Solvable model of quantum microcanonical states

Accepted versio

Geometric aspects of space-time reflection symmetry in quantum mechanics

For nearly two decades, much research has been carried out on properties of physical systems described by Hamiltonians that are not Hermitian in the conventional sense, but are symmetric under space-time reflection; that is, they exhibit PT symmetry. Such Hamiltonians can be used to model the behavior of closed quantum systems, but they can also be replicated in open systems for which gain and loss are carefully balanced, and this has been implemented in laboratory experiments for a wide range of systems. Motivated by these ongoing research activities, we investigate here a particular theoretical aspect of the subject by unraveling the geometric structures of Hilbert spaces endowed with the parity and time-reversal operations, and analyze the characteristics ofPT -symmetric Hamiltonians. A canonical relation between aPT -symmetric operator and a Hermitian operator is established in a geometric setting. The quadratic form corresponding to the parity operator, in particular, gives rise to a natural partition of the Hilbert space into two halves corresponding to states having positive and negative PT norm. Positive definiteness of the norm can be restored by introducing a conjugation operator C ; this leads to a positive-definite inner product in terms of CPT conjugation

Lateral orbitofrontal cortex promotes trial-by-trial learning of risky, but not spatial, biases

Individual choices are not made in isolation but are embedded in a series of past experiences, decisions, and outcomes. The effects of past experiences on choices, often called sequential biases, are ubiquitous in perceptual and value-based decision-making, but their neural substrates are unclear. We trained rats to choose between cued guaranteed and probabilistic rewards in a task in which outcomes on each trial were independent. Behavioral variability often reflected sequential effects, including increased willingness to take risks following risky wins, and spatial ‘win-stay/lose-shift’ biases. Recordings from lateral orbitofrontal cortex (lOFC) revealed encoding of reward history and receipt, and optogenetic inhibition of lOFC eliminated rats’ increased preference for risk following risky wins, but spared other sequential effects. Our data show that different sequential biases are neurally dissociable, and the lOFC’s role in adaptive behavior promotes learning of more abstract biases (here, biases for the risky option), but not spatial ones

Hamiltonian for the zeros of the Riemann zeta function

A Hamiltonian operator ^H is constructed with the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function. The classical limit of ^H is 2xp, which is consistent with the Berry- Keating conjecture. While ^H is not Hermitian in the conventional sense, i ^H is PT symmetric with a broken PT symmetry, thus allowing for the possibility that all eigenvalues of ^H are real. A heuristic analysis is presented for the construction of the metric operator to de ne an inner-product space, on which the Hamiltonian is Hermitian. If the analysis presented here can be made rigorous to show that ^H is manifestly self-adjoint, then this implies that the Riemann hypothesis holds true

pp32 (ANP32A) Expression Inhibits Pancreatic Cancer Cell Growth and Induces Gemcitabine Resistance by Disrupting HuR Binding to mRNAs

The expression of protein phosphatase 32 (PP32, ANP32A) is low in poorly differentiated pancreatic cancers and is linked to the levels of HuR (ELAV1), a predictive marker for gemcitabine response. In pancreatic cancer cells, exogenous overexpression of pp32 inhibited cell growth, supporting its long-recognized role as a tumor suppressor in pancreatic cancer. In chemotherapeutic sensitivity screening assays, cells overexpressing pp32 were selectively resistant to the nucleoside analogs gemcitabine and cytarabine (ARA-C), but were sensitized to 5-fluorouracil; conversely, silencing pp32 in pancreatic cancer cells enhanced gemcitabine sensitivity. The cytoplasmic levels of pp32 increased after cancer cells are treated with certain stressors, including gemcitabine. pp32 overexpression reduced the association of HuR with the mRNA encoding the gemcitabine-metabolizing enzyme deoxycytidine kinase (dCK), causing a significant reduction in dCK protein levels. Similarly, ectopic pp32 expression caused a reduction in HuR binding of mRNAs encoding tumor-promoting proteins (e.g., VEGF and HuR), while silencing pp32 dramatically enhanced the binding of these mRNA targets. Low pp32 nuclear expression correlated with high-grade tumors and the presence of lymph node metastasis, as compared to patients' tumors with high nuclear pp32 expression. Although pp32 expression levels did not enhance the predictive power of cytoplasmic HuR status, nuclear pp32 levels and cytoplasmic HuR levels associated significantly in patient samples. Thus, we provide novel evidence that the tumor suppressor function of pp32 can be attributed to its ability to disrupt HuR binding to target mRNAs encoding key proteins for cancer cell survival and drug efficacy

Bidirectional Associations Between Sibling Relationships and Parental Support During Adolescence

Sibling relationships and parental support are important for adolescents’ development and well-being, yet both are likely to change during adolescence. Since adolescents participate in both the sibling relationship and the parent–child relationship, we can expect sibling relationships and parental support to be associated with each other. Theoretically, it can be expected that there is either a spillover from one relationship to another (congruence hypothesis) or that one relationship can compensate for the other (compensation hypothesis). However, research examining these associations in adolescence is limited. The present study longitudinally investigated the bidirectional associations between sibling relationships and parental support during adolescence. For five consecutive years, data were collected using self-reports of 428 families, consisting of a father, a mother, and two adolescent siblings. The mean ages of the first-born (52.8% males) and second-born (47.7% males) were 15 and 13 years at T1, respectively. For the second-born siblings, prospective associations were found between sibling relationships and adolescent-reported parental support in early adolescence, with no differences between same-sex and mixed-sex dyads. These associations were not found for first-born siblings or for parents’ reports of support. The findings suggest a spillover from the sibling relationship to adolescent-reported parental support only in early adolescence. Findings and implications are discussed in terms of the congruence/spillover and the compensation hypothesis

Is the NEI-VFQ-25 a useful tool in identifying visual impairment in an elderly population?

