Riesz-Nágy singular functions revisited

In 1952 F. Riesz and Sz.Nágy published an example of a monotonic continuous function whose derivative is zero almost everywhere, that is to say, a singular function. Besides, the function was strictly increasing. Their example was built as the limit of a sequence of deformations of the identity function. As an easy consequence of the definition, the derivative, when it existed and was finite, was found to be zero. In this paper we revisit the Riesz-N´agy family of functions and we relate it to a system for real numberrepresentation which we call (t, t-1) expansions. With the help of these real number expansions we generalize the family. The singularity of the functions is proved through some metrical properties of the expansions used in their definition which also allows us to give a more precise way of determining when the derivative is 0 or infinity.

Effects of mineralocorticoid and K+ concentration on K+ secretion and ROMK channel expression in a mouse cortical collecting duct cell line.

The cortical collecting duct (CCD) plays a key role in regulated K(+) secretion, which is mediated mainly through renal outer medullary K(+) (ROMK) channels located in the apical membrane. However, the mechanisms of the regulation of urinary K(+) excretion with regard to K(+) balance are not well known. We took advantage of a recently established mouse CCD cell line (mCCD(cl1)) to investigate the regulation of K(+) secretion by mineralocorticoid and K(+) concentration. We show that this cell line expresses ROMK mRNA and a barium-sensitive K(+) conductance in its apical membrane. As this conductance is sensitive to tertiapin-Q, with an apparent affinity of 6 nM, and to intracellular acidification, it is probably mediated by ROMK. Overnight exposure to 100 nM aldosterone did not significantly change the K(+) conductance, while it increased the amiloride-sensitive Na(+) transport. Overnight exposure to a high K(+) (7 mM) concentration produced a small but significant increase in the apical membrane barium-sensitive K(+) conductance. The mRNA levels of all ROMK isoforms measured by qRT-PCR were not changed by altering the basolateral K(+) concentration but were decreased by 15-45% upon treatment with aldosterone (0.3 or 300 nM for 1 and 3 h). The paradoxical response of ROMK expression to aldosterone could possibly work as a preventative mechanism to avoid excessive K(+) loss which would otherwise result from the increased electrogenic Na(+) transport and associated depolarization of the apical membrane in the CCD. In conclusion, mCCD(cl1) cells demonstrate a significant K(+) secretion, probably mediated by ROMK, which is not stimulated by aldosterone but increased by overnight exposure to a high K(+) concentration.

Downregulation of cannabinoid receptor 1 from neuropeptide Y interneurons in the basal ganglia of patients with Huntington's disease and mouse models.

Cannabinoid receptor 1 (CB(1) receptor) controls several neuronal functions, including neurotransmitter release, synaptic plasticity, gene expression and neuronal viability. Downregulation of CB(1) expression in the basal ganglia of patients with Huntington's disease (HD) and animal models represents one of the earliest molecular events induced by mutant huntingtin (mHtt). This early disruption of neuronal CB(1) signaling is thought to contribute to HD symptoms and neurodegeneration. Here we determined whether CB(1) downregulation measured in patients with HD and mouse models was ubiquitous or restricted to specific striatal neuronal subpopulations. Using unbiased semi-quantitative immunohistochemistry, we confirmed previous studies showing that CB(1) expression is downregulated in medium spiny neurons of the indirect pathway, and found that CB(1) is also downregulated in neuropeptide Y (NPY)/neuronal nitric oxide synthase (nNOS)-expressing interneurons while remaining unchanged in parvalbumin- and calretinin-expressing interneurons. CB(1) downregulation in striatal NPY/nNOS-expressing interneurons occurs in R6/2 mice, Hdh(Q150/Q150) mice and the caudate nucleus of patients with HD. In R6/2 mice, CB(1) downregulation in NPY/nNOS-expressing interneurons correlates with diffuse expression of mHtt in the soma. This downregulation also occludes the ability of cannabinoid agonists to activate the pro-survival signaling molecule cAMP response element-binding protein in NPY/nNOS-expressing interneurons. Loss of CB(1) signaling in NPY/nNOS-expressing interneurons could contribute to the impairment of basal ganglia functions linked to HD.

Kenraaliluutnantti evp. K.L. Oesch 12/12 1974

Kirje 12.12.1974

Estimating uncertainty of alcohol-attributable fractions for infectious and chronic diseases.

Background: Alcohol is a major risk factor for burden of disease and injuries globally. This paper presents a systematic method to compute the 95% confidence intervals of alcohol-attributable fractions (AAFs) with exposure and risk relations stemming from different sources.Methods: The computation was based on previous work done on modelling drinking prevalence using the gamma distribution and the inherent properties of this distribution. The Monte Carlo approach was applied to derive the variance for each AAF by generating random sets of all the parameters. A large number of random samples were thus created for each AAF to estimate variances. The derivation of the distributions of the different parameters is presented as well as sensitivity analyses which give an estimation of the number of samples required to determine the variance with predetermined precision, and to determine which parameter had the most impact on the variance of the AAFs.Results: The analysis of the five Asian regions showed that 150 000 samples gave a sufficiently accurate estimation of the 95% confidence intervals for each disease. The relative risk functions accounted for most of the variance in the majority of cases.Conclusions: Within reasonable computation time, the method yielded very accurate values for variances of AAFs.

K. J. Gummerus Osakeyhtiö 10.11.1959 Direktionen

Kirje

Yli-insinööri K. J. Tolonen 9/11 1957

Kirje

Posterior quadrantic epilepsy surgery: technical variants, surgical anatomy, and case series.

OBJECTIVE: Patients with intractable epilepsy due to extensive lesions involving the posterior quadrant (temporal, parietal, and occipital lobes) form a small subset of epilepsy surgery. This study was done with a view to analyze our experience with this group of patients and to define the changes in the surgical technique over the last 15 years. We also describe the microsurgical technique of the different surgical variants used, along with their functional neuroanatomy. METHODS: In this series there were 13 patients with a median age of 17 years. All patients had extensive presurgical evaluation that provided concordant evidence localizing the lesion and seizure focus to the posterior quadrant. The objective of the surgery was to eliminate the effect of the epileptogenic tissue and preserve motor and sensory functions. RESULTS: During the course of this study period of 15 years, the surgical procedure performed evolved toward incorporating more techniques of disconnection and minimizing resection. Three technical variants were thus utilized in this series, namely, (i) anatomical posterior quadrantectomy (APQ), (ii) functional posterior quadrantectomy (FPQ), and (iii) periinsular posterior quadrantectomy (PIPQ). After a median follow-up period of 6 years, 12/13 patients had Engel's Class I seizure outcome. CONCLUSION: The results of surgery for posterior quadrantic epilepsy have yielded excellent seizure outcomes in 92% of the patients in the series with no mortality or major morbidity. The incorporation of disconnective techniques in multilobar surgery has maintained the excellent results obtained earlier with resective surgery.

K. J. Gummerus Osakeyhtiö 10/11 1959

Kirje 10.11.1959