From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond

The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observations in the twentieth century. The connection between the two areas was first observed through Montgomery's work on the pair correlation of zeros of the Riemann zeta function. As its generalizations and consequences have motivated much of the following work, and to this day remains one of the most important outstanding conjectures in the field, it occupies a central role in our discussion below. We describe some of the many techniques and results from the past sixty years, especially the important roles played by numerical and experimental investigations, that led to the discovery of the connections and progress towards understanding the behaviors. In our survey of these two areas, we describe the common mathematics that explains the remarkable universality. We conclude with some thoughts on what might lie ahead in the pair correlation of zeros of the zeta function, and other similar quantities.Comment: Version 1.1, 50 pages, 6 figures. To appear in "Open Problems in Mathematics", Editors John Nash and Michael Th. Rassias. arXiv admin note: text overlap with arXiv:0909.491

Higher-Order Nuclear-Polarizability Corrections in Atomic Hydrogen

Nuclear-polarizability corrections that go beyond unretarded-dipole approximation are calculated analytically for hydrogenic (atomic) S-states. These retardation corrections are evaluated numerically for deuterium and contribute -0.68 kHz, for a total polarization correction of 18.58(7) kHz. Our results are in agreement with one previous numerical calculation, and the retardation corrections completely account for the difference between two previous calculations. The uncertainty in the deuterium polarizability correction is substantially reduced. At the level of 0.01 kHz for deuterium, only three primary nuclear observables contribute: the electric polarizability, $\alpha_E$, the paramagnetic susceptibility, $\beta_M$, and the third Zemach moment, $_{(2)}$. Cartesian multipole decomposition of the virtual Compton amplitude and its concomitant gauge sum rules are used in the analysis.Comment: 26 pages, latex, 1 figure -- Submitted to Phys. Rev. C -- epsfig.sty require

Lack of effect of high-protein vs. high-carbohydrate meal intake on stress-related mood and eating behavior

<p>Abstract</p> <p>Background</p> <p>Consumption of meals with different macronutrients, especially high in carbohydrates, may influence stress-related eating behavior. We aimed to investigate whether consumption of high-protein vs. high-carbohydrate meals influences stress-related mood, food reward, i.e. 'liking' and 'wanting', and post-meal energy intake.</p> <p>Methods</p> <p>Participants (n = 38, 19m/19f, age = 25 ± 9 y, BMI = 25.0 ± 3.3 kg/m²) came to the university four times, fasted, once for a stress session receiving a high-protein meal, once for a rest session receiving a high-protein meal, once for a stress session receiving a high-carbohydrate meal and once for a rest session receiving a high-carbohydrate meal (randomized cross-over design). The high-protein and high-carbohydrate test meals (energy percentage protein/carbohydrate/fat 65/5/30 vs. 6/64/30) matched for energy density (4 kJ/g) and daily energy requirements (30%). Stress was induced using an ego-threatening test. Pre- and post-meal 'liking' and 'wanting' (for bread, filling, drinks, dessert, snacks, stationery (non-food alternative as control)) was measured by means of a computer test. Following the post-meal 'wanting' measurement, participants received and consumed their wanted food items (post-meal energy intake). Appetite profile (visual analogue scales), mood state (Profile Of Mood State and State Trait Anxiety Inventory questionnaires), and post-meal energy intake were measured.</p> <p>Results</p> <p>Participants showed increased feelings of depression and anxiety during stress (P < 0.01). Consumption of the test meal decreased hunger, increased satiety, decreased 'liking' of bread and filling, and increased 'liking' of placebo and drinks (P < 0.0001). Food 'wanting' decreased pre- to post-meal (P < 0.0001). The high-protein vs. high-carbohydrate test meal induced lower subsequent 'wanting' and energy intake (1.7 ± 0.3 MJ vs. 2.5 ± 0.4 MJ) only in individuals characterized by disinhibited eating behavior (factor 2 Three Factor Eating Questionnaire, n = 16), during rest (P ≤ 0.01). This reduction in 'wanting' and energy intake following the high-protein meal disappeared during stress.</p> <p>Conclusions</p> <p>Consumption of a high-protein vs. high-carbohydrate meal appears to have limited impact on stress-related eating behavior. Only participants with high disinhibition showed decreased subsequent 'wanting' and energy intake during rest; this effect disappeared under stress. Acute stress overruled effects of consumption of high-protein foods.</p> <p>Trial registration</p> <p>The study was registered in the Dutch Trial Register (<a href="http://www.trialregister.nl/trialreg/admin/rctview.asp?TC=2040">NTR1904</a>). The protocol described here in this study deviates from the trial protocol approved by the Medical Ethical Committee of the Maastricht University as it comprises only a part of the approved trial protocol.</p

Effects of acute treatment with a tryptophan-rich protein hydrolysate on plasma amino acids, mood and emotional functioning in older women

