyun; Zheng, Kai; Liu, Dongfei; Schubert, Dirk W.; Boccaccini, Aldo R.; Santos, Helder A.; Roether, Judith A. (2018)
    Electrospun hybrid scaffolds are an effective platform to deliver drugs site specifically for the prevention and treatment of diseases in addition to promote tissue regeneration because of the flexibility to load drugs therein. In the present study, electrospun hybrid scaffolds containing antibiotics were developed to support cellular activities and eliminate potential postoperative inflammation and infection. As a model drug, levofloxacin (LFX) was successfully incorporated into pure polyhydroxybutyrate/poly(epsilon-caprolactone) (PHB/PCL) scaffolds and PHB/PCL/sol-gel-derived silica (SGS) scaffolds. The influence of LFX on the morphology, mechanical performance, chemical structure, drug release profile, and antibacterial effect of the scaffolds was thoroughly and comparatively investigated. MG-63 osteoblast-like cell cultivation on both scaffolds certified that LFX inclusion did not impair the biocompatibility. In addition to the favorable cellular proliferation and differentiation, scaffolds containing both LFX and SGS displayed highly increased mineralization content. Therefore, the present multifunctional hybrid scaffolds are promising in tissue engineering applications.
  • Kirsebom, O. S.; Tengblad, O.; Lica, R.; Munch, M.; Riisager, K.; Fynbo, H. O. U.; Borge, M. J. G.; Madurga, M.; Marroquin, I.; Andreyev, A. N.; Berry, T. A.; Christensen, E. R.; Fernandez, P. Diaz; Doherty, D. T.; Van Duppen, P.; Fraile, L. M.; Gallardo, M. C.; Greenlees, P. T.; Harkness-Brennan, L. J.; Hubbard, N.; Huyse, M.; Jensen, J. H.; Johansson, H.; Jonson, B.; Judson, D. S.; Konki, J.; Lazarus, I.; Lund, M. V.; Marginean, N.; Marginean, R.; Perea, A.; Mihai, C.; Negret, A.; Page, R. D.; Pucknell, V.; Rahkila, P.; Sorlin, O.; Sotty, C.; Swartz, J. A.; Sorensen, H. B.; Toernqvist, H.; Vedia, V.; Warr, N.; De Witte, H. (2018)
    The C-12(alpha,gamma)O-16 reaction plays a central role in astrophysics, but its cross section at energies relevant for astrophysical applications is only poorly constrained by laboratory data. The reduced a width, gamma(11), of the bound 1(-) level in O-16 is particularly important to determine the cross section. The magnitude of gamma(11) is determined via sub-Coulomb a-transfer reactions or the beta-delayed a decay of N-16, but the latter approach is presently hampered by the lack of sufficiently precise data on the beta-decay branching ratios. Here we report improved branching ratios for the bound 1(-) level [b(beta,11) = (5.02 +/- 0.10) x 10(-2)] and for beta-delayed alpha emission [b(beta alpha) = (1.59 +/- 0.06) x 10(-5)]. Our value for b(beta alpha) is 33% larger than previously held, leading to a substantial increase in gamma(11). Our revised value for gamma(11) is in good agreement with the value obtained in a-transfer studies and the weighted average of the two gives a robust and precise determination of gamma(11), which provides significantly improved constraints on the C-12(alpha,gamma) cross section in the energy range relevant to hydrostatic He burning.
  • Viciano-Chumillas, Marta; Koprowiak, Florian; Mutikainen, Ilpo; Wernsdorfer, Wolfgang; Mallah, Talal; Bolvin, Helene (2017)
    We report a bimetallic holmium(III) complex showing a S-shaped magnetic hysteresis at low temperature. The complex is investigated by x-ray crystallography, magnetometry, single crystal microsquid measurements, and first-principles calculations. A model Hamiltonian including electronic and nuclear magnetic moments is used to fit all experimental data. We conclude that the Ho(III) may be described as non-Kramers doublets with respective gaps of Delta(A) = 0.8 and Delta(B) = 10 cm(-1) and that there is a small ferromagnetic coupling of J = 1 cm(-1) ((H) over cap (S) = -JS(A) . S-B). As in previous works, the hysteresis arise from the hyperfine structure of the Ho(III) ions. The S-shaped form of the hysteresis reflects the avoided crossing of the electronic states in the non-Kramers doublets.
