Glucose,not cellobiose,is the repeating unit of cellulose and why that is important

Despite nomenclature conventions of the International Union of Pure and Applied Chemistry and the International Union of Biochemistry and Molecular Biology, the repeating unit of cellulose is often said to be cellobiose instead of glucose. This review covers arguments regarding the repeating unit in cellulose molecules and crystals based on biosynthesis, shape, crystallographic symmetry, and linkage position. It is concluded that there is no good reason to disagree with the official nomenclature. Statements that cellobiose is the repeating unit add confusion and limit thinking on the range of possible shapes of cellulose. Other frequent flaws in drawings with cellobiose as the repeating unit include incorporation of O-1 as the linkage oxygen atom instead of O-4 (the O-1 hydroxyl is the leaving group in glycoside synthesis). Also, n often erroneously represents the number of cellobiose units when n should denote the degree of polymerization i.e., the number of glucose residues in the polysaccharide.     

Predicting the cell-wall compositions of <Emphasis Type="Italic">Pinus radiata</Emphasis> (radiata pine) wood using ATR and transmission FTIR spectroscopies

Because plant cell walls vary in their polysaccharide compositions and lignin contents, their monosaccharide compositions and lignin contents are often determined, but these analyses are time consuming and laborious. We therefore investigated Fourier transform infrared (FTIR) spectroscopy coupled with partial least squares (PLS) regression analysis as a way of rapidly predicting the monosaccharide compositions and lignin contents of the cell walls of compression wood (CW) and opposite wood (OW) of the gymnosperm Pinus radiata. The effects were investigated of sample moisture content (ambient or dry) and sample particle size (large particles, < 0.422 mm or small particles, < 0.178 mm) of milled wood on attenuated total reflectance (ATR) and transmission FTIR spectra, as well as the PLS-1 models and subsequent predictions. PLS-1 models were built using mixtures of CW and OW as the training set, to provide a linear range of monosaccharide compositions and lignin contents. Models were externally validated by predicting another set of wood mixtures before predicting CW and OW of a separate test set. Most of the monosaccharide amounts in the separate test set were best predicted by ATR spectroscopy of ambient large particles, achieving the lowest standard error values for the monosaccharides arabinose (0.36%), xylose (1.05%), galactose (1.79%), glucose (6.32%), and 4-O-methylglucuronic acid (0.20%). The results show the feasibility of using ATR spectroscopy of ambient large particles for the rapid prediction of monosaccharide compositions and lignin contents of plant cell walls.     

Preparation of phthalocyanine-bound myristoyl celluloses for photocurrent generation system

The influences of two structural modifications on the photocurrent generation performance of the Langmuir–Blodgett (LB) film of the 6-O-phthalocyaninyl cellulose derivative were investigated. These structural modifications were the substituent groups at the O-2 and O-3 positions, and the central metal of the phthalocyanine moiety. Specifically, 6-O-Zn/phthalocyaninyl- (8a) and Pd/phthalocyaninyl (8b) -2,3-di-O-myristoylcelluloses were prepared instead of 6-O-Zn/phthalocyaninyl-2,3-di-O-myristylcellulose (2). The LB monolayer film of compound 8a on an indium thin oxide electrode showed higher photocurrent generation performance than that of compound 2. This suggested that myristoyl groups (C-14 acyl groups) were more beneficial to photocurrent generation than myristyl groups (C-14 alkyl groups), as the substituent at the O-2 and O-3 positions. The LB monolayer film of compound 8b showed photocurrent generation from 500 to 700 nm, although a blue-shift in the Q-band maximum was observed. The photocurrent generation performance of compound 8b was significantly higher than that of compound 8a. This indicated that Pd was more beneficial to photocurrent generation than Zn. The film of compound 8b prepared by the horizontal lifting method showed better photocurrent generation performance than that prepared by the vertical dipping method. Consequently, compound 8b is a complementary material to the porphyrin-appended cellulose derivative (1) for photocurrent generation system.     

On the syzygies and Hodge theory of nodal hypersurfaces

We give lower bounds for the degree of the syzygies involving the partial derivatives of a homogeneous polynomial defining an even dimensional nodal hypersurface. This implies the validity of formulas due to M. Saito, L. Wotzlaw and the author for the graded pieces with respect to the Hodge filtration of the top cohomology of the hypersurface complement in many new cases. A classical result by Severi on the position of the singularities of a nodal surface in \(\mathbb {P}^3\) is improved and applications to deformation theory of nodal surfaces are given.     

