Matrix Scaling and Balancing via Box Constrained Newton's Method and Interior Point Methods

In this paper, we study matrix scaling and balancing, which are fundamental problems in scientific computing, with a long line of work on them that dates back to the 1960s. We provide algorithms for both these problems that, ignoring logarithmic factors involving the dimension of the input matrix and the size of its entries, both run in time $\widetilde{O}\left(m\log \kappa \log^2 (1/\epsilon)\right)$ where $\epsilon$ is the amount of error we are willing to tolerate. Here, $\kappa$ represents the ratio between the largest and the smallest entries of the optimal scalings. This implies that our algorithms run in nearly-linear time whenever $\kappa$ is quasi-polynomial, which includes, in particular, the case of strictly positive matrices. We complement our results by providing a separate algorithm that uses an interior-point method and runs in time $\widetilde{O}(m^{3/2} \log (1/\epsilon))$. In order to establish these results, we develop a new second-order optimization framework that enables us to treat both problems in a unified and principled manner. This framework identifies a certain generalization of linear system solving that we can use to efficiently minimize a broad class of functions, which we call second-order robust. We then show that in the context of the specific functions capturing matrix scaling and balancing, we can leverage and generalize the work on Laplacian system solving to make the algorithms obtained via this framework very efficient.Comment: To appear in FOCS 201

k-server via multiscale entropic regularization

We present an $O((\log k)^2)$-competitive randomized algorithm for the $k$-server problem on hierarchically separated trees (HSTs). This is the first $o(k)$-competitive randomized algorithm for which the competitive ratio is independent of the size of the underlying HST. Our algorithm is designed in the framework of online mirror descent where the mirror map is a multiscale entropy. When combined with Bartal's static HST embedding reduction, this leads to an $O((\log k)^2 \log n)$-competitive algorithm on any $n$-point metric space. We give a new dynamic HST embedding that yields an $O((\log k)^3 \log \Delta)$-competitive algorithm on any metric space where the ratio of the largest to smallest non-zero distance is at most $\Delta$

Porphyrin Layers at Cu/Au(111)–Electrolyte Interfaces: In Situ EC-STM Study

The coadsorption of porphyrin molecules (TMPyP: tetra(N-methyl-4-pyridyl)-porphyrin), sulfate anions and copper on a Au(111) electrode was investigated by the use of cyclic voltammetry (CV) and in situ electrochemical scanning tunneling microscopy. With decreasing electrode potential the following sequence of surface phases was found: (I) an ordered $$\left( {\sqrt 3 \times \sqrt 7 } \right)R19.1^\circ - {\text{S}}{{\text{O}}_4}^{{2 - }}$$ structure on the unreconstructed Au(111)-(1 × 1) surface; (II) a disordered SO42−-layer on the still unreconstructed Au(111)-(1 × 1); (III) a $$\left( {\sqrt 3 \times \sqrt 3 } \right)R30^\circ$$ coadsorption structure of 2/3 ML Cu and 1/3 ML SO42−; (IV) a completed 1 ML Cu covered by a layer of mobile, i.e. not imaged, SO42− anions, moreover, a coadsorption layer of disordered porphyrin molecules and still mobile SO42− anions; (V) overpotentially deposited Cu-multilayers terminated by the well known Moire-type modulated $$\left( {\sqrt 3 \times \sqrt 7 } \right)R19.1^\circ - {\text{S}}{{\text{O}}_4}^{{2 - }}$$ structure (similar to bulk Cu(111)) and covered by a dense layer of flat lying TMPyP molecules showing a growing square as well as hexagonally ordered arrangement, and at even more negative potential values and low Cu concentrations in the solution (VI) a pseudomorphic underpotentially deposited Cu-monolayer covered by a $$\left( {\sqrt 3 \times \sqrt 7 } \right)R19.1^\circ - {\text{S}}{{\text{O}}_4}^{{2 - }}$$ layer and a dense, ordered porphyrin layer ontop. The formation of the various phases is driven by the potential dependent surface charge density and the resultant electrostatic interaction with the respective ions. A severe imbalance between the copper deposition and desorption current in the CV spectra suggests also the formation of CuTMPyP-metalloporphyrin on the surface which diffuses into the bulk solution

Family dairy farms in the Podlasie province, Poland: farm typology according to farming system

