Further analysis of the connected moments expansion

We apply the connected moments expansion to simple quantum--mechanical examples and show that under some conditions the main equations of the approach are no longer valid. In particular we consider two--level systems, the harmonic oscillator and the pure quartic oscillator.Comment: 19 pages; 2 tables; 4 figure

Variational collocation for systems of coupled anharmonic oscillators

We have applied a collocation approach to obtain the numerical solution to the stationary Schr\"odinger equation for systems of coupled oscillators. The dependence of the discretized Hamiltonian on scale and angle parameters is exploited to obtain optimal convergence to the exact results. A careful comparison with results taken from the literature is performed, showing the advantages of the present approach.Comment: 14 pages, 10 table

Solution to the Equations of the Moment Expansions

We develop a formula for matching a Taylor series about the origin and an asymptotic exponential expansion for large values of the coordinate. We test it on the expansion of the generating functions for the moments and connected moments of the Hamiltonian operator. In the former case the formula produces the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We choose the harmonic oscillator and a strongly anharmonic oscillator as illustrative examples for numerical test. Our results reveal some features of the connected-moments expansion that were overlooked in earlier studies and applications of the approach

A new method for the solution of the Schrodinger equation

We present a new method for the solution of the Schrodinger equation applicable to problems of non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: An asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wave function and, finally, a short distance scale, in which the wave function is sizable. The key feature of our method is the introduction of an arbitrary parameter in the last two scales, which is then used to optimize a perturbative expansion in a suitable parameter. We apply the method to the quantum anharmonic oscillator and find excellent results.Comment: 4 pages, 4 figures, RevTex

Chiral quark-soliton model in the Wigner-Seitz approximation

In this paper we study the modification of the properties of the nucleon in the nucleus within the quark-soliton model. This is a covariant, dynamical model, which provides a non-linear representation of the spontaneously broken SU(2)_L X SU(2)_R symmetry of QCD. The effects of the nuclear medium are accounted for by using the Wigner-Seitz approximation and therefore reducing the complex many-body problem to a simpler single-particle problem. We find a minimum in the binding energy at finite density, a change in the isoscalar nucleon radius and a reduction of the in-medium pion decay constant. The latter is consistent with a partial restoration of chiral symmetry at finite density, which is predicted by other models.Comment: 30 pages, 13 figures; uses REVTeX and epsfi

“Hard to say, hard to understand, hard to live”: possible associations between neurologic language impairments and suicide risk

In clinical practice, patients with language impairments often exhibit suicidal ideation (SI) and suicidal behavior (SB, covering the entire range from suicide attempts, SA, to completed suicides). However, only few studies exist regarding this subject. We conducted a mini-review on the possible associations between neurologic language impairment (on the motor, comprehension, and semantic sides) and SI/SB. Based on the literature review, we hypothesized that language impairments exacerbate psychiatric comorbidities, which, in turn, aggravate language impairments. Patients trapped in this vicious cycle can develop SI/SB. The so-called “affective prosody” provides some relevant insights concerning the interaction between the different language levels and the world of emotions. This hypothesis is illustrated in a clinical case that we reported, consisting of the case of a 74-year old woman who was admitted to a psychiatric emergency department (ED) after a failed SA. Having suffered an ischemic stroke two years earlier, she suffered from incomplete Broca’s aphasia and dysprosody. She also presented with generalized anxiety and depressive symptoms. We observed that her language impairments were both aggravated by the exacerbations of her anxiety and depressive symptoms. In this patient, who had deficits on the motor side, these exacerbations were triggered by her inability to express herself, her emotional status, and suffering. SI was fluctuant, and—one year after the SA—she completed suicide. Further studies are needed to ascertain possible reciprocal and interacting associations between language impairments, psychiatric comorbidities, and SI/SB. They could enable clinicians to better understand their patient’s specific suffering, as brought on by language impairment, and contribute to the refining of suicide risk detection in this sub-group of affected patients

Relationship between Breast Cancer Surgical Treatment and Psychiatric Symptomatology: Which Sociodemographic and Clinical Factors Could Influence It? A Preliminary Study