BACKGROUND: The use of self-report questionnaires to substitute for visual acuity measurement has been limited. We examined the association between visual impairment and self reported visual function in a population sample of older people in the UK. METHODS: Cross sectional study of people aged more than 75 years who initially participated in a trial of health screening. The association between 25-item National Eye Institute Visual Function Questionnaire (NEI-VFQ) scores and visual impairment (defined as an acuity of less than 6/18 in the better eye) was examined using logistic regression. RESULTS: Visual acuity and NEI-VFQ scores were obtained from 1807 participants (aged 77 to 101 years, 36% male), from 20 general practices throughout the UK. After adjustment for age, gender, practice and NEI-VFQ sub-scale scores, those complaining of poor vision in general were 4.77 times (95% CI 3.03 to 7.53) more likely to be visually impaired compared to those who did not report difficulty. Self-reported limitations with social functioning and dependency on others due to poor vision were also associated with visual impairment (odds ratios, 2.52, 95% CI 1.55 to 4.11; 1.73, 95% CI 1.05 to 2.86 respectively). Those reporting difficulties with near vision and colour vision were more likely to be visually impaired (odds ratios, 2.32, 95% CI 1.30 to 4.15; 2.25, 95% CI 1.35 to 3.73 respectively). Other NEI-VFQ sub-scale scores were unrelated to measures of acuity. Similar but weaker odds ratios were found with reduced visual acuity (defined as less than 6/12 in the better eye). Although differences in NEI-VFQ scores were small, scores were strongly associated with visual acuity, binocular status, and difference in acuity between eyes. CONCLUSION: NEI-VFQ questions regarding the quality of general vision, social functioning, visual dependency, near vision and colour vision are strongly and independently associated with an objective measure of visual impairment in an elderly population

Using twins to better understand sibling relationships

We compared the nature of the sibling relationship in dyads of varying genetic relatedness, employing a behavioural genetic design to estimate the contribution that genes and the environment have on this familial bond. Two samples were used—the Sisters and Brothers Study consisted of 173 families with two target non-twin children (mean ages = 7.42 and 5.22 years respectively); and the Twins, Family and Behaviour study included 234 families with two target twin children (mean age = 4.70 years). Mothers and fathers reported on their children’s relationship with each other, via a postal questionnaire (the Sisters and Brothers Study) or a telephone interview (the Twins, Family and Behaviour study). Contrary to expectations, no mean level differences emerged when monozygotic twin pairs, dizygotic twin pairs, and non-twin pairs were compared on their sibling relationship quality. Behavioural genetic analyses also revealed that the sibling bond was modestly to moderately influenced by the genetic propensities of the children within the dyad, and moderately to substantially influenced by the shared environment common to both siblings. In addition, for sibling negativity, we found evidence of twin-specific environmental influence—dizygotic twins showed more reciprocity than did non-twins. Our findings have repercussions for the broader application of results from future twin-based investigations

Interactive effects of mGlu5 and 5-HT2A receptors on locomotor activity in mice

RationaleMetabotropic glutamate (mGlu) receptors have been suggested to play a role in neuropsychiatric disorders including schizophrenia, drug abuse, and depression. Because serotonergic hallucinogens increase glutamate release and mGlu receptors modulate the response to serotonin (5-HT)(2A) activation, the interactions between serotonin 5-HT(2A) receptors and mGlu receptors may prove to be important for our understanding of these diseases.ObjectiveWe tested the effects of the serotonergic hallucinogen and 5-HT(2A) agonist, 2,5-dimethoxy-4-methylamphetamine (DOM), and the selective 5-HT(2A) antagonist, M100907, on locomotor activity in the mouse behavioral pattern monitor (BPM) in mGlu5 wild-type (WT) and knockout (KO) mice on a C57 background.ResultsBoth male and female mGlu5 KO mice showed locomotor hyperactivity and diminished locomotor habituation compared with their WT counterparts. Similarly, the mGlu5-negative allosteric modulator 2-methyl-6-(phenylethynyl)pyridine (MPEP) also increased locomotor hyperactivity, which was absent in mGlu5 KO mice. The locomotor hyperactivity in mGlu5 receptor KO mice was potentiated by DOM (0.5 mg/kg, subcutaneously (SC)) and attenuated by M100907 (1.0 mg/kg, SC). M100907 (0.1 mg/kg, SC) also blocked the hyperactivity induced by MPEP.ConclusionsThese studies demonstrated that loss of mGlu5 receptor activity either pharmacologically or through gene deletion leads to locomotor hyperactivity in mice. Additionally, the gene deletion of mGlu5 receptors increased the behavioral response to the 5-HT(2A) agonist DOM, suggesting that mGlu5 receptors either mitigate the behavioral effects of 5-HT(2A) hallucinogens or that mGlu5 KO mice show an increased sensitivity to 5-HT(2A) agonists. Taken together, these studies indicate a functional interaction between mGlu5 and 5-HT(2A) receptors