The Strong Influence of Structure Polymorphism on the Conductivity of Peptide Fibrils

Peptide fibril nanostructures have been advocated as components of future biotechnology and nanotechnology devices. However, the ability to exploit the fibril functionality for applications, such as catalysis or electron transfer, depends on the formation of well‐defined architectures. Fibrils made of peptides substituted with aromatic groups are described presenting efficient electron delocalization. Peptide self‐assembly under various conditions produced polymorphic fibril products presenting distinctly different conductivities. This process is driven by a collective set of hydrogen bonding, electrostatic, and π‐stacking interactions, and as a result it can be directed towards formation of a distinct polymorph by using the medium to enhance specific interactions rather than the others. This method facilitates the detailed characterization of different polymorphs, and allows specific conditions to be established that lead to the polymorph with the highest conductivity.     

Optimization of Adiabatic Selective Pulses

Adiabatic RF pulses play an important role in spin inversion due to their robust behavior in presence of inhomogeneous RF fields. These pulses are characterized by the trajectory swept by the tip of theB_effvector and the rate of motion upon it. In this paper, a method is described for optimizing adiabatic inversion pulses to achieve a frequency-selective magnetization inversion over a given bandwidth in a shorter time and to improve slice profile. An efficient adiabatic pulse is used as an initial condition. This pulse allows for flexibility in choosing its parameters; in particular, the transition sharpness may be traded off against the inverted bandwidth. The considerations for selecting the parameters of the pulse according to the requirements of the design are discussed. The optimization process then improves the slice profile by optimizing the rate of motion along the trajectory of the pulse while preserving the trajectory itself. The adiabatic behavior of the optimized pulses is fully preserved over a twofold range of variation in the RF amplitude which is sufficient for imaging applications in commercial high-field MRI machines. Design examples demonstrate the superiority of the optimized pulses over the conventional sech/tanh pulse.     

On the Vertices of the d-Dimensional Birkhoff Polytope

Let us denote by Ω _n the Birkhoff polytope of n×n doubly stochastic matrices. As the Birkhoff–von Neumann theorem famously states, the vertex set of Ω _n coincides with the set of all n×n permutation matrices. Here we consider a higher-dimensional analog of this basic fact. Let $\varOmega^{(2)}_{n}$ be the polytope which consists of all tristochastic arrays of order n. These are n×n×n arrays with nonnegative entries in which every line sums to 1. What can be said about $\varOmega ^{(2)}_{n}$ ’s vertex set? It is well known that an order-n Latin square may be viewed as a tristochastic array where every line contains n?1 zeros and a single 1 entry. Indeed, every Latin square of order n is a vertex of $\varOmega^{(2)}_{n}$ , but as we show, such vertices constitute only a vanishingly small subset of $\varOmega^{(2)}_{n}$ ’s vertex set. More concretely, we show that the number of vertices of $\varOmega ^{(2)}_{n}$ is at least $(L_{n})^{\frac{3}{2}-o(1)}$ , where L _n is the number of order-n Latin squares. We also briefly consider similar problems concerning the polytope of n×n×n arrays where the entries in every coordinate hyperplane sum to 1, improving a result from Kravtsov (Cybern. Syst. Anal., 43(1):25–33, 2007). Several open questions are presented as well.     

An upper bound on the number of high-dimensional permutations

What is the higher-dimensional analog of a permutation? If we think of a permutation as given by a permutation matrix, then the following definition suggests itself: A d-dimensional permutation of order n is an n×n×...×n=[n] ^d+1 array of zeros and ones in which every line contains a unique 1 entry. A line here is a set of entries of the form {(x ₁,...,x _i?1,y,x _i+1,...,x _d+1)|n≥y≥1} for some index d+1≥i≥1 and some choice of x _j ∈ [n] for all j ≠ i. It is easy to observe that a one-dimensional permutation is simply a permutation matrix and that a two-dimensional permutation is synonymous with an order-n Latin square. We seek an estimate for the number of d-dimensional permutations. Our main result is the following upper bound on their number $$\left( {(1 + o(1))\frac{n} {{e^d }}} \right)^{n^d } .$$ We tend to believe that this is actually the correct number, but the problem of proving the complementary lower bound remains open. Our main tool is an adaptation of Brégman’s [1] proof of the Minc conjecture on permanents. More concretely, our approach is very close in spirit to Schrijver’s [11] and Radhakrishnan’s [10] proofs of Brégman’s theorem.     

