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For any finitely generated group $$G$$ G , two complexity functions $$\alpha _G$$ αG and $$\beta _G$$ βG are defined to measure the maximal possible gap between the norm of an automorphism (respectively, outer automorphism) of $$G$$ G and the norm of its inverse. Restricting attention to free groups $$F_r$$ Fr , the exact asymptotic behaviour of $$\alpha _2$$ α2 and $$\beta _2$$ β2 is computed. For rank $$r\geqslant 3$$ r⩾3 , polynomial lower bounds are provided for $$\alpha _r$$ αr and $$\beta _r$$ βr , and the existence of a polynomial upper bound is proved for $$\beta _r$$ βr .

This manuscript reports on the fabrication of closed-cell aluminium alloy foams reinforced with carbon nanotubes (CNTs) through a novel approach that combines the powder metallurgy method with colloidal processing step that grants uniform dispersion of CNTs into the aqueous suspension of all powder components. Spraying the as prepared suspension into liquid nitrogen followed by lyophilisation enables obtaining homogeneous spherical granules to be used in the powder metallurgy method. Besides ensuring good dispersion of all powder components in the system, the non-agglomerated form of CNTs and the expansion upon foaming foster their structural integrity under stretched conditions in the final foams for an efficient load transfer.

In 2009 a novel swine-origin Influenza A H1N1 virus was identified in Mexico and Southern California. Since it was first recognized, neurological complications including acute necrotizing encephalopathy (ANE) have been globally documented in association with this viral infection. ANE is mostly known to occur in the paediatric population. We describe a fatal case of ANE in a previously healthy 40-year-old man infected with influenza A H1N1 virus presenting with severe neurologic decline. Computed tomography (CT) scan and magnetic resonance imaging (MRI) findings were consistent with ANE. CT and MR findings typically documented in paediatric cases of ANE - including bilateral thalamic necrosis with petechial hemorrhage - have been seldom described in adulthood.

Supratentorial hemangioblastomas (HBs) are exceedingly rare tumors accounting for 5%-10% of all HBs and usually present in the setting of von Hippel-Lindau (VHL) disease. Isolated HBs of the central nervous system also occur as a result of spontaneous mutation in the absence of any clinical manifestations of VHL disease. Of 13 temporal lobe HBs, only one non-VHL case was reported in the hippocampus. We describe the TRICKS findings in a case of isolated hemangioblastoma in the hippocampus without VHL disease. To our knowledge, this is the second case report of a hippocampal non-VHL hemangioblastoma.

Dural arteriovenous fistulas (DAVF) are vascular malformations rarely occurring in the paediatric population1,2,3. Prompt diagnosis and treatment are mandatory to prevent life-threatening complications including congestive heart failure and severe brain injury1,2. We describe the case of a female newborn with an orbital lymphangioma treated for a posterior fossa DAVF. We emphasize the role of MR imaging as a useful non-invasive tool in the diagnosis of these malformations and in the evaluation of associated brain parenchymal lesions.

This study used diffusion tensor tractography to evaluate the diffusion parameters of the corpsus callosum and asymmetry in the diffusion parameters of the corticospinal tracts in children with congenital hemiparesis. Precision moving critically correlates with the integrity of the pyramidal tracts as evidenced in congenital hemiparesis by the correlation found between corticospinal lesions and motor deficits. Therefore we hypothesize that diffusion parameters correlate with the severity of hemiparesis measured using the Bayley Scales of Infant Development.

In hemimegalencephaly, MR imaging often reveals mid-sagittal band-like structures between the lateral ventricles. We describe the clinical presentation, morphologic abnormalities, conventional MR imaging, diffusion tensor MR and fiber tract (FT) reconstruction in a 14-year-old boy with unilateral hemimegalencephaly. We retrospectively examined MR images to determine whether these structures are aberrant mid-sagittal fibers.

Desmoplastic fibroma (DF) is a rare non-metastasizing benign neoplasm of the bone characterized by aggressive local infiltration, also known as desmoid tumour. Desmoplastic fibroma of the mandible may recur locally when incompletely excised. In particular it can occur adjacent to and display contiguous extension along the mandibular nerve. This case report describes the imaging findings of a histopathologically proven desmoplastic fibroma involving the right mandibular region in a three-year-old Italian girl. We also discuss the usefulness of different imaging modalities (CT and MRI) in DF diagnosis and treatment.

The persistent hypoglossal artery is a rare perseverance of an embryonic vessel connecting the anterior and posterior circulations and is generally considered an incidental finding. This report describes a patient with a basilar dependence on a persistent hypoglossal artery visualized at CT angiography. The pertinent findings and clinical implications of this anomalous vessel are discussed.

