Golden Ratio Versus Pi as Random Sequence Sources for Monte Carlo Integration

We discuss here the relative merits of these numbers as possible random sequence sources. The quality of these sequences is not judged directly based on the outcome of all known tests for the randomness of a sequence. Instead, it is determined implicitly by the accuracy of the Monte Carlo integration in a statistical sense. Since our main motive of using a random sequence is to solve real world problems, it is more desirable if we compare the quality of the sequences based on their performances for these problems in terms of quality/accuracy of the output. We also compare these sources against those generated by a popular pseudo-random generator, viz., the Matlab rand and the quasi-random generator ha/ton both in terms of error and time complexity. Our study demonstrates that consecutive blocks of digits of each of these numbers produce a good random sequence source. It is observed that randomly chosen blocks of digits do not have any remarkable advantage over consecutive blocks for the accuracy of the Monte Carlo integration. Also, it reveals that pi is a better source of a random sequence than theta when the accuracy of the integration is concerned

Should Pruning be a Pre-Processor of any Linear System?

There are many real-world problems whose mathematical models turn out to be linear systems Ax = b, where A is an m x n matrix. Each equation of the linear system is an information. An information, in a physical problem, such as 4 mangoes, 6 bananas, and 5 oranges cost $10, is mathematically modeled as an equation 4x(sub 1) + 6x(sub 2) + 5x(sub 3) = 10 , where x(sub 1), x(sub 2), x(sub 3) are each cost of one mango, that of one banana, and that of one orange, respectively. All the information put together in a specified context, constitutes the physical problem and need not be all distinct. Some of these could be redundant, which cannot be readily identified by inspection. The resulting mathematical model will thus have equations corresponding to this redundant information and hence are linearly dependent and thus superfluous. Consequently, these equations once identified should be better pruned in the process of solving the system. The benefits are (i) less computation and hence less error and consequently a better quality of solution and (ii) reduced storage requirements. In literature, the pruning concept is not in vogue so far although it is most desirable. It is assumed that at least one information, i.e. one equation is known to be correct and which will be our first equation. In a numerical linear system, the system could be slightly inconsistent or inconsistent of varying degree. If the system is too inconsistent, then we should fall back on to the physical problem (PP), check the correctness of the PP derived from the material universe, modify it, if necessary, and then check the corresponding mathematical model (MM) and correct it. In nature/material universe, inconsistency is completely nonexistent. If the MM becomes inconsistent, it could be due to error introduced by the concerned measuring device and/or due to assumptions made on the PP to obtain an MM which is relatively easily solvable or simply due to human error. No measuring device can usually measure a quantity with an accuracy greater that 0.005% or, equivalently with a relative error less than 0.005%. Hence measurement error is unavoidable in a numerical linear system when the quantities are continuous (or even discrete with extremely large number). Assumptions, though not desirable, are usually made when we find the problem sufficiently difficult to be solved within the available means/tools/resources and hence distort the PP and the corresponding MM. The . error thus introduced in the system could (not always necessarily though) make the system somewhat inconsistent. If the inconsistency (contradiction) is too much then one should definitely not proceed to solve the system in terms of getting a least-squares solution or the minimum-norm least-squares solution. All these solutions will be invariably of no real-world use. If, on the other hand, inconsistency is reasonably low, i.e. the system is near-consistent or, equivalently, has near-linearly-dependent rows, then the foregoing solutions are useful. Pruning in such a near-consistent system should be performed based on the desired accuracy and on the definition of near-linear dependence. In this article, we discuss pruning over various kinds of linear systems and strongly suggest its use as a pre-processor or as a part of an algorithm. Ideally pruning should (i) be a part of the solution process (algorithm) of the system, (ii) reduce both computational error and complexity of the process, and (iii) take into account the numerical zero defined in the context. These are precisely what we achieve through our proposed O(mn2) algorithm presented in Matlab, that uses a subprogram of solving a single linear equation and that has embedded in it the pruning

Prediction of early weight gain during psychotropic treatment using a combinatorial model with clinical and genetic markers.

