Lattice-point enumerators of ellipsoids

Minkowski's second theorem on successive minima asserts that the volume of a 0-symmetric convex body K over the covolume of a lattice \Lambda can be bounded above by a quantity involving all the successive minima of K with respect to \Lambda. We will prove here that the number of lattice points inside K can also accept an upper bound of roughly the same size, in the special case where K is an ellipsoid. Whether this is also true for all K unconditionally is an open problem, but there is reasonable hope that the inductive approach used for ellipsoids could be extended to all cases.Comment: 9 page

Some extremal functions in Fourier analysis, III

We obtain the best approximation in $L^1(\R)$, by entire functions of exponential type, for a class of even functions that includes $e^{-\lambda|x|}$, where $\lambda >0$, $\log |x|$ and $|x|^{\alpha}$, where $-1 < \alpha < 1$. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.Comment: 26 pages. Submitte

On the error term in Weyl's law for the Heisenberg manifolds (II)

In this paper we study the mean square of the error term in the Weyl's law of an irrational $(2l+1)$-dimensional Heisenberg manifold . An asymptotic formula is established

Bridging Alone: Religious Conservatism, Marital Homogamy, and Voluntary Association Membership

This study characterizes social insularity of religiously conservative American married couples by examining patterns of voluntary associationmembership. Constructing a dataset of 3938 marital dyads from the second wave of the National Survey of Families and Households, the author investigates whether conservative religious homogamy encourages membership in religious voluntary groups and discourages membership in secular voluntary groups. Results indicate that couples’ shared affiliation with conservative denominations, paired with beliefs in biblical authority and inerrancy, increases the likelihood of religious group membership for husbands and wives and reduces the likelihood of secular group membership for wives, but not for husbands. The social insularity of conservative religious groups appears to be reinforced by homogamy—particularly by wives who share faith with husbands

Short-term prediction of threatening and violent behaviour in an Acute Psychiatric Intensive Care Unit based on patient and environment characteristics

<p>Abstract</p> <p>Background</p> <p>The aims of the present study were to investigate clinically relevant patient and environment-related predictive factors for threats and violent incidents the first three days in a PICU population based on evaluations done at admittance.</p> <p>Methods</p> <p>In 2000 and 2001 all 118 consecutive patients were assessed at admittance to a Psychiatric Intensive Care Unit (PICU). Patient-related conditions as actuarial data from present admission, global clinical evaluations by physician at admittance and clinical nurses first day, a single rating with an observer rated scale scoring behaviours that predict short-term violence in psychiatric inpatients (The Brøset Violence Checklist (BVC)) at admittance, and environment-related conditions as use of segregation or not were related to the outcome measure Staff Observation Aggression Scale-Revised (SOAS-R). A multiple logistic regression analysis with SOAS-R as outcome variable was performed.</p> <p>Results</p> <p>The global clinical evaluations and the BVC were effective and more suitable than actuarial data in predicting short-term aggression. The use of segregation reduced the number of SOAS-R incidents.</p> <p>Conclusions</p> <p>In a naturalistic group of patients in a PICU segregation of patients lowers the number of aggressive and threatening incidents. Prediction should be based on clinical global judgment, and instruments designed to predict short-term aggression in psychiatric inpatients.</p> <p>Trial registrations</p> <p><a href="http://www.clinicaltrials.gov/ct2/show/NCT00184119">NCT00184119</a>/<a href="http://www.clinicaltrials.gov/ct2/show/NCT00184132">NCT00184132</a></p

Sex-Dependent Shared and Non-Shared Genetic Architecture Across Mood and Psychotic Disorders

BACKGROUND: Sex differences in incidence and/or presentation of schizophrenia (SCZ), major depressive disorder (MDD), and bipolar disorder (BIP) are pervasive. Previous evidence for shared genetic risk and sex differences in brain abnormalities across disorders suggest possible shared sex-dependent genetic risk. / METHODS: We conducted the largest to date genome-wide genotype–by–sex (GxS) interaction of risk for these disorders, using 85,735 cases (33,403 SCZ, 19,924 BIP, 32,408 MDD) and 109,946 controls from the Psychiatric Genomics Consortium (PGC) and iPSYCH. / RESULTS: Across disorders, genome-wide significant SNP-by-sex interaction was detected for a locus encompassing NKAIN2 (rs117780815; p=3.2×10−8), that interacts with sodium/potassium-transporting ATPase enzymes implicating neuronal excitability. Three additional loci showed evidence (p<1×10−6) for cross-disorder GxS interaction (rs7302529, p=1.6×10−7; rs73033497, p=8.8×10−7; rs7914279, p=6.4×10−7) implicating various functions. Gene-based analyses identified GxS interaction across disorders (p=8.97×10−7) with transcriptional inhibitor SLTM. Most significant in SCZ was a MOCOS gene locus (rs11665282; p=1.5×10−7), implicating vascular endothelial cells. Secondary analysis of the PGC-SCZ dataset detected an interaction (rs13265509; p=1.1×10−7) in a locus containing IDO2, a kynurenine pathway enzyme with immunoregulatory functions implicated in SCZ, BIP, and MDD. Pathway enrichment analysis detected significant GxS of genes regulating vascular endothelial growth factor (VEGF) receptor signaling in MDD (pFDR<0.05). / CONCLUSIONS: In the largest genome-wide GxS analysis of mood and psychotic disorders to date, there was substantial genetic overlap between the sexes. However, significant sex-dependent effects were enriched for genes related to neuronal development, immune and vascular functions across and within SCZ, BIP, and MDD at the variant, gene, and pathway enrichment levels

Quantitative EEG findings in patients with acute, brief depression combined with other fluctuating psychiatric symptoms: a controlled study from an acute psychiatric department

<p>Abstract</p> <p>Background</p> <p>Patients with brief depressive episodes and concurrent rapidly fluctuating psychiatric symptoms do not fit current diagnostic criteria and they can be difficult to diagnose and treat in an acute psychiatric setting. We wanted to study whether these patients had signs of more epileptic or organic brain dysfunction than patients with depression without additional symptomatology.</p> <p>Methods</p> <p>Sixteen acutely admitted patients diagnosed with a brief depressive episode as well as another concurrent psychiatric diagnosis were included. Sixteen patients with major depression served as controls. Three electroencephalographic studies (EEG) were visually interpreted and the background activity was also analysed with quantitative electroencephalography (QEEG).</p> <p>Results</p> <p>The group with brief depression and concurrent symptoms had multiple abnormal features in their standard EEG compared to patients with major depression, but they did not show significantly more epileptiform activity. They also had significantly higher temporal QEEG delta amplitude and interhemispheric temporal delta asymmetry.</p> <p>Conclusion</p> <p>Organic brain dysfunction may be involved in the pathogenesis of patients with brief depressive episodes mixed with rapidly fluctuating psychiatric symptoms. This subgroup of depressed patients should be investigated further in order to clarify the pathophysiology and to establish the optimal evaluation scheme and treatment in an acute psychiatric setting.</p