  • Lagus, Heli; Kankuri, Esko; Nuutila, Kristo; Juteau, Susanna; Sarlomo-Rikala, Maarit; Vuola, Jyrki (2018)
    Cellular grafts used for skin repair require rapid integration with the host tissue to remain viable and especially to nourish the epidermal cells. Here, we evaluated the responses in the split-thickness skin grafts (STSGs) grafted on three differently treated wound beds: directly on excised wound bed (EX), on an artificial dermal template (DT) and on granulation tissue (GT) induced by cellulose sponge. In ten burn patients, after excision, a test area was divided into three sections: One transplanted with STSG instantaneously and two sections had a pre-treatment for 2 weeks with either DT or a cellulose sponge inducing granulation tissue formation and thereafter grafted with STSGs. One week after grafting, the STSGs on GT demonstrated most endothelial CD31(+) staining, largest average vessel diameters as well as most CD163(+) staining of M2-like macrophages and most MIB1(+) proliferating epidermal cells, suggesting an active regenerative environment. STSGs on DT had smallest vessel diameters and the least CD163(+) macrophages. STSGs on EX had the least CD31(+) cells and the least MIB1(+) proliferating cells. After 3 months, this reactivity in STSGs had subsided, except increased dermal cell proliferation was observed in STSGs on EX. Results show that pre-treatment of wound bed and induction of granulation tissue formation can accelerate host-graft interaction by stimulating graft vasculature and inducing cell proliferation.
  • Chaput, J. -P.; Barnes, J. D.; Tremblay, M. S.; Fogelholm, M.; Hu, G.; Lambert, E. V.; Maher, C.; Maia, J.; Olds, T.; Onywera, V.; Sarmiento, O. L.; Standage, M.; Tudor-Locke, C.; Katzmarzyk, P. T. (2018)
    ObjectiveStudies examining associations between movement behaviours (i.e. physical activity, sedentary behaviour and sleep duration) and obesity focus on average values of these movement behaviours, despite important within-country and between-country variability. A better understanding of movement behaviour inequalities is important for developing public health policies and behaviour-change interventions. The objective of this ecologic analysis at the country level was to determine if inequality in movement behaviours is a better correlate of obesity than average movement behaviour volume in children from all inhabited continents of the world. MethodsThis multinational, cross-sectional study included 6,128 children 9-11years of age. Moderate-to-vigorous physical activity (MVPA), total sedentary time (SED) and sleep period time were monitored over 7 consecutive days using waist-worn accelerometry. Screen time was self-reported. Inequality in movement behaviours was determined using Gini coefficients (ranging from 0 [complete equality] to 1 [complete inequality]). ResultsThe largest inequality in movement behaviours was observed for screen time (Gini of 0.32; medium inequality), followed by MVPA (Gini of 0.21; low inequality), SED (Gini of 0.07; low inequality) and sleep period time (Gini of 0.05; low inequality). Average MVPA (hd(-1)) was a better correlate of obesity than MVPA inequality (r=-0.77 vs. r=0.00, p=0.03). Average SED (hd(-1)) was also a better correlate of obesity than SED inequality (r=0.52 vs. r=-0.32, p=0.05). Differences in associations for screen time and sleep period time were not statistically significant. MVPA in girls was found to be disproportionally lower in countries with more MVPA inequality. ConclusionsFindings from this study show that average MVPA and SED should continue to be used in population health studies of children as they are better correlates of obesity than inequality in these behaviours. Moreover, the findings suggest that MVPA inequality could be greatly reduced through increases in girls' MVPA alone.