Psychotropic drugs can induce significant (>5%) weight gain (WG) already after 1 month of treatment, which is a good predictor for major WG at 3 and 12 months. The large interindividual variability of drug-induced WG can be explained in part by genetic and clinical factors. The aim of this study was to determine whether extensive analysis of genes, in addition to clinical factors, can improve prediction of patients at risk for more than 5% WG at 1 month of treatment. Data were obtained from a 1-year naturalistic longitudinal study, with weight monitoring during weight-inducing psychotropic treatment. A total of 248 Caucasian psychiatric patients, with at least baseline and 1-month weight measures, and with compliance ascertained were included. Results were tested for replication in a second cohort including 32 patients. Age and baseline BMI were associated significantly with strong WG. The area under the curve (AUC) of the final model including genetic (18 genes) and clinical variables was significantly greater than that of the model including clinical variables only (AUCfinal: 0.92, AUCclinical: 0.75, P<0.0001). Predicted accuracy increased by 17% with genetic markers (Accuracyfinal: 87%), indicating that six patients must be genotyped to avoid one misclassified patient. The validity of the final model was confirmed in a replication cohort. Patients predicted before treatment as having more than 5% WG after 1 month of treatment had 4.4% more WG over 1 year than patients predicted to have up to 5% WG (P≤0.0001). These results may help to implement genetic testing before starting psychotropic drug treatment to identify patients at risk of important WG

Prospective associations of depression subtypes with cardio-metabolic risk factors in the general population.

The mechanisms and temporal sequence underlying the association between major depressive disorder (MDD) and cardio-metabolic diseases are still poorly understood. Recent research suggests subtyping depression to study the mechanisms underlying its association with biological correlates. Accordingly, our aims were to (1) assess the prospective associations of the atypical, melancholic and unspecified subtypes of MDD with changes of fasting glucose, high-density lipoprotein-cholesterol, triglycerides, systolic blood pressure and the incidence of the metabolic syndrome, (2) determine the potential mediating role of inflammatory marker or adipokine concentrations, eating behaviors and changes in waist circumference during follow-up. Data stemmed from CoLaus|PsyCoLaus, a prospective cohort study including 35-66-year-old randomly selected residents of an urban area. Among the Caucasian participants who underwent the physical and psychiatric baseline evaluations, 2813 (87% participation rate) also accepted the physical follow-up exam (mean follow-up duration=5.5 years). Symptoms of mental disorders were elicited using a semi-structured interview. The atypical MDD subtype, and only this subtype, was prospectively associated with a higher incidence of the metabolic syndrome (OR=2.49; 95% CI 1.30-4.77), a steeper increase of waist circumference (β=2.41; 95% CI 1.19-3.63) and independently of this, with a steeper increase of the fasting glucose level (β=131; 95% CI 38-225) during follow-up. These associations were not attributable to or mediated by inflammatory marker or adipokine concentrations, eating behaviors, comorbid psychiatric disorders or lifestyle factors. Accordingly, our results further support the subtyping of MDD and highlight the particular need for prevention and treatment of metabolic consequences in patients with atypical MDD

The specificity of the familial aggregation of early-onset bipolar disorder: A controlled 10-year follow-up study of offspring of parents with mood disorders.

BACKGROUND: Two major sources of heterogeneity of mood disorders that have been demonstrated in clinical, family and genetic studies are the mood disorder subtype (i.e. bipolar (BPD) and major depressive disorder (MDD)) and age of onset of mood episodes. Using a prospective high-risk study design, our aims were to test the specificity of the parent-child transmission of BPD and MDD and to establish the risk of psychopathology in offspring in function of the age of onset of the parental disorder. METHODS: Clinical information was collected on 208 probands (n=81 with BPD, n=64 with MDD, n=63 medical controls) as well as their 202 spouses and 372 children aged 6-17 years at study entry. Parents and children were directly interviewed every 3 years (mean duration of follow-up=10.6 years). Parental age of onset was dichotomized at age 21. RESULTS: Offspring of parents with early onset BPD entailed a higher risk of BPD HR=7.9(1.8-34.6) and substance use disorders HR=5.0(1.1-21.9) than those with later onset and controls. Depressive disorders were not significantly increased in offspring regardless of parental mood disorder subtype or age of onset. LIMITATIONS: Limited sample size, age of onset in probands was obtained retrospectively, age of onset in co-parents was not adequately documented, and a quarter of the children had no direct interview. CONCLUSIONS: Our results provide support for the independence of familial aggregation of BPD from MDD and the heterogeneity of BPD based on patterns of onset. Future studies should further investigate correlates of early versus later onset BPD

Influence of MCHR2 and MCHR2-AS1 Genetic Polymorphisms on Body Mass Index in Psychiatric Patients and In Population-Based Subjects with Present or Past Atypical Depression.