RATIONALE: Effective functioning of the neurotransmitter serotonin is important for optimal cognitive and emotional function. Dietary supplements able to increase availability to the brain of the precursor amino acid, tryptophan (TRP), and thereby enhance serotonin synthesis, can have measurable impact on these psychological processes. OBJECTIVES: This study involves a randomised controlled trial of a TRP-rich egg-white protein hydrolysate (DSM Nutritional Products Ltd., Switzerland) on plasma amino acids, cognition, mood and emotional processing in older women. METHODS: Following a baseline test day without treatment, 60 healthy women aged 45–65 years received drinks containing either 2 or 4 g of TRP-rich protein hydrolysate product or 3.11 g casein hydrolysate as a control. One hour later, they undertook a 2-h battery of cognitive and emotional tests. RESULTS: The TRP-rich protein hydrolysate produced the expected dose-dependent increase in the ratio of plasma TRP to competing large neutral amino acids. TRP-rich protein hydrolysate (2 g only) prevented both the decline in wellbeing and increase in fatigue seen over the test session in the control group. This treatment dose resulted in a significant shift in emotional processing towards positive words and reduced negative bias in assessing negative facial expressions. Effects on cognition were small and not statistically reliable and are not reported here. However, there was no evidence for any adverse effects. CONCLUSIONS: Consumption of a low dose of TRP-rich protein hydrolysate may have beneficial effects on emotional function that could promote feelings of wellbeing, possibly conferring resistance to deterioration in mood in healthy subjects or depressive episodes

Intrauterine Growth Retarded Progeny of Pregnant Sows Fed High Protein:Low Carbohydrate Diet Is Related to Metabolic Energy Deficit

High and low protein diets fed to pregnant adolescent sows led to intrauterine growth retardation (IUGR). To explore underlying mechanisms, sow plasma metabolite and hormone concentrations were analyzed during different pregnancy stages and correlated with litter weight (LW) at birth, sow body weight and back fat thickness. Sows were fed diets with low (6.5%, LP), adequate (12.1%, AP), and high (30%, HP) protein levels, made isoenergetic by adjusted carbohydrate content. At −5, 24, 66, and 108 days post coitum (dpc) fasted blood was collected. At 92 dpc, diurnal metabolic profiles were determined. Fasted serum urea and plasma glucagon were higher due to the HP diet. High density lipoprotein cholesterol (HDLC), %HDLC and cortisol were reduced in HP compared with AP sows. Lowest concentrations were observed for serum urea and protein, plasma insulin-like growth factor-I, low density lipoprotein cholesterol, and progesterone in LP compared with AP and HP sows. Fasted plasma glucose, insulin and leptin concentrations were unchanged. Diurnal metabolic profiles showed lower glucose in HP sows whereas non-esterified fatty acids (NEFA) concentrations were higher in HP compared with AP and LP sows. In HP and LP sows, urea concentrations were 300% and 60% of AP sows, respectively. Plasma total cholesterol was higher in LP than in AP and HP sows. In AP sows, LW correlated positively with insulin and insulin/glucose and negatively with glucagon/insulin at 66 dpc, whereas in HP sows LW associated positively with NEFA. In conclusion, IUGR in sows fed high protein∶low carbohydrate diet was probably due to glucose and energy deficit whereas in sows with low protein∶high carbohydrate diet it was possibly a response to a deficit of indispensable amino acids which impaired lipoprotein metabolism and favored maternal lipid disposal

Psychological Stress-Induced, IDO1-Dependent Tryptophan Catabolism: Implications on Immunosuppression in Mice and Humans

It is increasingly recognized that psychological stress influences inflammatory responses and mood. Here, we investigated whether psychological stress (combined acoustic and restraint stress) activates the tryptophan (Trp) catabolizing enzyme indoleamine 2,3-dioxygenase 1(IDO1) and thereby alters the immune homeostasis and behavior in mice. We measured IDO1 mRNA expression and plasma levels of Trp catabolites after a single 2-h stress session and in repeatedly stressed (4.5-days stress, 2-h twice a day) naïve BALB/c mice. A role of cytokines in acute stress-induced IDO1 activation was studied after IFNγ and TNFα blockade and in IDO1−/− mice. RU486 and 1-Methyl-L-tryptophan (1-MT) were used to study role of glucocorticoids and IDO1 on Trp depletion in altering the immune and behavioral response in repeatedly stressed animals. Clinical relevance was addressed by analyzing IDO1 activity in patients expecting abdominal surgery. Acute stress increased the IDO1 mRNA expression in brain, lung, spleen and Peyer's patches (max. 14.1±4.9-fold in brain 6-h after stress) and resulted in a transient depletion of Trp (−25.2±6.6%) and serotonin (−27.3±4.6%) from the plasma measured 6-h after stress while kynurenine levels increased 6-h later (11.2±9.3%). IDO1 mRNA up-regulation was blocked by anti-TNFα and anti-IFNγ treatment. Continuous IDO1 blockade by 1-MT but not RU486 treatment normalized the anti-bacterial defense and attenuated increased IL-10 inducibility in splenocytes after repeated stress as it reduced the loss of body weight and behavioral alterations. Moreover, kynurenic acid which remained increased in 1-MT treated repeatedly stressed mice was identified to reduce the TNFα inducibility of splenocytes in vitro and in vivo. Thus, psychological stress stimulates cytokine-driven IDO1 activation and Trp depletion which seems to have a central role for developing stress-induced immunosuppression and behavioral alteration. Since patients showed Trp catabolism already prior to surgery, IDO is also a possible target enzyme for humans modulating immune homeostasis and mood