The aim of this paper is to establish a farm typology according to the dairy farming systems in the western part of the Podlasie province. Data of 39 variables was collected by a survey to owners of 123 family farms. A two-stage multivariate analysis was conducted in order to determine farm typology. Three principal components were detected, explaining 80.4% of the total variance. The cluster analysis identified five groups of farms. In two groups the cow productivity is the biggest in the area. A third group contains the smallest and lowest cow productivity farms, with high proportion of non-agricultural activities. One of the two remaining groups has better soil quality and medium cow productivity. The other group has low or medium soil quality but cow productivity is higher than in the fourth group. The SWOT analysis shows different weaknesses and strengths for different groups, as well as those common to a larger number of groups. Weaknesses are related to small farm size, large number of workers, low or medium soil quality and low or medium level of technology. Strengths are related to a large share of fodder crops, low livestock density, diversification of agrarian activities and acceptable cow productivity. On the other hand, general opportunities are linked to the EU-CAP evolution and to the presence of cooperatives in the region, whereas general threats derive from a hypothetic increase of feed prices and quantity of milk produced in the EU, which could lead to a fall in milk prices.El objetivo de este trabajo es establecer tipologías de sistemas lecheros en el oeste de Podlasia (Polonia). Se analizaron 39 variables a partir de encuestas realizadas a propietarios de 123 explotaciones. Tras el análisis multivariante en dos etapas (factorial y cluster) se encontraron tres componentes principales que explican el 80,4% de la varianza total y se obtuvieron cinco grupos de explotaciones. En dos de los grupos la productividad de las vacas es la mayor de la zona. Un tercer grupo tiene las granjas más pequeñas y menos productivas, con una mayor proporción de actividades no agrarias. El cuarto tiene los suelos de mejor calidad y una productividad de las vacas media y el quinto tiene suelos de calidad media o baja pero una productividad de las vacas superior. En general, las debilidades están relacionadas con una escasa dimensión de las granjas, un elevado número de trabajadores, una baja o media calidad de los suelos y un bajo o mediano nivel de tecnología. Las fortalezas están relacionadas con la abundancia de cultivos forrajeros, una carga ganadera baja, una aceptable diversificación agraria y una aceptable productividad de las vacas. Las principales oportunidades están ligadas a la evolución de la PAC de la UE y a la presencia de cooperativas para la comercialización de la leche. Las principales amenazas derivan de los posibles incrementos de precios de los alimentos para el ganado y de leche producida en la UE, que puede conducir a una caída de los precios de venta de la leche

Local stimulation of articular cartilage repair by transplantation of encapsulated chondrocytes overexpressing human fibroblast growth factor 2 (FGF-2) in vivo

Background Defects of articular cartilage are an unsolved problem in orthopaedics. In the present study, we tested the hypothesis that gene transfer of human fibroblast growth factor 2 (FGF-2) via transplantation of encapsulated genetically modified articular chondrocytes stimulates chondrogenesis in cartilage defects in vivo. Methods Lapine articular chondrocytes overexpressing a lacZ or a human FGF-2 gene sequence were encapsulated in alginate and further characterized. The resulting lacZ or FGF-2 spheres were applied to cartilage defects in the knee joints of rabbits. In vivo, cartilage repair was assessed qualitatively and quantitatively at 3 and 14 weeks after implantation. Results In vitro, bioactive FGF-2 was secreted, leading to a significant increase in the cell numbers in FGF-2 spheres. In vivo, FGF-2 continued to be expressed for at least 3 weeks without leading to differences in FGF-2 concentrations in the synovial fluid between treatment groups. Histological analysis revealed no adverse pathologic effects on the synovial membrane at any time point. FGF-2 gene transfer enhanced type II collagen expression and individual parameters of chondrogenesis, such as the cell morphology and architecture of the new tissue. Overall articular cartilage repair was significantly improved at both time points in vivo. Conclusions The data suggest that localized overexpression of FGF-2 enhances the repair of cartilage defects via stimulation of chondrogenesis, without adverse effects on the synovial membrane. These results may lead to the development of safe gene-based therapies for human articular cartilage defects

Gene Transfer of a Human Insulin-Like Growth Factor I cDNA Enhances Tissue Engineering of Cartilage

