Computing with rational symmetric functions and applications to invariant theory and PI-algebras

Let the formal power series f in d variables with coefficients in an arbitrary field be a symmetric function decomposed as a series of Schur functions, and let f be a rational function whose denominator is a product of binomials of the form (1 - monomial). We use a classical combinatorial method of Elliott of 1903 further developed in the Partition Analysis of MacMahon in 1916 to compute the generating function of the multiplicities (i.e., the coefficients) of the Schur functions in the expression of f. It is a rational function with denominator of a similar form as f. We apply the method to several problems on symmetric algebras, as well as problems in classical invariant theory, algebras with polynomial identities, and noncommutative invariant theory.Comment: 37 page

Fabrication of living soft matter by symbiotic growth of unicellular microorganisms

We report the fabrication of living soft matter made as a result of the symbiotic relationship of two unicellular microorganisms. The material is composed of bacterial cellulose produced in situ by acetobacter (Acetobacter aceti NCIMB 8132) in the presence of photosynthetic microalgae (Chlamydomonas reinhardtii cc-124), which integrates into a symbiotic consortium and gets embedded in the produced cellulose composite. The same concept of growing living materials can be applied to other symbiotic microorganism pairs similar to the combination of algae and fungi in lichens, which is widespread in Nature. We demonstrate the in situ growth and immobilisation of the C. reinhardtii cells in the bacterial cellulose matrix produced by the simultaneous growth of acetobacter. The effect of the growth media composition on the produced living materials was investigated. The microstructure and the morphology of the produced living biomaterials were dependent on the shape of the growth culture container and media stirring conditions, which control the access to oxygen. As the photosynthetic C. reinhardtii cells remain viable and produce oxygen as they spontaneously integrate into the matrix of the bacterial cellulose generated by the acetobacter, such living materials have the potential for various applications in bio-hydrogen generation from the immobilised microalgae. The proposed approach for building living soft matter can provide new ways of immobilising other commercially important microorganisms in a bacterial cellulose matrix as a result of symbiosis with acetobacter without the use of synthetic binding agents and in turn increase their production efficiency

Artificial leaf device for hydrogen generation from immobilised C. reinhardtii microalgae

We developed a fully biomimetic leaf-like device for hydrogen production which allows incorporated fabric-immobilised microalgae culture to be simultaneously hydrated with media and harvested from the produced hydrogen in a continuous flow regime without the need to replace the algal culture. Our leaf device produces hydrogen by direct photolysis of water resulting from redirecting the photosynthetic pathways in immobilised microalgae due to the lack of oxygen. In contrast to the many other reports in the literature on batch photobioreactors producing hydrogen from suspension culture of microalgae, we present the first report where this is done in a continuous manner from a fabric-immobilised microalgae culture. The reported artificial leaf device maximises the sunlight energy utilisation per gram of algae and can be upscaled cheaply and easily to cover large areas. We compared the production of hydrogen from both immobilised and suspended cultures of C. reinhardtii microalgae under sulphur, phosphorus and oxygen deprived conditions. The viability and potential of this approach is clearly demonstrated. Even though this is a first prototype, the hydrogen yield of our artificial leaf device is twenty times higher per gram of algae than in previously the reported batch reactors. Such leaf-like devices could potentially be made from flexible plastic sheets and installed on roofs and other sun-exposed surfaces that are inaccessible by photovoltaic cells. The ability to continuously produce inexpensive hydrogen by positioning inexpensive sheets onto any surface could have an enormous importance in the field of biofuels. The proposed new concept can provide a cleaner and very inexpensive way of bio-hydrogen generation by flexible sheet-like devices