Obesity development during psychotropic treatments represents a major health issue in psychiatry. Melanin-concentrating hormone receptor 2 (MCHR2) is a central receptor involved in energy homeostasis. MCHR2 shares its promoter region with MCHR2-AS1, a long antisense non-coding RNA. The aim of this study was to determine whether tagging single nucleotide polymorphisms (tSNPs) of MCHR2 and MCHR2-AS1 are associated with the body mass index (BMI) in the psychiatric and in the general population. The influence of MCHR2 and MCHR2-AS1 tSNPs on BMI was firstly investigated in a discovery psychiatric sample (n1 = 474). Positive results were tested for replication in two other psychiatric samples (n2 = 164, n3 = 178) and in two population-based samples (CoLaus, n4 = 5409; GIANT, n5 = 113809). In the discovery sample, TT carriers of rs7754794C>T had 1.08 kg/m2 (p = 0.04) lower BMI as compared to C-allele carriers. This observation was replicated in an independent psychiatric sample (-2.18 kg/m2; p = 0.009). The association of rs7754794C>T and BMI seemed stronger in subjects younger than 45 years (median of age). In the population-based sample, a moderate association was observed (-0.17 kg/m2; p = 0.02) among younger individuals (<45y). Interestingly, this association was totally driven by patients meeting lifetime criteria for atypical depression, i.e. major depressive episodes characterized by symptoms such as an increased appetite. Indeed, patients with atypical depression carrying rs7754794-TT had 1.17 kg/m2 (p = 0.04) lower BMI values as compared to C-allele carriers, the effect being stronger in younger individuals (-2.50 kg/m2; p = 0.03; interaction between rs7754794 and age: p-value = 0.08). This study provides new insights on the possible influence of MCHR2 and/or MCHR2-AS1 on obesity in psychiatric patients and on the pathophysiology of atypical depression

Anomalous codeposition of cobalt and ruthenium from chloride-sulfate baths

Codeposition of Ru and Co was studied at room temperature and at 50oC with various Ru3+ and Co2+ concentrations in the electrolyte. The codeposition of Co and Ru proved to be anomalous since no pure Ru could be obtained in the presence of Co2+ in the electrolyte, but a significant Co incorporation into the deposit was detected at potentials where the deposition of pure Co was not possible. The composition of the deposits varied monotonously with the change of the concentration ratio of Co2+ and Ru3+. The deposition of Ru was much hindered and the current efficiency was a few percent only when the molar fraction of Co in the deposit was low. Continuous deposits could be obtained only when the molar fraction of Co in the deposit was at least 40 at.%. The deposit morphology was related to the molar fraction of Co in the deposit. The X-ray diffractograms are in conformity with a hexagonal close-packed alloy and indicate the formation of nanocrystalline deposits. Two-pulse plating did not lead to a multilayer but to a Co-rich alloy. Magnetoresistance of the samples decreased with increasing Ru content

N-acetylcysteine in a Double-Blind Randomized Placebo-Controlled Trial: Toward Biomarker-Guided Treatment in Early Psychosis.

Biomarker-guided treatments are needed in psychiatry, and previous data suggest oxidative stress may be a target in schizophrenia. A previous add-on trial with the antioxidant N-acetylcysteine (NAC) led to negative symptom reductions in chronic patients. We aim to study NAC's impact on symptoms and neurocognition in early psychosis (EP) and to explore whether glutathione (GSH)/redox markers could represent valid biomarkers to guide treatment. In a double-blind, randomized, placebo-controlled trial in 63 EP patients, we assessed the effect of NAC supplementation (2700 mg/day, 6 months) on PANSS, neurocognition, and redox markers (brain GSH [GSHmPFC], blood cells GSH levels [GSHBC], GSH peroxidase activity [GPxBC]). No changes in negative or positive symptoms or functional outcome were observed with NAC, but significant improvements were found in favor of NAC on neurocognition (processing speed). NAC also led to increases of GSHmPFC by 23% (P = .005) and GSHBC by 19% (P = .05). In patients with high-baseline GPxBC compared to low-baseline GPxBC, subgroup explorations revealed a link between changes of positive symptoms and changes of redox status with NAC. In conclusion, NAC supplementation in a limited sample of EP patients did not improve negative symptoms, which were at modest baseline levels. However, NAC led to some neurocognitive improvements and an increase in brain GSH levels, indicating good target engagement. Blood GPx activity, a redox peripheral index associated with brain GSH levels, could help identify a subgroup of patients who improve their positive symptoms with NAC. Thus, future trials with antioxidants in EP should consider biomarker-guided treatment

Impact of HSD11B1 polymorphisms on BMI and components of the metabolic syndrome in patients receiving psychotropic treatments.