Nutritional therapies for mental disorders

According to the Diagnostic and Statistical Manual of Mental Disorders, 4 out of the 10 leading causes of disability in the US and other developed countries are mental disorders. Major depression, bipolar disorder, schizophrenia, and obsessive compulsive disorder (OCD) are among the most common mental disorders that currently plague numerous countries and have varying incidence rates from 26 percent in America to 4 percent in China. Though some of this difference may be attributable to the manner in which individual healthcare providers diagnose mental disorders, this noticeable distribution can be also explained by studies which show that a lack of certain dietary nutrients contribute to the development of mental disorders. Notably, essential vitamins, minerals, and omega-3 fatty acids are often deficient in the general population in America and other developed countries; and are exceptionally deficient in patients suffering from mental disorders. Studies have shown that daily supplements of vital nutrients often effectively reduce patients' symptoms. Supplements that contain amino acids also reduce symptoms, because they are converted to neurotransmitters that alleviate depression and other mental disorders. Based on emerging scientific evidence, this form of nutritional supplement treatment may be appropriate for controlling major depression, bipolar disorder, schizophrenia and anxiety disorders, eating disorders, attention deficit disorder/attention deficit hyperactivity disorder (ADD/ADHD), addiction, and autism. The aim of this manuscript is to emphasize which dietary supplements can aid the treatment of the four most common mental disorders currently affecting America and other developed countries: major depression, bipolar disorder, schizophrenia, and obsessive compulsive disorder (OCD)

Functional connectivity underlying hedonic response to food in female adolescents with atypical AN: the role of somatosensory and salience networks.

Atypical anorexia nervosa (AN) usually occurs during adolescence. Patients are often in the normal-weight range at diagnosis; however, they often present with signs of medical complications and severe restraint over eating, body dissatisfaction, and low self-esteem. We investigated functional circuitry underlying the hedonic response in 28 female adolescent patients diagnosed with atypical AN and 33 healthy controls. Participants were shown images of food with high (HC) or low (LC) caloric content in alternating blocks during functional MRI. The HC > LC contrast was calculated. Based on the previous literature on full-threshold AN, we hypothesized that patients would exhibit increased connectivity in areas involved in sensory processing and bottom-up responses, coupled to increased connectivity from areas related to top-down inhibitory control, compared with controls. Patients showed increased connectivity in pathways related to multimodal somatosensory processing and memory retrieval. The connectivity was on the other hand decreased in patients in salience and attentional networks, and in a wide cerebello-occipital network. Our study was the first investigation of food-related neural response in atypical AN. Our findings support higher somatosensory processing in patients in response to HC food images compared with controls, however HC food was less efficient than LC food in engaging patients' bottom-up salient responses, and was not associated with connectivity increases in inhibitory control regions. These findings suggest that the psychopathological mechanisms underlying food restriction in atypical AN differ from full-threshold AN. Elucidating the mechanisms underlying the development and maintenance of eating behavior in atypical AN might help designing specific treatment strategies

Serotonin, genetic variability, behaviour, and psychiatric disorders - a review

Brain monoamines, and serotonin in particular, have repeatedly been shown to be linked to different psychiatric conditions such as depression, anxiety, antisocial behaviour, and dependence. Many studies have implicated genetic variability in the genes encoding monoamine oxidase A (MAOA) and the serotonin transporter (5HTT) in modulating susceptibility to these conditions. Paradoxically, the risk variants of these genes have been shown, in vitro, to increase levels of serotonin, although many of the conditions are associated with decreased levels of serotonin. Furthermore, in adult humans, and monkeys with orthologous genetic polymorphisms, there is no observable correlation between these functional genetic variants and the amount or activity of the corresponding proteins in the brain. These seemingly contradictory data might be explained if the association between serotonin and these behavioural and psychiatric conditions were mainly a consequence of events taking place during foetal and neonatal brain development. In this review we explore, based on recent research, the hypothesis that the dual role of serotonin as a neurotransmitter and a neurotrophic factor has a significant impact on behaviour and risk for neuropsychiatric disorders through altered development of limbic neurocircuitry involved in emotional processing, and development of the serotonergic neurons, during early brain development