Percolation in the Harmonic Crystal and Voter Model in three dimensions

We investigate the site percolation transition in two strongly correlated systems in three dimensions: the massless harmonic crystal and the voter model. In the first case we start with a Gibbs measure for the potential, $U=\frac{J}{2} \sum_{} (\phi(x) - \phi(y))^2$, $x,y \in \mathbb{Z}^3$, $J > 0$ and $\phi(x) \in \mathbb{R}$, a scalar height variable, and define occupation variables $\rho_h(x) =1,(0)$ for $\phi(x) > h (<h)$. The probability $p$ of a site being occupied, is then a function of $h$. In the voter model we consider the stationary measure, in which each site is either occupied or empty, with probability $p$. In both cases the truncated pair correlation of the occupation variables, $G(x-y)$, decays asymptotically like $|x-y|^{-1}$. Using some novel Monte Carlo simulation methods and finite size scaling we find accurate values of $p_c$ as well as the critical exponents for these systems. The latter are different from that of independent percolation in $d=3$, as expected from the work of Weinrib and Halperin [WH] for the percolation transition of systems with $G(r) \sim r^{-a}$ [A. Weinrib and B. Halperin, Phys. Rev. B 27, 413 (1983)]. In particular the correlation length exponent $\nu$ is very close to the predicted value of 2 supporting the conjecture by WH that $\nu= \frac{2}{a}$ is exact.Comment: 8 figures. new version significantly different from the old one, includes new results, figures et

Capillary structured suspensions from in situ hydrophobized calcium carbonate particles suspended in a polar liquid media

© 2017 American Chemical Society. We demonstrate that capillary suspensions can be formed from hydrophilic calcium carbonate particles suspended in a polar continuous media and connected by capillary bridges formed of minute amounts of an immiscible secondary liquid phase. This was achieved in two different polar continuous phases, water and glycerol, and three different oils, oleic acid, isopropyl myristate, and peppermint oil as a secondary liquid phase. The capillary structuring of the suspension was made possible through local in situ hydrophobization of the calcium carbonate particles dispersed in the polar media by adding very small amounts of oleic acid to the secondary liquid phase. We observed a strong increase in the viscosity of the calcium carbonate suspension by several orders of magnitude upon addition of the secondary oil phase compared with the same suspension without secondary liquid phase or without oleic acid. The stability and the rheological properties of the obtained capillary structured materials were studied in relation to the physical properties of the system such as the particle size, interfacial tension between the primary and secondary liquid phases, as well as the particle contact angle at this liquid-liquid interface. We also determined the minimal concentrations of the secondary liquid phase at fixed particle concentration as well as the minimal particle concentration at fixed secondary phase concentration needed to form a capillary suspension. Capillary suspensions formed by this method can find application in structuring pharmaceutical and food formulations as well as a variety of home and personal care products

Cancer bioimprinting and cell shape recognition for diagnosis and targeted treatment

Cancer incidence and mortality have both increased in the last decade and are predicted to continue to rise. Diagnosis and treatment of cancers are often hampered by the inability to specifically target neoplastic cells. Bioimprinting is a promising new approach to overcome shortfalls in cancer targeting. Highly specific recognition cavities can be made into polymer matrices to mimic lock-and-key actions seen in in vivo biological systems. Early studies concentrated on molecules and were inhibited by template size complexity. Surface imprinting allows the capture of increasingly complex motifs from polypeptides to single cell organisms and mammalian cells. Highly specific cell shape recognition can also be achieved by cell interaction with imprints that can be made into polymer matrices to mimic biological systems at a molecular level. Bioimprinting has also been used to achieve nanometre scale resolution imaging of cancer cells. Studies of bioimprint-based drug delivery on cancer cells have been recently trialled in vitro and show that this approach can potentially improve existing chemotherapeutic approaches. This review focuses on the possible applications of bioimprinting with particular regards to cancer understanding, diagnosis and therapy. Cell imprints, incorporated into biosensors can allow the limits of detection to be improved or negate the need for extensive patient sample processing. Similar cell imprinting platforms can be used for nanoscale imaging of cancer morphology, as well as to investigate topographical signalling of cancer cells in vitro. Lastly, bioimprints also have applications as selective drug delivery vehicles to tumours with the potential to decrease chemotherapy-related side effects