  • Al-Ani, Anas Aaqel Salim Salim; Mutluay, Murat; Tjaderhane, Leo; Tezvergil-Mutluay, Arzu (2019)
    The purpose of this in vitro study was to evaluate and compare the effect of dimethyl sulfoxide (DMSO) or ethanol on the permeability, stiffness and collagen dissociation of demineralized dentin. Dentin cubes (2 x 2 x 2 mm) were demineralized in EDTA and incubated in DMSO or ethanol (0.01, 0.1, 1, 5, 10, 20, 50 and 100%) (n = 10/group) for 30s, followed by 100% HEMA incubation. Extracted HEMA was quantified. For elastic modulus (E), demineralized dentin beams (6 x 2 x 1 mm) were incubated in DMSO or ethanol (1, 10, 20, 50 and 100%) for 10, 30 or 60 min at 3-point bending. Additional demineralized dentin discs (1 mm) were incubated in DMSO (1, 10, 50 and 100%) for 10, 30 and 60 min and the optical clearing effect was observed. The data were analyzed using ANOVA and Tukey's test (alpha = 0.05) using SigmaPlot (Systat Software Inc., San Jose, CA). Compared to controls, HEMA uptake was significantly higher with all DMSO concentrations, and with 0.1% or higher ethanol concentrations (p <0.05). HEMA uptake in DMSO-incubated specimens (0.01, 5 and 10%) was significantly higher than with the ethanol incubation. Significant increase in elastic moduli was observed with 50-100% DMSO- and only with 100% ethanol after 10 min incubation. The optical clearing effect of 50-100% DMSO-incubated dentin disks was observed starting from 10 min. The pretreatment of dentin surfaces with low concentrations of DMSO resulted in significant improvement of the penetration of monomers to demineralized dentin matrices. Increase in penetration of monomers combined with a reversible stiffening of dentin collagenous matrix may explain the previously shown increase in durability of wet- or dry-bonded adhesive interfaces with DMSO treatment.
  • Zhang, Yanwen; Sachan, Ritesh; Pakarinen, Olli H.; Chisholm, Matthew F.; Liu, Peng; Xue, Haizhou; Weber, William J. (2015)
    A long-standing objective in materials research is to effectively heal fabrication defects or to remove pre-existing or environmentally induced damage in materials. Silicon carbide (SiC) is a fascinating wide-band gap semiconductor for high-temperature, high-power and high-frequency applications. Its high corrosion and radiation resistance makes it a key refractory/structural material with great potential for extremely harsh radiation environments. Here we show that the energy transferred to the electron system of SiC by energetic ions via inelastic ionization can effectively anneal pre-existing defects and restore the structural order. The threshold determined for this recovery process reveals that it can be activated by 750 and 850 keV Si and C self-ions, respectively. The results conveyed here can contribute to SiC-based device fabrication by providing a room-temperature approach to repair atomic lattice structures, and to SiC performance prediction as either a functional material for device applications or a structural material for high-radiation environments.
  • Videen, Gorden; Muinonen, Karri (2015)
  • Bultmann-Mellin, Insa; Conradi, Anne; Maul, Alexandra C.; Dinger, Katharina; Wempe, Frank; Wohl, Alexander P.; Imhof, Thomas; Wunderlich, F. Thomas; Bunck, Alexander C.; Nakamura, Tomoyuki; Koli, Katri; Bloch, Wilhelm; Ghanem, Alexander; Heinz, Andrea; Von Melchner, Harald; Sengle, Gerhard; Sterner-Kock, Anja (2015)
    Recent studies have revealed an important role for LTBP-4 in elastogenesis. Its mutational inactivation in humans causes autosomal recessive cutis laxa type 1C (ARCL1C), which is a severe disorder caused by defects of the elastic fiber network. Although the human gene involved in ARCL1C has been discovered based on similar elastic fiber abnormalities exhibited by mice lacking the short Ltbp-4 isoform (Ltbp4S(-/-)), the murine phenotype does not replicate ARCL1C. We therefore inactivated both Ltbp-4 isoforms in the mouse germline to model ARCL1C. Comparative analysis of Ltbp4S(-/-) and Ltbp4-null (Ltbp4(-/-)) mice identified Ltbp-4L as an important factor for elastogenesis and postnatal survival, and showed that it has distinct tissue expression patterns and specific molecular functions. We identified fibulin-4 as a previously unknown interaction partner of both Ltbp-4 isoforms and demonstrated that at least Ltbp-4L expression is essential for incorporation of fibulin-4 into the extracellular matrix (ECM). Overall, our results contribute to the current understanding of elastogenesis and provide an animal model of ARCL1C.