A three-year-old girl developed spastic diplegia to the right and irregular tonc-clonic movements. Phenobarbital was started because of suspected seizure activity. The Pediatric unit asked for brain MR imaging to investigate neurological symptoms. MR and diffusion tensor imaging showed a haemorrhagic vein of Galen aneurysmal malformation (choroidal type) that shifted the corticospinal tract fibres to one side and the corpus callosum was moved forward. Vein of Galen aneurysmal malformations (VGAM) are characterized by multiple arteriovenous connections draining into a markedly enlarged median draining vein. This ectatic vein is not the vein of Galen, but its embryonic precursor, the median prosencephalic vein of Markowski. During normal development, the posterior portion of the median prosencephalic vein persists as the vein of Galen, while its anterior portion regresses in parallel with the formation of the internal cerebral veins (ICV). With the advent of endovascular neurointerventional techniques, the prospects for successful treatment of these lesions, once dismal, are now much improved. MR and diffusion tensor imaging can help in diagnosis and to guide endovascular interventional procedures.

Acute cerebellitis is an inflammatory process commonly involving both cerebellar hemispheres. Bilateral cerebellar hemispheres involvement is the most common finding. It typically occurs as a primary infectious, post-infectious or post-vaccination disorder, but is also a disease entity with heterogeneous pathogenesis including paraneoplasia. Acute cerebellitis is usually a benign, self-limiting and rarely fatal disease. Typically, cerebellar atrophy is a late consequence of the syndrome. We describe the radiological features of a case of pseudotumoural hemicerebellitis with emphasis on MRI and spectroscopy findings as non-invasive diagnostic tools to avoid unnecessary surgical procedures.

We describe a case of listerial rhombencephalitis in a previously healthy 37-year-old woman. The diagnosis was based on the clinical findings, results of cerebrospinal fluid analysis, blood culture and MR imaging. The specific treatment was started after culture results were available, and the patient made a full clinical recovery.

Refractures of cemented vertebrae occasionally occur after vertebroplasty. It is unclear whether such fractures are procedure-related or part of the natural course of osteoporosis and neoplasy. Our aim was to identify why there is an increased risk of subsequent fracture in cemented vertebrae. We retrospectively analyzed the incidence and possible causative mechanism of refracture in patients who had received vertebroplasty for multiple levels of vertebral compression fracture and the reduction of pain after a subsequent vertebroplasty procedure. A total of 356 patients were evaluated with follow-up from June 2003 to September 2008. We identified 59 refractured patients (54 osteoporotic and four neoplastic). Refractures of cemented vertebrae after vertebroplasty occurred in 59 patients (16%: 98% osteoporotic and 2% neoplastic). Refractures occurred in 8% at the same level as the first vetebroplasty, 31% at an inferior level, 19% at a superior level, 41% at superior and inferior levels and 1% at superior and same levels. Pain was significantly reduced after retreatment in 45 patients (76%) with a moderate reduction in 14 patients (24 %). In conclusion, significant anterior vertebral height restoration increases the risk of subsequent fracture in cemented vertebrae.

Full geometry optimizations within given molecular symmetries have been performed on the chair and boat forms involved in the Cope rearrangement of 1,5-hexadiene using highly correlated methods (MR-CISD and MR-AQCC) and extended basis sets. These optimizations are based on analytic gradient procedures developed within the COLUMBUS program system and are the first ones for the Cope rearrangement, which have been carried out at a multireference, post-CASSCF level. By comparison of MR-CISD and MR-AQCC results, the importance of size-extensivity corrections is clearly demonstrated. Computed energetic stabilities with respect to 1,5-hexadiene and bis-allyl are in good agreement with experimental data. Only a single saddle point for the chair form of C2h symmetry is found in contrast to CASSCF results, but in agreement with CASPT2N and MRMP2 investigations. Thus, we confirm these previous results showing that the mechanism of the Cope rearrangement of 1,5-hexadiene is concerted via an aromatic transition state.

In this paper it is proved that the set of primitive elements of a non-Abelian free group has density zero, i.e. the ratio of primitive elements in increasingly large balls is arbitrarily small. Two notions of density (natural and exponential density) are defined and some of their properties are studied. A class of subsets of the free group (graphical sets) is defined restricting the occurrence of adjacent letters in the reduced word for an element, and the relation between graphical sets and the set of primitive elements is studied and used to prove the above result.