On the power of rewinding simulators in functional encryption

In a seminal work, Boneh, Sahai and Waters (BSW) [TCC’11] showed that for functional encryption the indistinguishability notion of security (IND-Security) is weaker than simulation-based security (SIM-Security), and that SIM-Security is in general impossible to achieve. This has opened up the door to a plethora of papers showing feasibility and new impossibility results. Nevertheless, the quest for better definitions that (1) overcome the limitations of IND-Security and (2) the known impossibility results, is still open. In this work, we explore the benefits and the limits of using efficient rewinding black-box simulators to argue security. To do so, we introduce a new simulation-based security definition, that we call rewinding simulation-based security (RSIM-Security), that is weaker than the previous ones but it is still sufficiently strong to not meet pathological schemes as it is the case for IND-Security (that is implied by the RSIM). This is achieved by retaining a strong simulation-based flavour but adding more rewinding power to the simulator having care to guarantee that it can not learn more than what the adversary would learn in any run of the experiment. What we found is that for RSIM  the BSW impossibility result does not hold and that IND-Security is equivalent to RSIM-Security for attribute-based encryption in the standard model. Nevertheless, we prove that there is a setting where rewinding simulators are of no help. The adversary can put in place a strategy that forces the simulator to rewind continuously.     

Distributional Transformations Without Orthogonality Relations

Distributional transformations characterized by equations relating expectations of test functions weighted by a given biasing function on the original distribution to expectations of the test function’s higher derivatives with respect to the transformed distribution play a great role in Stein’s method and were, in great generality, first considered by Goldstein and Reinert (J Theoret Probab 18(1):237–260, 2005. doi: 10.1007/s10959-004-2602-6). We prove two abstract existence and uniqueness results for such distributional transformations, generalizing their \(X-P\)-bias transformation. On the one hand, we show how one can abandon previously necessary orthogonality relations by subtracting an explicitly known polynomial depending on the test function from the test function itself. On the other hand, we prove that for a given nonnegative integer m, it is possible to obtain the expectation of the m-th derivative of the test function with respect to the transformed distribution in the defining equation, even though the biasing function may have \(k<m\) sign changes, if these two numbers have the same parity. We explain how these results can be used to guarantee the existence of two different generalizations of the zero-bias transformation by Goldstein and Reinert (Ann Appl Probab 7(4):935–952, 1997. doi: 10.1214/aoap/1043862419). Further applications include the derivation of Stein-type characterizations without needing to solve any Stein equation and the presentation of a general framework for estimating the distance from the distribution of a given real random variable X to that of a random variable Z, whose distribution is characterized by some mth-order linear differential operator. We also explain the fact that, in general, the biased distribution depends on the choice of the sign change points, if these are ambiguous. This new phenomenon does not appear in the framework from Goldstein and Reinert (2005).     

The Matsumoto–Yor Property and Its Converse on Symmetric Cones

The Matsumoto–Yor (MY) property of the generalized inverse Gaussian and gamma distributions has many generalizations. As was observed in Letac and Weso?owski (Ann Probab 28:1371–1383, 2000), the natural framework for the multivariate MY property is symmetric cones; however, they prove their results for the cone of symmetric positive definite real matrices only. In this paper, we prove the converse to the symmetric cone-variate MY property, which extends some earlier results. The smoothness assumption for the densities of respective variables is reduced to continuity only. This enhancement was possible due to the new solution of a related functional equation for real functions defined on symmetric cones.     

On a Characterization of Idempotent Distributions on Discrete Fields and on the Field of <Emphasis Type="Italic">p</Emphasis>-Adic Numbers

We prove the following theorem. Let X be a discrete field, and \(\xi \) and \(\eta \) be independent identically distributed random variables with values in X and distribution \(\mu \). The random variables \(S=\xi +\eta \) and \(D=(\xi -\eta )^2\) are independent if and only if \(\mu \) is an idempotent distribution. A similar result is also proved in the case when \(\xi \) and \(\eta \) are independent identically distributed random variables with values in the field of p-adic numbers \({\mathbf {Q}}_p\), where \(p>2\), assuming that the distribution \(\mu \) has a continuous density.     

Distance-regular Cayley graphs with least eigenvalue $$$$

We classify the distance-regular Cayley graphs with least eigenvalue \(-2\) and diameter at most three. Besides sporadic examples, these comprise of the lattice graphs, certain triangular graphs, and line graphs of incidence graphs of certain projective planes. In addition, we classify the possible connection sets for the lattice graphs and obtain some results on the structure of distance-regular Cayley line graphs of incidence graphs of generalized polygons.     

Linearly embeddable designs

We address the problem of determining when a plane algebraic cubic curve is complete as an (n, 3)-arc in \(\mathrm {PG}(2,q)\). Theoretical results are given for absolutely irreducible singular cubic curves, while computer based results are given for \(q\le 81\).