  • Costantini, Alice; Valta, Helena; Baratang, Nissan Vida; Yap, Patrick; Bertola, Débora R.; Yamamoto, Guilherme L.; Kim, Chong A.; Chen, Jiani; Wierenga, Klaas J.; Fanning, Elizabeth A.; Escobar, Luis; McWalter, Kirsty; McLaughlin, Heather; Willaert, Rebecca; Begtrup, Amber; Alm, Jessica J.; Reinhardt, Dieter P.; Mäkitie, Outi; Campeau, Philippe M. (2019)
    Heterozygous pathogenic variants in the FN1 gene, encoding fibronectin (FN), have recently been shown to be associated with a skeletal disorder in some individuals affected by spondylometaphyseal dysplasia with “corner fractures” (SMD-CF). The most striking feature characterizing SMD-CF is irregularly shaped metaphyses giving the appearance of “corner fractures”. An array of secondary features, including developmental coxa vara, ovoid vertebral bodies and severe scoliosis, may also be present. FN is an important extra cellular matrix component for bone and cartilage development. Here we report five patients affected by this subtype of SMD-CF caused by five novel FN1 missense mutations: p.Cys123Tyr, p.Cys169Tyr, p.Cys213Tyr, p.Cys231Trp and p.Cys258Tyr. All individuals shared a substitution of a cysteine residue, disrupting disulfide bonds in the FN type-I assembly domains located in the N-terminal assembly region. The abnormal metaphyseal ossification and “corner fracture” appearances were the most remarkable clinical feature in these patients. In addition, generalized skeletal fragility with low-trauma bilateral femoral fractures was identified in one patient. Interestingly, the distal femoral changes in this patient healed with skeletal maturation. Our report expands the phenotypic and genetic spectrum of the FN1-related SMD-CF and emphasizes the importance of FN in bone formation and possibly also in the maintenance of bone strength.
  • Savolainen, M.; Ritvanen, A.; Hukki, J.; Vuola, P.; Telkka, J.; Leikola, J. (2017)
    Correction of calvarial defects after calvarial vault reconstruction (CVR) is challenging in craniosynostosis patients of advanced age and typically employs autologous bone. Demineralized bone matrix (DBM) is a potential alternative material for autologous bone, but its use has not been extended to correct calvarial defects. CVR patients operated at the Department of Plastic Surgery, Helsinki University Hospital, during 2008-2010 were retrospectively reviewed. Inclusion criteria of the study were CVR patients who received DBM plate, with or without bone dust, on calvarial defects and who had suitable uncovered defect on the contralateral side as control. This study included 17 craniosynostosis and one positional plagiocephaly patient, whose mean age was 6.9 years (range 0.9-19 years). The mean follow-up time was 5.6 years. The fusion degree of all defects was measured from 1 week to 1 year postoperatively using three-dimensional computed tomography (3D CT) images by the OsiriX (R) method. Medical records were reviewed for DBM-related complications. A total of 26 defects were covered with a DBM plate (mean area 11.1 cm(2)) and 26 control defects were identified (mean area 7.8 cm2). The mean fusion degree of the DBM defects was 74% and 54% for the controls (p <0.001). The mean fusion degree of nine DBM defects that lacked bone dust deposition was 66% and 55% for the nine controls (p <0.059). The difference between the DBM and control defects was statistically significant for patients older than 30 months (p <0.03). No DBM-related complication was observed. DBM plate is a safe and useful material to promote ossification in calvarial defects in CVR. Furthermore, DBM appears to be more effective in older patients (> 30 months) than in younger patients or when used with bone dust. (C) 2016 British Association of Plastic, Reconstructive and Aesthetic Surgeons. Published by Elsevier Ltd. All rights reserved.
  • Tanskanen, Antti J.; Lukkarinen, Jani; Vatanen, Kari (2018)
    In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen stochastically based on the random projection method. Randomness of factors has the consequence that correlation and covariance matrices are well preserved in a linear factor representation. It also enables derivation of probabilistic bounds for the accuracy of the random factor representation of time-series, their cross-correlations and covariances. As an application, we analyze reproduction of time-series and their cross-correlation coefficients in the well-diversified Russell 3,000 equity index.