Encoding and Processing of Alphanumeric Information by Chemical Mixtures

A novel infochemical device that is based on ¹H NMR readout of chemical information is presented. This chemical encoding system utilizes two measurable parameters of homogeneous mixtures, chemical shift and peak integration, for three different applications: 1) a text‐encoding device that is based on spectral representation of a sequence of symbols, 2) encoding of 21‐digit binary numbers, each represented by an NMR spectrum, and their algebraic manipulations, such as addition and subtraction, and 3) encoding of 21‐digit decimal numbers. The first application enables molecular information storage and encryption. The relative concentration of each component, as measured by the relevant peak integration, can represent a symbol. The second application of this system, in addition to its obvious memory capability, enables mathematical operations. The NMR spectrum of a given mixture represents a 21‐digit binary number where each of the peaks encodes for a specific digit. In any of the input mixtures (numbers) each compound is either present or absent, representing either 1 or 0, respectively. We used the various binary numbers to carry out addition operations by combining two or more solutions (numbers). Subtraction operations were also preformed by digital processing of the information. The third application is the representation of decimal numbers. As before, each of the peaks encodes for a specific digit. In any of the input mixtures each compound is present in one of 10 different relative concentrations, representing the 10 digits of a decimal number.     

On the Hopf–Schur group of a field

Let k be any field. We consider the Hopf–Schur group of k, defined as the subgroup of the Brauer group of k consisting of classes that may be represented by homomorphic images of finite-dimensional Hopf algebras over k. We show here that twisted group algebras and abelian extensions of k are quotients of cocommutative and commutative finite-dimensional Hopf algebras over k, respectively. As a consequence we prove that any tensor product of cyclic algebras over k is a quotient of a finite-dimensional Hopf algebra over k, revealing so that the Hopf–Schur group can be much larger than the Schur group of k.     

Sonochemical Coatings of ZnO and CuO Nanoparticles Inhibit Streptococcus mutans Biofilm Formation on Teeth Model

Antibiotic resistance has prompted the search for new agents that can inhibit bacterial growth. We recently reported on the antibiofilm activities of nanosized ZnO and CuO nanoparticles (NPs) synthesized by using sonochemical irradiation. In this study, we examined the antibacterial activity of ZnO and CuO NPs in a powder form and also examined the antibiofilm behavior of teeth surfaces that were coated with ZnO and CuO NPs using sonochemistry. Free ZnO and CuO NPs inhibited biofilm formation of Streptococcus mutans . Furthermore, by using the sonochemical procedure, we were able to coat teeth surfaces that inhibited bacterial colonization.     

Between arrow and Gibbard-Satterthwaite; A representation theoretic approach

A central theme in social choice theory is that of impossibility theorems, such as Arrow’s theorem [Arr63] and the Gibbard-Satterthwaite theorem [Gib73, Sat75], which state that under certain natural constraints, social choice mechanisms are impossible to construct. In recent years, beginning in Kalai [Kal01], much work has been done in finding robust versions of these theorems, showing “approximate” impossibility remains even when most, but not all, of the constraints are satisfied. We study a spectrum of settings between the case where society chooses a single outcome (à-la-Gibbard-Satterthwaite) and the choice of a complete order (as in Arrow’s theorem). We use algebraic techniques, specifically representation theory of the symmetric group, and also prove robust versions of the theorems that we state. Our relaxations of the constraints involve relaxing of a version of “independence of irrelevant alternatives”, rather than relaxing the demand of a transitive outcome, as is done in most other robustness results.     

Targeting Bone Metastases with a Bispecific Anticancer and Antiangiogenic Polymer–Alendronate–Taxane Conjugate

A polymer therapeutic designed for combination anticancer and antiangiogenic therapy inhibited the proliferation of prostate carcinoma cells and the proliferation, migration, and tube‐formation of endothelial cells. The nanoconjugate was formed from an N‐(2‐hydroxypropyl)methacrylamide (HPMA) copolymer, the bisphosphonate alendronate (for bone targeting), and the chemotherapy agent paclitaxel (PTX), which is cleaved by cathepsin B (see scheme).

     

Projective Resolutions for Modules over Infinite Groups

We define a notion of complexity for modules over group rings of infinite groups. This generalizes the notion of complexity for modules over group algebras of finite groups. We show that if M is a module over the group ring kG, where k is any ring and G is any group, and M has f-complexity (where f is some complexity function) over some set of finite index subgroups of G, then M has f-complexity over G (up to a direct summand). This generalizes the Alperin-Evens Theorem, which states that if the group G is finite then the complexity of M over G is the maximal complexity of M over an elementary abelian subgroup of G. We also show how we can use this generalization in order to construct projective resolutions for the integral special linear groups, SL(n, ℤ), where n ≥ 2.