BACKGROUND: Metabolic syndrome (MetS) associated with psychiatric disorders and psychotropic treatments represents a major health issue. 11β-Hydroxysteroid dehydrogenase type 1 (11β-HSD1) is an enzyme that catalyzes tissue regeneration of active cortisol from cortisone. Elevated enzymatic activity of 11β-HSD1 may lead to the development of MetS. METHODS: We investigated the association between seven HSD11B1 gene (encoding 11β-HSD1) polymorphisms and BMI and MetS components in a psychiatric sample treated with potential weight gain-inducing psychotropic drugs (n=478). The polymorphisms that survived Bonferroni correction were analyzed in two independent psychiatric samples (nR1=168, nR2=188) and in several large population-based samples (n1=5338; n2=123 865; n3>100 000). RESULTS: HSD11B1 rs846910-A, rs375319-A, and rs4844488-G allele carriers were found to be associated with lower BMI, waist circumference, and diastolic blood pressure compared with the reference genotype (Pcorrected<0.05). These associations were exclusively detected in women (n=257) with more than 3.1 kg/m, 7.5 cm, and 4.2 mmHg lower BMI, waist circumference, and diastolic blood pressure, respectively, in rs846910-A, rs375319-A, and rs4844488-G allele carriers compared with noncarriers (Pcorrected<0.05). Conversely, carriers of the rs846906-T allele had significantly higher waist circumference and triglycerides and lower high-density lipoprotein-cholesterol exclusively in men (Pcorrected=0.028). The rs846906-T allele was also associated with a higher risk of MetS at 3 months of follow-up (odds ratio: 3.31, 95% confidence interval: 1.53-7.17, Pcorrected=0.014). No association was observed between HSD11B1 polymorphisms and BMI and MetS components in the population-based samples. CONCLUSIONS: Our results indicate that HSD11B1 polymorphisms may contribute toward the development of MetS in psychiatric patients treated with potential weight gain-inducing psychotropic drugs, but do not play a significant role in the general population

Influence of CRTC1 Polymorphisms on Body Mass Index and Fat Mass in Psychiatric Patients and the General Adult Population.

IMPORTANCE There is a high prevalence of obesity in psychiatric patients, possibly leading to metabolic complications and reducing life expectancy. The CREB-regulated transcription coactivator 1 (CRTC1) gene is involved in energy balance and obesity in animal models, but its role in human obesity is unknown. OBJECTIVE To determine whether polymorphisms within the CRTC1 gene are associated with adiposity markers in psychiatric patients and the general population. DESIGN, SETTING, AND PARTICIPANTS Retrospective and prospective data analysis and population-based samples at Lausanne and Geneva university hospitals in Switzerland and a private clinic in Lausanne, Switzerland. The effect of 3 CRTC1 polymorphisms on body mass index (BMI) and/or fat mass was investigated in a discovery cohort of psychiatric outpatients taking weight gain-inducing psychotropic drugs (sample 1, n = 152). The CRTC1 variant that was significantly associated with BMI and survived Bonferroni corrections for multiple comparison was then replicated in 2 independent psychiatric samples (sample 2, n = 174 and sample 3, n = 118) and 2 white population-based samples (sample 4, n = 5338 and sample 5, n = 123 865). INTERVENTION Noninterventional studies. MAIN OUTCOME AND MEASURE Difference in BMI and/or fat mass between CRTC1 genotype groups. RESULTS Among the CRTC1 variants tested in the first psychiatric sample, only rs3746266A>G was associated with BMI (Padjusted = .003). In the 3 psychiatric samples, carriers of the rs3746266 G allele had a lower BMI than noncarriers (AA genotype) (sample 1, P = .001; sample 2, P = .05; and sample 3, P = .0003). In the combined analysis, excluding patients taking other weight gain-inducing drugs, G allele carriers (n = 98) had a 1.81-kg/m2 lower BMI than noncarriers (n = 226; P < .0001). The strongest association was observed in women younger than 45 years, with a 3.87-kg/m2 lower BMI in G allele carriers (n = 25) compared with noncarriers (n = 48; P < .0001), explaining 9% of BMI variance. In the population-based samples, the T allele of rs6510997C>T (a proxy of the rs3746266 G allele; r2 = 0.7) was associated with lower BMI (sample 5, n = 123 865; P = .01) and fat mass (sample 4, n = 5338; P = .03). The strongest association with fat mass was observed in premenopausal women (n = 1192; P = .02). CONCLUSIONS AND RELEVANCE These findings suggest that CRTC1 contributes to the genetics of human obesity in psychiatric patients and the general population. Identification of high-risk subjects could contribute to a better individualization of the pharmacological treatment in psychiatry