The repair of articular cartilage lesions remains a clinical problem. Two novel approaches to cartilage formation, gene transfer and tissue engineering, have been limited by short-term transgene expression in transplanted chondrocytes and inability to deliver regulatory signals to engineered tissues according to specific temporal and spatial patterns. We tested the hypothesis that the transfer of a cDNA encoding the human insulin-like growth factor I (IGF-I) can provide sustained gene expression in cell-polymer constructs in vitro and in vivo and enhance the structural and functional properties of tissue-engineered cartilage. Bovine articular chondrocytes genetically modified to overexpress human IGF-I were seeded into polymer scaffolds, cultured in bioreactors in serum-free medium, and implanted subcutaneously in nude mice; constructs based on nontransfected or lacZ-transfected chondrocytes served as controls. Transgene expression was maintained throughout the duration of the study, more than 4 weeks in vitro followed by an additional 10 days either in vitro or in vivo. Chondrogenesis progressed toward the formation of cartilaginous tissue that was characterized by the presence of glycosaminoglycans, aggrecan, and type II collagen, and the absence of type I collagen. IGF-I constructs contained increased amounts of glycosaminoglycans and collagen and confined-compression equilibrium moduli as compared with controls; all groups had subnormal cellularity. The amounts of glycosaminoglycans and collagen per unit DNA in IGF-I constructs were markedly higher than in constructs cultured in serum-supplemented medium or native cartilage. This enhancement of chondrogenesis by spatially defined overexpression of human IGF-I suggests that cartilage tissue engineering based on genetically modified chondrocytes may be advantageous as compared with either gene transfer or tissue engineering alone

Local stimulation of articular cartilage repair by transplantation of encapsulated chondrocytes overexpressing human fibroblast growth factor 2 (FGF-2) in vivo

Background Defects of articular cartilage are an unsolved problem in orthopaedics. In the present study, we tested the hypothesis that gene transfer of human fibroblast growth factor 2 (FGF-2) via transplantation of encapsulated genetically modified articular chondrocytes stimulates chondrogenesis in cartilage defects in vivo. Methods Lapine articular chondrocytes overexpressing a lacZ or a human FGF-2 gene sequence were encapsulated in alginate and further characterized. The resulting lacZ or FGF-2 spheres were applied to cartilage defects in the knee joints of rabbits. In vivo, cartilage repair was assessed qualitatively and quantitatively at 3 and 14 weeks after implantation. Results In vitro, bioactive FGF-2 was secreted, leading to a significant increase in the cell numbers in FGF-2 spheres. In vivo, FGF-2 continued to be expressed for at least 3 weeks without leading to differences in FGF-2 concentrations in the synovial fluid between treatment groups. Histological analysis revealed no adverse pathologic effects on the synovial membrane at any time point. FGF-2 gene transfer enhanced type II collagen expression and individual parameters of chondrogenesis, such as the cell morphology and architecture of the new tissue. Overall articular cartilage repair was significantly improved at both time points in vivo. Conclusions The data suggest that localized overexpression of FGF-2 enhances the repair of cartilage defects via stimulation of chondrogenesis, without adverse effects on the synovial membrane. These results may lead to the development of safe gene-based therapies for human articular cartilage defects

Improved Tissue Repair in Articular Cartilage Defects in Vivo by rAAV-Mediated Overexpression of Human Fibroblast Growth Factor 2

Therapeutic gene transfer into articular cartilage is a potential means to stimulate reparative activities in tissue lesions. We previously demonstrated that direct application of recombinant adeno-associated virus (rAAV) vectors to articular chondrocytes in their native matrix in situ as well as sites of tissue damage allowed for efficient and sustained reporter gene expression. Here we test the hypothesis that rAAV-mediated overexpression of fibroblast growth factor 2 (FGF-2), one candidate for enhancing the repair of cartilage lesions, would lead to the production of a biologically active factor that would facilitate the healing of articular cartilage defects. In vitro, FGF-2 production from an rAAV-delivered transgene was sufficient to stimulate chondrocyte proliferation over a prolonged period of time. In vivo, application of the therapeutic vector significantly improved the overall repair, filling, architecture, and cell morphology of osteochondral defects in rabbit knee joints. Differences in matrix synthesis were also observed, although not to the point of statistical significance. This process may further benefit from cosupplementation with other factors. These results provide a basis for rAAV application to sites of articular cartilage damage to deliver agents that promote tissue repair