This study aimed to investigate psychiatric symptomatology in a sample of patients affected by breast cancer undergoing surgery, evaluating the potential mediators on perceived stress levels, depression and hopelessness. The study was conducted on eighty-five patients with breast cancer, admitted consecutively to the Breast Unit of the IRCCS Ospedale Policlinico San Martino, between May 2018 and December 2019. Sociodemographic (age of diagnosis, gender, marital and occupational status, educational level, having children) and clinical (type and side of surgery, previous breast surgery, neoadjuvant chemotherapy and axillary dissection) characteristics were investigated through a semi-structured interview. The following rating scales were administered: Beck Depression Inventory, Beck Hopelessness Scale, and Perceived Stress Scale. Our findings indicate that the presence of children and of a partner was associated with a lower total score on the clinical dimensions evaluated. Furthermore, we found demolitive surgery to be a mediator between perceived stress and hopelessness, while history of previous breast surgery was found to be a mediator between demolitive surgery and perceived stress. In conclusion, patients affected by breast cancer undergoing more complex and demolitive surgery or with history of previous breast surgery should be mostly monitored from a psychological and psychiatric point of view from the beginning of treatments to evaluate the first manifestations of psychiatric symptomatology

Hyper/neuroinflammation in COVID-19 and suicide etiopathogenesis: Hypothesis for a nefarious collision?

open13Accumulating scientific and clinical evidence highlighted pathological hyperinflammation as a cardinal feature of SARS-CoV-2 infection and acute COVID-19 disease. With the emergence of long COVID-19 syndrome, several chronic health consequences, including neuropsychiatric sequelae, have gained attention from the public and medical communities. Since inflammatory mediators have also been accredited as putative biomarkers of suicidal ideations and behaviors, hyper- and neuroinflammation might share some colliding points, overlapping and being interconnected in the context of COVID-19. This review aims to provide a summary of current knowledge on the molecular and cellular mechanisms of COVID-19-associated hyper/neuroinflammation with focus on their relevance to the inflammatory hypothesis of suicide development. Subsequently, strategies to alleviate COVID-19 hyper/neuroinflammation by immunomodulatory agents (many of which at experimental stages) as well as psychopharmacologic/psychotherapeutic approaches are also mentioned. While suicide risk in COVID-19 survivors - until now little known - needs further analysis through longitudinal studies, current observations and mechanistic postulates warrant additional attention to this possibly emerging mental health concern.openCostanza, A.; Amerio, A.; Aguglia, A.; Serafini, G.; Amore, M.; Hasler, R.; Ambrosetti, J.; Bondolfi, G.; Sampogna, G.; Berardelli, I.; Fiorillo, A.; Pompili, M.; Nguyen, K.D.Costanza, A.; Amerio, A.; Aguglia, A.; Serafini, G.; Amore, M.; Hasler, R.; Ambrosetti, J.; Bondolfi, G.; Sampogna, G.; Berardelli, I.; Fiorillo, A.; Pompili, M.; Nguyen, K. D

Eigenvalue Problem in Two Dimensions for an Irregular Boundary II: Neumann Condition

We formulate a systematic elegant perturbative scheme for determining the eigenvalues of the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions when the normal derivative of {\psi} vanishes on an irregular closed curve. Unique feature of this method, unlike other perturbation schemes, is that it does not require a separate formalism to treat degeneracies. Degenerate states are handled equally elegantly as the non-degenerate ones. A real parameter, extracted from the parameters defining the irregular boundary, serves as a perturbation parameter in this scheme as opposed to earlier schemes where the perturbation parameter is an artificial one. The efficacy of the proposed scheme is gauged by calculating the eigenvalues for elliptical and supercircular boundaries and comparing with the results obtained numerically. We also present a simple and interesting semi-empirical formula, determining the eigenspectrum of the 2D Helmholtz equation with the Dirichlet or the Neumann condition for a supercircular boundary. A comparison of the eigenspectrum for several low-lying modes obtained by employing the formula with the corresponding numerical estimates shows good agreement for a wide range of the supercircular exponent.Comment: 26 pages, 12 figure