Diszkrét és folytonos: a gráfelmélet, algebra, analízis és geometria találkozási pontjai = Discrete and Continuous: interfaces between graph theory, algebra, analysis and geometry

Sok eredmény született a gráfok növekvő konvergens sorozataival és azok limesz-objektumaival, ill. az ezek vizsgálatára szolgáló gráf-algebrákkal kapcsolatban. Kidolgozásra kerültek a nagyon nagy sűrű gráfok (hálózatok) matematikai elméletének alapjai, és ezek alkalmazásai az extremális gráfelmélet területén. Aktív és eredményes kutatás folyt a diszkrét matematika más, klasszikus matematikai területekkel való kapcsolatával kapcsolatban: topológia (a topológiai módszer alkalmazása gráfok magjára, ill a csomók elmélete), geometriai szerkezetek merevsége (a Molekuláris Sejtés bizonyítása 2 dimenzióban), diszkrét geometriai (Bang sejtésének bizonyítása), véges geometriák (lefogási problémák, extremális problémák q-analogonjai), algebra (félcsoport varietások, gráfhatványok színezése), számelmélet (additív számelmélet, Heilbronn probléma), továbbá gráfalgoritmusok (stabilis párosítások, biológiai alkalmazások)) területén. | Several results were obtained in connection with convergent growing sequences of graphs and their limit objects, and with graph algebras facilitating their study. Basic concepts for the study of very large dense graphs were worked out, along with their applications to extremal graph theory. Active and successful research was conducted concerning the interaction of discrete mathematics with other, classical areas of mathematics: topology (applications of topology in the study of kernels of graphs, and the theory of knots), rigidity of geometric structures (proof of the Molecular Conjecture in 2 dimensions), discrete geometry (proof of the conjecture of Bang), finite geometries (blocking problems, q-analogues of extremal problems), algebra (semigroup varieties, coloring of graph powers), number theory (additive number theory, heilbronn problem), and graph algorithms (stable matchings, applications in biology)

Ionic mechanisms limiting cardiac repolarization-reserve in humans compared to dogs.

The species-specific determinants of repolarization are poorly understood. This study compared the contribution of various currents to cardiac repolarization in canine and human ventricle. Conventional microelectrode, whole-cell patch-clamp, molecular biological and mathematical modelling techniques were used. Selective IKr block (50–100 nmol l−1 dofetilide) lengthened AP duration at 90% of repolarization (APD90) >3-fold more in human than dog, suggesting smaller repolarization reserve in humans. Selective IK1 block (10 μmol l−1 BaCl2) and IKs block (1 μmol l−1 HMR-1556) increased APD90 more in canine than human right ventricular papillary muscle. Ion current measurements in isolated cardiomyocytes showed that IK1 and IKs densities were 3- and 4.5-fold larger in dogs than humans, respectively. IKr density and kinetics were similar in human versus dog. ICa and Ito were respectively ∼30% larger and ∼29% smaller in human, and Na+–Ca2+ exchange current was comparable. Cardiac mRNA levels for the main IK1 ion channel subunit Kir2.1 and the IKs accessory subunit minK were significantly lower, but mRNA expression of ERG and KvLQT1 (IKr and IKsα-subunits) were not significantly different, in human versus dog. Immunostaining suggested lower Kir2.1 and minK, and higher KvLQT1 protein expression in human versus canine cardiomyocytes. IK1 and IKs inhibition increased the APD-prolonging effect of IKr block more in dog (by 56% and 49%, respectively) than human (34 and 16%), indicating that both currents contribute to increased repolarization reserve in the dog. A mathematical model incorporating observed human–canine ion current differences confirmed the role of IK1 and IKs in repolarization reserve differences. Thus, humans show greater repolarization-delaying effects of IKr block than dogs, because of lower repolarization reserve contributions from IK1 and IKs, emphasizing species-specific determinants of repolarization and the limitations of animal models for human disease

Factors influencing algal photobiohydrogen production in algal-bacterial co-cultures

Algal-bacterial co-cultures represent an alternative way for algal biohydrogen generation. Efficient algal hydrogen production requires anaerobiosis and electrons accessible for the algal FeFe-hydrogenases. A number of factors strongly influence the development of this optimal environment. Various algal strains were tested for hydrogen evolution with a selected bacterial partner, a fully hydrogenase deficient Escherichia coli. During the hunt for the most efficient algae strains, gas-to-liquid phase ratio, algal optical density and algal cell size were identified as crucial factors influencing algal hydrogen evolution rate, accumulated algal hydrogen yield, carbon dioxide and oxygen levels as well as acetic acid consumption in illuminated algal-bacterial cultures. The highest accumulated hydrogen yields were observed for the different algal partners under similar experimental setup. The combination of a gas-to-liquid phase ratio of 1/1 with an algae cell density of 3.96 * 10(8) algae cell ml(-1) (OD750:1) resulted in the highest accumulated algal hydrogen yields under continuous illumination of similar to 50 mu mol m(-2) s(-1) light at 25 degrees C irrespective of the applied algae strain. Accumulated hydrogen yield was also strongly influenced by the algal cell size, smaller cell size correlated with higher hydrogen evolution rate. The highest accumulated algal hydrogen yield (88.98 +/- 2.19 ml H-2 l(-1) d(-1)) was obtained with Chlorella sp. MACC 360 -E. coli Delta hypF co-culture

Bacterial symbionts enhance photo-fermentative hydrogen evolution of Chlamydomonas algae

The association of photosynthesizingChlamydomonasalgae and actively respiring bacterial partners represents an alternative, efficient and sustainable approach for biohydrogen generation.</p