Design of Selective Adiabatic Inversion Pulses Using the Adiabatic Condition

Adiabatic RF pulses play an important role in spin inversion due to their robust behavior in the presence of inhomogeneous RF fields. These pulses are characterized by the trajectory swept by the tip of theB_effvector and the rate of motion along it. In this paper, we describe a method by which optimized modulation functions can be constructed to render insensitivity toB₁inhomogeneity over a predeterminedB₁range and over a wide band of frequencies. This is accomplished by requiring that the optimized pulse fulfill the adiabatic condition over this range ofB₁inhomogeneity and over the desired frequency band for the complete duration of the pulse. A trajectory similar to the well-known sech/tanh adiabatic pulse, i.e., a half-ellipse, is used. The optimization process improves the slice profile by optimizing the rate of motion along this trajectory. The optimized pulse can be tailored to the specific design requirements; in particular, the transition sharpness may be traded off against the inverted bandwidth. Two design examples, including experimental results, demonstrate the superiority of the optimized pulses over the conventional sech/tanh pulse: in the first example, a large frequency band is to be inverted using a weak RF amplitude in a short time. In the second example, a pulse with a very sharp transition is required.     

Tetracyanido(difluorido)phosphates M+[PF2(CN)4]−

The systematic study of the reaction of M[PF₆] salts and Me₃SiCN led to a synthetic method for the synthesis and isolation of a series of salts containing the unprecedented [PF₂(CN)₄]^? ion in good yields. The reaction temperature, pressure, and stoichiometry were optimized. The crystal structures of M[PF₂(CN)₄] (M=[nBu₄N]⁺, Ag⁺, K⁺, Li⁺, H₅O₂⁺) were determined. X‐ray crystallography showed the exclusive formation of the cis isomer in accord with ³¹P and ¹⁹F solution NMR spectroscopy data. Starting with the K[PF₂(CN)₄] the room temperature ionic liquid EMIm[PF₂(CN)₄] was prepared exhibiting a rather low viscosity.     

Ln(14)Na(3)Ru(6)O(36) (ln = pr, nd): two new complex lanthanide-containing oxides of ruthenium

The lanthanide-containing ruthenium oxides Ln14Na3Ru6O36 (Ln = Pr, Nd) were prepared as single crystals from molten sodium hydroxide. The two compounds crystallize in the rhombohedral space group Rc with cell constants of a = 9.7380(2) and 9.6781(2) Angstrom and c = 55.5716(18) and 55.4156(18) Angstrom for Ln14Na3Ru6O36 (Ln = Pr, Nd), respectively. The structure of the two compounds is composed of two types of slabs that alternate in an AB fashion. Each slab consists of three layers and are arranged to yield a unit cell with a 12-layer structure. Both compounds exhibit magnetic behavior consistent with canted antiferromagnetism.     

Summand absorbing submodules of a module over a semiring

An R-module V over a semiring R lacks zero sums (LZS) if $x+y=0$ implies $x=y=0$. More generally, we call a submodule W of V “summand absorbing” (SA) in V if $?x,y\in V:x+y\in W?x\in W,y\in W$. These arise in tropical algebra and modules over idempotent semirings, as well as modules over semirings of sums of squares. We explore the lattice of finite sums of SA-submodules, obtaining analogs of the Jordan–Hölder theorem, the noetherian theory, and the lattice-theoretic Krull dimension. We pay special attention to finitely generated SA-submodules, and describe their explicit generation.