Counting Linear Extensions: Parameterizations by Treewidth.

We consider the # P -complete problem of counting the number of linear extensions of a poset ( # LE ) ; a fundamental problem in order theory with applications in a variety of distinct areas. In particular, we study the complexity of # LE parameterized by the well-known decompositional parameter treewidth for two natural graphical representations of the input poset, i.e., the cover and the incomparability graph. Our main result shows that # LE is fixed-parameter intractable parameterized by the treewidth of the cover graph. This resolves an open problem recently posed in the Dagstuhl seminar on Exact Algorithms. On the positive side we show that # LE becomes fixed-parameter tractable parameterized by the treewidth of the incomparability graph.

[The effect of brilliant cresyl blue on erythrocyte degeneration in patients after acute stroke]. / Zmeny v rozpade erytrocytov úcinkom briliantkrezylovej modrej u pacientov po náhlej mozgovej cievnej príhode.

The authors investigated the disintegration of red cells by the action of brilliant cresyl blue in patients after an acute cerebrovascular attack and compared them with the disintegration in blood donors. In the patients the disintegration was assessed within 24 hours after the attack and after one year. The disintegration was assessed in two incubation solutions i.e. in isotonic saline and in Krebs-Ringer solution after three hours incubation at 37 degrees C. It was revealed that in the control group the disintegration of erythrocytes in isotonic saline is much greater than in Krebs-Ringer solution. The difference between the action of the two solutions is highly significant. In patients immediately after the attack as well as in the group which did not survive the period of one year (7 patients) and the group which survived the period of one year (8 patients) the difference in disintegration in the two solutions is significant but at a lower level of significance. It is thus smaller than in the control group. However, in the group which survived for one year this difference is again highly significant, similarly as in the control group. The author discusses the problem of metabolic influencing of the elasticity and deformability of the red cell membrane and its impact on the rheology of blood.

[Changes in circulation of the blood in cerebral arteries in relation to age]. / Zmeny krvného prietoku v mozgových artériách v závislosti od veku.

The authors examined 12 people under 40 years and 12 above 40 years, mostly healthy volunteers. They investigated the rate of blood flow in the median cerebral artery after compression of the homolateral and contralateral internal carotid. They found that in more advanced age the rate of flow in the mentioned arteries is significantly reduced. During compression tests in more advanced age the decline in the flow rate is more marked in the median cerebral artery on the side of compression. In the other arteries the flow is promoted but the age dependence is not marked. The authors conclude from these findings that with advancing age the possibilities of autoregulation deteriorate more than those of the collateral circulation via Willis' circle.

[Cerebral circulation using transcranial and extracranial doppler ultrasonography in a patient with vertigo and ischemia in the area of the brain stem]. / Vysetrenie mozgovej cirkulácie pomocou transkraniálnej a extrakraniálnej dopplerovskej ultrasonografie u pacientov s vertigom a ischémiou v oblasti mozgového kmena.

The authors examined 32 patients with vertigo, 17 patients with focal ischaemia of the brain stem and 24 patients without signs of affections of the central nervous system by transcranial and extracranial Doppler ultrasonography. They measured the flow velocity in the basilar artery (BA), in the intracranial portion of the vertebral artery (VA) and in the extracranial portion of the internal carotid artery (ICA). In patients with vertigo they investigated functional and organic changes in the area of the cervical spine. They found significant differences in the flow velocities between groups as well as in different indices calculated from the assessed values. The lowest flow velocities were recorded in patients with focal ischaemia of the brain stem. The authors evaluate the influence of haemodynamics and disease of the cervical spine on the development of vertigo.

[Glucose-6-phosphate dehydrogenase and catalase in the erythrocytes of patients with cerebral ischemia attacks]. / Glukóza-6-fosfátdehydrogenáza a kataláza v erytrocytoch chorých s ischemickou mozgovou príhodou.

The authors assessed the activity of glucose-6-phosphate dehydrogenase and catalase in 73 patients with ischaemic cerebral attacks. They compared the results with a control group of 23 patients with vertebrogenic diseases. They recorded a mild decrease of activity of the above enzymes and draw attention to possible oxidation damage under conditions of cerebral hypoxia.

[Erythrocyte deformability in patients with acute ischemic cerebrovascular stroke]. / Sledovanie deformability erytrocytov u pacientov s náhlou ischemickou mozgovou cievnou príhodou.

The authors investigated in a group of 40 patients the deformability of the red cells, using the disintegration method by means of brilliant cresyl blue. The control group was formed by blood donors from the blood transfusion station. The disintegration of the red cells was investigated in vitro in isotonic NaCl solution and in Krebs-Ringer solution with two concentrations of brilliant cresyl blue, i.e. 0.25 and 0.5 nmol/l1. It was revealed that the disintegration of red cells was significantly lower in Krebs-Ringer solution in blood donors and patients in both concentrations of brilliant cresyl blue that in isotonic NaCl. In patients where blood samples were collected within 24 hours after the attack, no significant difference was found in the disintegration of red cells as compared with blood donors. There was no significant difference in the disintegration of red cells in patients 24 hours after the attack and 10 to 20 days after the attack. The authors conclude that in the above conditions no substantial changes in the deformability of the red cells occur.

[Levels of homovanillic acid and 5-hydroxyindoleacetic acid in the cerebrospinal fluid in patients with focal cerebral ischemia]. / Koncentrácia kyseliny homovanilovej a 5-hydroxyindoloctovej v CSL u pacientov s loziskovou ischémiou mozgu.

The investigated group comprised 35 patients where clinical examination revealed focal cerebral ischaemia in the area of the a. cerebri media. In the group of elderly patients above 60 years, as compared with controls, the homovanillic acid (HVA) and 5-hydroxyindolacetic acid (5-HIAA) concentration in cerebrospinal fluid was elevated. In the group of patients under 60 years no changes in the concentration of these metabolites were found. In older patients the increased level of metabolites in cerebrospinal fluid persisted also after three days following the attack, while in younger patients the elevated HVA and 5-HIAA levels were found only in specimens collected up to three days.