The Landscape of the Spiked Tensor Model

We consider the problem of estimating a large rank-one tensor u ^⊗k ∈ (ℝⁿ)^⊗k , k ≥ 3 , in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio λ  _Bayes = O(1) above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably, no polynomial-time algorithm is known that achieved this goal unless λ ≥ Cn^{(k − 2)/4} , and even powerful semidefinite programming relaxations appear to fail for 1 ≪ λ ≪ n^{(k − 2)/4} . In order to elucidate this behavior, we consider the maximum likelihood estimator, which requires maximizing a degree-k homogeneous polynomial over the unit sphere in n dimensions. We compute the expected number of critical points and local maxima of this objective function and show that it is exponential in the dimensions n , and give exact formulas for the exponential growth rate. We show that (for λ larger than a constant) critical points are either very close to the unknown vector u or are confined in a band of width Θ(λ^{−1/(k − 1)}) around the maximum circle that is orthogonal to u . For local maxima, this band shrinks to be of size Θ(λ^{−1/(k − 2)}) . These “uninformative” local maxima are likely to cause the failure of optimization algorithms. © 2019 Wiley Periodicals, Inc.     

A new rigidity result for holomorphic maps

In this paper we determine which vanishing order of a holomorphic map f at a point of the (non necessarily regular) boundary of a very generic domain of is required for f to be constant. In particular this vanishing order is 1 if the boundary is Dini-smooth whereas it is at least β/α if f locally maps a Dini-smooth corner of opening πα into a Dini-smooth corner of opening πβ. Finally an analogous result is stated for the case of a holomorphic map f which maps a cusp into a cusp.     

Incorporating the effect of ionic strength in free energy calculations using explicit ions

The incorporation of explicit ions to mimic the effect of ionic strength or to neutralize the overall charge on a system in free energy calculations using molecular dynamics simulations is investigated. The difference in the free energy of hydration between two triosephosphate isomerase inhibitors calculated at five different ion concentrations is used as an example. We show that the free energy difference can be highly sensitive to the presence of explicit ions even in cases where the mutation itself does not involve a change in the overall charge. The effect is most significant if the molecule carries a net charge close to the site mutated. Furthermore, it is shown that the introduction of a small number of ions can lead to very severe sampling problems suggesting that in practical calculations convergence can best be achieved by incorporating either no counterions or by simulating at high ionic strength to ensure sufficient sampling of the ion distribution.     

Magnetic nanoparticle assemblies on denatured DNA show unusual magnetic relaxivity and potential applications for MRI

Denatured (substantially single-stranded) herring sperm DNA acts as a template for the preparation of magnetic nanowires, forming stable aqueous suspensions, which exhibit unprecedentedly high relaxivity at low field, suggesting that the material may be a potentially useful reagent for MRI.     

Regioselective epoxide ring opening. Steroselective synthesis of a tetrahydropyran ring

The stereoselective synthesis of a 2-substituted tetrahydropyran with adjacent alkoxy-bearing stereogenic centre is described. The key steps of this synthesis were the stereoselective epoxidation of an allylic alcohol and the regioselective epoxide ring opening by lithium aluminum hydride. The regio and stereoselective synthesis of a trihydroxyselenide and a trihydroxysulfide is also described. The latter compounds are not suitable for cyclization to tetrahydrofuran ring.     

Calculation of affinities of peptides for proteins

Several methodologies were employed to calculate the Gibbs standard free energy of binding for a collection of protein-ligand complexes, where the ligand is a peptide and the protein is representative for various protein families. Almost 40 protein-ligand complexes were employed for a continuum approach, which considers the protein and the peptide at the atomic level, but includes solvent as a polarizable continuum. Five protein-ligand complexes were employed for an all-atom approach that relies on a combination of the double decoupling method with thermodynamic integration and molecular dynamics. These affinities were also computed by means of the linear interaction energy method. Although it generally proved rather difficult to predict the absolute free energies correctly, for some protein families the experimental ranking order was correctly reproduced by the continuum and all-atom approach. Considerable attention has also been given to correctly analyze the affinities of charged peptides, where it is required to judge the effect of one or more ions that are being decoupled in an all-atom approach to preserve electroneutrality. The various methods are further judged upon their merits.     

Diastereoselective synthesis of 2-phenylselenenyl-1,3-anti-diols and 2-phenylselenenyl-1,3-anti-azido-alcohols via hydroxy and azido-selenenylation reactions

A method to synthesize 2-phenylselenenyl-1,3-anti-diols and 2-phenyl- selenenyl-1,3-anti-azidoalcohols via hydroxy- or azido-selenenylation of trans-allylic alcohols is reported. Moreover, the first example of hydroxyl-selenenylation of an allylic azide is presented. Yields ranging from moderate to good and diastereomeric ratios up to 95:5 are achieved.     

Preparation and Chemical and Biological Studies of the Novel Complex μ-1,4,5-triphenyl-1,3,4-triazole-2-thiolate-bis[dichlorotriethylphosphineplatinum(II)]a

The mesoionic compound, 1,4,5-triazole-2-thiolate, is a versatile ligand, capable of binding metal centres in different ways. The present study shows how it reacts with the bridging platinum(II) complex μ-dichlorobis[(chlorotriethylphosphineplatinum(II)], [Pt₂(PEt₃)₂Cl₄], originating a bimetallic complex. Both the sulphur atom and nitrogen 3 behave as basic sites, coordinating different platinum centres. An interesting isomerization process, shown by ³¹P{¹H} n.m.r. spectroscopy, occurs at the S-bonded platinum moiety, resulting in a fluxional behaviour of the complex. It is also shown to target CT-DNA with moderate binding affinity.To the memory of Dr. Wagner M. Teles (1971–2004).     

Direct determination of t,t-muconic acid in human urine by two-dimensional liquid chromatography

The accurate determination of E,E-2,4-hexadiendioic acid (t,t-muconic acid), an important urinary biomarker of benzene exposure, is directly performed in human urine by a new two-dimensional liquid chromatographic method. After a first partial separation of urine components by a reversed-phase mechanism and the focalisation of the anionic analytes on a small anion-chromatographic column, a conventional ion-chromatographic analysis with UV detection is carried out. The analytical procedure is fully controlled by the HPLC instrumentation software using an eight-port switch valve. If compared with conventional one-dimensional procedures, the new method produces chromatograms containing a limited number of well resolved peaks and consequently allows better analytical performances: no interfering peaks, absence of bias, repeatability better than 5% in the concentration range 0.09-5 mg dm-3 and a detection limit of 4.0 micrograms dm-3 (alpha = beta = 0.05) for the analysis of real samples.