Going Off the Grid: Iterative Model Selection for Biclustered Matrix Completion

We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column graphs. We present a novel iterative procedure for directly minimizing an information criterion to select an appropriate amount of row and column smoothing, namely, to perform model selection. We also discuss how to exploit the special structure of the problem to scale up the estimation and model selection procedure via the Hutchinson estimator, combined with a stochastic Quasi-Newton approach. Supplementary material for this article is available online.     

On the distribution of the sum of digits of sums $$a+b$$ a + b

The Ramanujan Journal - Let $${\mathcal {A}}$$ , $${\mathcal {B}}$$ be large subsets of $$\{1,\ldots ,N\}$$ . We study the distribution of the sum of binary digits of the sums $$a+b$$ with...     

Self-similar asymptotic behavior for the solutions of a linear coagulation equation

In this paper we consider the long-time asymptotics of a linear version of the Smoluchowski equation which describes the evolution of a tagged particle moving in a random distribution of fixed particles. The volumes v of these particles are independently distributed according to a probability distribution which decays asymptotically as a power law $v^{?\sigma }$. The validity of the equation has been rigorously proved in [22] taking as a starting point a particle model and for values of the exponent $\sigma >3$, but the model can be expected to be valid, on heuristic grounds, for $\sigma >\frac{5}{3}$. The resulting equation is a non-local linear degenerate parabolic equation. The solutions of this equation display a rich structure of different asymptotic behaviors according to the different values of the exponent σ. Here we show that for $\frac{5}{3}<\sigma <2$ the linear Smoluchowski equation is well-posed and that there exists a unique self-similar profile which is asymptotically stable.     

S‐Adenosyl Methionine Cofactor Modifications Enhance the Biocatalytic Repertoire of Small Molecule C‐Alkylation

A tandem enzymatic strategy to enhance the scope of C‐alkylation of small molecules via the in situ formation of S‐adenosyl methionine (SAM) cofactor analogues is described. A solvent‐exposed channel present in the SAM‐forming enzyme SalL tolerates 5′‐chloro‐5′‐deoxyadenosine (ClDA) analogues modified at the 2‐position of the adenine nucleobase. Coupling SalL‐catalyzed cofactor production with C‐(m)ethyl transfer to coumarin substrates catalyzed by the methyltransferase (MTase) NovO forms C‐(m)ethylated coumarins in superior yield and greater substrate scope relative to that obtained using cofactors lacking nucleobase modifications. Establishing the molecular determinants that influence C‐alkylation provides the basis to develop a late‐stage enzymatic platform for the preparation of high value small molecules.     

Evaluation of Co and Zn competitive sorption by zeolitic material synthesized from fly ash using 60Co and 65Zn as radioindicators

Journal of Radioanalytical and Nuclear Chemistry - Zeolitic material prepared by hydrothermal treatment of brown coal fly ash was used for sorption separation of Co2+ and Zn2+ ions from single and...     

New multifunctional heterobinuclear palladium (II) complexes based on organometallic dithiocarbazate ligands

In the research of new compounds with multifunctional applications, heterobinuclear palladium (II) complexes based on organometallic dithiocarbazates (DTCZs) have been isolated. The organometallic DTCZ ligands of the general formula [{(η⁵-C₅H₄)-CH=NNHC(S)SCH₃}]MLn [MLn = Re (CO)₃ ( 2a ); Mn (CO)₃ ( 2b ); FeCp ( 2c )] were prepared by the reaction between formyl organometallic precursors ( 1a−c ) with S-methyldithiocarbazate. Subsequently, a two-step reaction of 2a−c with: (i) K₂[PdCl₄] and (ii) PPh₃ yielded heterobinuclear complexes [Pd{MLn(η⁵-C₅H₄)-CH=NNHC(S)SCH₃}–(Cl)(PPh₃)] [MLn = Re (CO)₃ ( 3a ); Mn (CO)₃ ( 3b ); FeCp ( 3c )]. All compounds were characterized by conventional spectroscopic techniques (infrared spectroscopy, nuclear magnetic resonance spectroscopy, mass spectrometry and elemental analysis). In addition, the molecular structures of 2a , 2c and 3c were determined by single-crystal X-ray diffraction. The new palladium (II) complexes ( 3a−c ) were evaluated as antiproliferative agents against non-small cell lung cancer cells (H1299 cells). Complexes 3a and 3b containing cyrhetrenyl- and cymantrenyl-DTCZ ligands, respectively, were more active than their ferrocenyl analogue 3c . The activity was associated with the electron-withdrawing properties of the (η⁵-C₅H₄)M (CO)₃ moieties and their better lipophilicity than that of the ferrocenyl analogue. In addition, we studied the capacity of metalloligands ( 2a−c ) and palladium (II) complexes ( 3a−c ) to remove methylene blue in water under UV–visible light irradiation. The results established that the complexes showed moderate efficiency and were less active than their corresponding free ligands.     

Partial control of delay-coordinate maps

Nonlinear Dynamics - Delay-coordinate maps have been widely used recently to study nonlinear dynamical systems, where there is only access to the time series of one of their variables. Here, we...     

Nano-liquid chromatography combined with a sustainable microextraction based on natural deep eutectic solvents for analysis of phthalate esters

The separation of 11 phthalic acid ester (PAEs) was carried out by nano-liquid chromatography coupled to ultraviolet and MS detection. Preliminary experiments were achieved in order to select suitable stationary phases and chromatographic conditions. The baseline separation was obtained, for all compounds, with an XBridge^TM C₁₈ column in less than 15 min, working in step gradient mode. The sensitivity of the method was improved by on-column focusing. PAEs were extracted from alcoholic and nonalcoholic beverages using vortex-assisted emulsification dispersive liquid–liquid microextration and natural deep eutectic solvents. The whole method was validated in terms of linearity, sensitivity, precision, recovery, and repeatability. Combination of both off-line sample preparation preconcentration and large injection volume led to obtain LOQs in the range 5–47 ng/mL. The developed nano-LC-UV method was extended to MS detection to confirm the presence of PAEs in some beverages commercialized in different types of packaging.     

A type III porous-thermo-elastic problem with quasi-static microvoids

Meccanica - In this work we study, from the numerical point of view, a one-dimensional thermoelastic problem where the thermal law is of type III. Quasi-static microvoids are also assumed within...     

A sharp integral inequality for closed spacelike submanifolds immersed in the de Sitter space

Archiv der Mathematik - In this paper, we establish a sharp integral inequality for n-dimensional closed spacelike submanifolds with constant scalar curvature immersed with parallel normalized mean...