Let F be a finitely generated free group, and let n denote its rank. A subgroup H of F is said to be automorphism-fixed, or auto-fixed for short, if there exists a set S of automorphisms of F such that H is precisely the set of elements fixed by every element of S; similarly, H is 1-auto-fixed if there exists a single automorphism of F whose set of fixed elements is precisely H. We show that each auto-fixed subgroup of F is a free factor of a 1-auto-fixed subgroup of F. We show also that if (and only if) n≥3, then there exist free factors of 1-auto-fixed subgroups of F which are not auto-fixed subgroups of F. A 1-auto-fixed subgroup H of F has rank at most n, by the Bestvina–Handel Theorem, and if H has rank exactly n, then H is said to be a maximum-rank 1-auto-fixed subgroup of F, and similarly for auto-fixed subgroups. Hence a maximum-rank auto-fixed subgroup of F is a (maximum-rank) 1-auto-fixed subgroup of F. We further prove that if H is a maximum-rank 1-auto-fixed subgroup of F, then the group of automorphisms of F which fix every element of H is free abelain of rank at most n−1. All of our results apply also to endomorphisms.

1. The kinetics of non-radioactive bilirubin were investigated in 100 patients with chronic non-haemolytic unconjugated hyperbilirubinaemia and in nine normal volunteers. 2. The patients with Gilbert's syndrome were divided on the basis of a two-compartment model into two distinct groups: group 1 (74 patients) with decreased hepatic uptake and conjugation of bilirubin and a bilirubin turnover rate within the normal range, and group 2 (26 patients) having normal uptake, impaired conjugation and increased bilirubin turnover rate. 3. On the basis of these findings, studies were made of early pigment production in four patients of group 1, in six patients of group 2 and in four of the normal volunteers, with [14C]glycine and ş-[3H]aminolaevulinic acid. 4. After receiving injections of labelled haem precursors, the four patients in group 1 had a normal rate of incorporation of both tracers, whereas abnormalities in incorporation were found in group 2. Four patients showed an increase of the first component of the early peak of [14C]bilirubin as well as of the early peak of [3H]bilirubin, suggesting an increased turnover of hepatic haem. Two patients showed an increased incorporation of [14C]glycine characterized by the fusion of the two early peaks, whereas the incorporation of the δ-[3H]aminolaevulinic acid was normal, indicating the presence of a primary shunt hyperbilirubinaemia. 5. The results confirm that Gilbert's syndrome is a heterogeneous condition with respect to bilirubin turnover rate. The population of Gilbert's syndrome with increased bilirubin turnover rate comprises not only patients with an increased haem erythroid turnover, but also patients with increased metabolism of nonerythroid haem protein in the liver.

Integral perturbed angular correlation experiments have been carried out on recoilimplanted15C nuclei in iron. The 739 keV5/2+ level of15C was populated via the14C(d, p)15C* reaction. Using the known g-factor and lifetime of the state, effective internal fields of -12.4±1.1 kG and -10.9±1.5 kG were determined at room temperature and 77 K, respectively. A conduction electron polarization hyperfine field of about -20 kG was deduced from the data.

Liver plasma membranes isolated from rats with chronic dietary iron overload showed a large modification of their phospholipid fatty acid composition. Specifically, a significant decrease in polyunsaturated fatty acids and a parallel increase in saturated fatty acids was observed. This pattern was consistent with thein vivo occurrence of lipoperoxidative reactions in the liver plasma membranes. However, neither change in the cholesterol/phospholipid molar ratio nor in the lipid/protein ratio was detected. Direct measurement of the plasma membrane fluidity state by electron spin resonance spectrometry did not reveal any difference between control and iron-treated rats. These findings indicate that chronic dietary iron overload can induce lipid peroxidation of rat liver plasma membranes, but this event does not bring about modification in the physical state of the membrane.

1. Benzodiazepine receptors were studied in rats with hepatic encephalopathy due to fulminant hepatic failure induced by galactosamine. [3H]-Diazepam binding studies on brain synaptic membranes of rats with mild and severe encephalopathy show a significant increase in the number of receptors in both stages of coma. 2. [3H]Diazepam binding to synaptic membrane preparations from rats in the mild or severe stage of encephalopathy hyper-responded to the stimulatory effect of γ-aminobutyric acid (GABA) applied in vitro at doses which for control rat preparations were in a subthreshold range. The effect of GABA was shown to be specific, since it was blocked by bicuculline methiodide. The sensitivity of benzodiazepine receptors in hepatic encephalopathy to nanomolar concentrations of GABA, which induced a significant increase in their affinity, seems to indicate a functional supersensitivity of benzodiazepine receptors in vivo in both mild and severe stages of encephalopathy. 3. The phenomena described may be attributed to a partial degeneration of nerve terminals in hepatic encephalopathy, leading to a supersensitivity of benzodiazepine receptors, which parallels the previously described denervation supersensitivity of GABA receptors present in this animal model of fulminant hepatic failure. These findings may account for the brain hypersensitivity to sedatives administered to patients with liver diseases. 4. The administration in vivo of a benzodiazepine antagonist, 2-phenylpyrazolo [4,3-c]-quinolin-3(5H)-one, counteracted the hypersensitivity of benzodiazepine receptors in the mild stage of encephalopathy. In fact, electrophysiological studies with visually evoked potential recordings in rats in the mild stage of encephalopathy 30-60 min after the administration of the drug showed a recovery of the wave pattern, and this electrophysiological finding was substantiated by the demonstration that both the number and the affinity of benzodiazepine receptors were strongly reduced.

In rats with chronic dietary iron overload, a higher amount of liver ferritin L-subunit mRNA was found mainly engaged on polysomes, whereas in control rats ferritin L-subunit mRNA molecules were largely stored in ribonucleoprotein particles. On the other hand, ferritin H-subunit mRNA was unchanged by chronic iron load and remained in the inactive cytoplasmic pool. In agreement with previous reports, in rats acutely treated with parenteral iron, only the ferritin L-subunit mRNA increased in amount, whereas both ferritin subunit mRNAs shifted to polysomes. This may indicate that, whereas in acute iron overload the hepatocyte operates a translation shift of both ferritin mRNAs to confront rapidly the abrupt entry of iron into the cell, during chronic iron overload it responds to the slow iron influx by translating a greater amount of L-subunit mRNA to synthesize isoferritins more suitable for long-term iron storage.

At the beginning the problem, as expressed by the heads of the Company which posed it, was in essence to find out whether, within the framework of a limited and well-defined expansion to level off in 1961, the existing capacity for stocks at a port used for shipping overseas would or would not be sufficient (it was thought it would not be). If more warehouses were shown to be needed, the amount of this extra capacity was to be worked out. It was very quickly discovered by an examination of the situation that the real problem would be rather to advise rules of stock management so as to take the best advantage of the existing stock capacity, in this way reducing the investment in buildings and maintenance to a minimum. Study of the model confirmed that the new management rules would make it unnecessary to increase the existing stock capacity. The model has the following characteristics: non-stationary process (e.g. an ever-changing situation), and an absence of any hypothesis on even the type of decision as to the method of renewing stock. Dynamic Programming used for this set of circumstances has made it possible to arrive at optimum management rules, demonstrating, incidentally, the power of this method in the study of non-stationary processes.

Halothane, but not methoxyflurane, was found to cause specific hepatocellular damage, the hepatotoxicity being prompt but transient. The hepatotoxicity was demonstrated by the elevation in the serum activity of xanthine oxidase, a highly sensitive marker for acute liver damage.

1. In the search to identify peripheral toxins which could be responsible for the supersensitivity of brain benzodiazepine receptors in experimental models of hepatic encephalopathy, [3H]diazepam-binding studies have been performed on brain tissues of normal rats treated with ammonium chloride, dimethyldisulphide and octanoic acid administered alone or in combination. 2. The subacute administration of the three toxins in combination induced a 30% increase in the number of benzodiazepine recognition sites. The administration of these toxins alone or in combination showed that this increase was mainly linked to the synergistic action of dimethyldisulphide or octanoic acid with ammonia, since dimethyldisulphide plus octanoic acid was ineffective. 3. These observations seem to reinforce the suggestion that these three toxins are able to induce neurochemical derangements similar to those described in experimental hepatic encephalopathy.

Summary Halothane anesthesia was found to be hepatotoxic in the rat, as demonstrated by a significant elevation of serum xanthine oxidase (SXO) level. SXO appeared to be a more sensitive marker of liver damage than serum, glutamic oxalacetic transaminsa. SXO was found to be elevated also following exposure to relative hypoxia.

We report a reproducible model of experimental allergic neuritis (EAN) with severe clinical signs and consistent pathological features in mice. Pertussis toxin (PT) in the presence or absence of murine recombinant interleukin‐12 (mrIL‐12) was used as an adjuvant with bovine peripheral nerve myelin (BPNM) to induce clinical EAN in SJL/J mice. After immunization with a combination of BPNM in complete Freund's adjuvant (CFA) and PT, mice developed severe consistent signs of EAN. The additional treatment of immunized mice with mrIL‐12 prolonged the course of EAN characterized by earlier clinical signs of the disease and delayed the recovery stage. Mice injected with BPNM and CFA without PT developed mild clinical signs. Histological examination of the caudae equinae and the sciatic nerves taken from mice with clinical signs of EAN during the recovery stage revealed severe demyelination, remyelination and remnants of mononuclear cell infiltration. Moderate to severe EAN can be induced in SJL/J mice by the injection of a combination of BPNM in CFA and PT. This model can provide a better understanding of mechanism of demyelination in infiltrating peripheral neuropathy.