Significant Conditions on the Two-electron Reduced Density Matrix from the Constructive Solution of N-representability

We recently presented a constructive solution to the N-representability problem of the two-electron reduced density matrix (2-RDM)---a systematic approach to constructing complete conditions to ensure that the 2-RDM represents a realistic N-electron quantum system [D. A. Mazziotti, Phys. Rev. Lett. 108, 263002 (2012)]. In this paper we provide additional details and derive further N-representability conditions on the 2-RDM that follow from the constructive solution. The resulting conditions can be classified into a hierarchy of constraints, known as the (2,q)-positivity conditions where the q indicates their derivation from the nonnegativity of q-body operators. In addition to the known T1 and T2 conditions, we derive a new class of (2,3)-positivity conditions. We also derive 3 classes of (2,4)-positivity conditions, 6 classes of (2,5)-positivity conditions, and 24 classes of (2,6)-positivity conditions. The constraints obtained can be divided into two general types: (i) lifting conditions, that is conditions which arise from lifting lower (2,q)-positivity conditions to higher (2,q+1)-positivity conditions and (ii) pure conditions, that is conditions which cannot be derived from a simple lifting of the lower conditions. All of the lifting conditions and the pure (2,q)-positivity conditions for q>3 require tensor decompositions of the coefficients in the model Hamiltonians. Subsets of the new N-representability conditions can be employed with the previously known conditions to achieve polynomially scaling calculations of ground-state energies and 2-RDMs of many-electron quantum systems even in the presence of strong electron correlation

Structure of Fermionic Density Matrices: Complete N-representability Conditions

We present a constructive solution to the N-representability problem---a full characterization of the conditions for constraining the two-electron reduced density matrix (2-RDM) to represent an N-electron density matrix. Previously known conditions, while rigorous, were incomplete. Here we derive a hierarchy of constraints built upon (i) the bipolar theorem and (ii) tensor decompositions of model Hamiltonians. Existing conditions D, Q, G, T1, and T2, known classical conditions, and new conditions appear naturally. Subsets of the conditions are amenable to polynomial-time computations of strongly correlated systems

Superfluidity of a perfect quantum crystal

In recent years, experimental data were published which point to the possibility of the existence of superfluidity in solid helium. To investigate this phenomenon theoretically we employ a hierarchy of equations for reduced density matrices which describes a quantum system that is in thermodynamic equilibrium below the Bose-Einstein condensation point, the hierarchy being obtained earlier by the author. It is shown that the hierarchy admits solutions relevant to a perfect crystal (immobile) in which there is a frictionless flow of atoms, which testifies to the possibility of superfluidity in ideal solids. The solutions are studied with the help of the bifurcation method and some their peculiarities are found out. Various physical aspects of the problem, among them experimental ones, are discussed as well.Comment: 24 pages with 2 figures, version accepted for publication in Eur.Phys.J.

The class of the locus of intermediate Jacobians of cubic threefolds

We study the locus of intermediate Jacobians of cubic threefolds within the moduli space of complex principally polarized abelian fivefolds, and its generalization to arbitrary genus - the locus of abelian varieties with a singular odd two-torsion point on the theta divisor. Assuming that this locus has expected codimension (which we show to be true for genus up to 5), we compute the class of this locus, and of is closure in the perfect cone toroidal compactification, in the Chow, homology, and the tautological ring. We work out the cases of genus up to 5 in detail, obtaining explicit expressions for the classes of the closures of the locus of products of an elliptic curve and a hyperelliptic genus 3 curve, in moduli of principally polarized abelian fourfolds, and of the locus of intermediate Jacobians in genus 5. In the course of our computation we also deal with various intersections of boundary divisors of a level toroidal compactification, which is of independent interest in understanding the cohomology and Chow rings of the moduli spaces.Comment: v2: new section 9 on the geometry of the boundary of the locus of intermediate Jacobians of cubic threefolds. Final version to appear in Invent. Mat

Cd(II) and Pb(II) complexes of the polyether ionophorous antibiotic salinomycin

<p>Abstract</p> <p>Background</p> <p>The natural polyether ionophorous antibiotics are used for the treatment of coccidiosis in poultry and ruminants. They are effective agents against infections caused by Gram-positive microorganisms. On the other hand, it was found that some of these compounds selectively bind lead(II) ions in <it>in vivo </it>experiments, despite so far no Pb(II)-containing compounds of defined composition have been isolated and characterized. To assess the potential of polyether ionophores as possible antidotes in the agriculture, a detailed study on their <it>in vitro </it>complexation with toxic metal ions is required. In the present paper we report for the first time the preparation and the structure elucidation of salinomycin complexes with ions of cadmium(II) and lead(II).</p> <p>Results</p> <p>New metal(II) complexes of the polyether ionophorous antibiotic salinomycin with Cd(II) and Pb(II) ions were prepared and structurally characterized by IR, FAB-MS and NMR techniques. The spectroscopic information and elemental analysis data reveal that sodium salinomycin (SalNa) undergoes a reaction with heavy metal(II) ions to form [Cd(Sal)₂(H₂O)₂] (<b>1</b>) and [Pb(Sal)(NO₃)] (<b>2</b>), respectively. Abstraction of sodium ions from the cavity of the antibiotic is occurring during the complexation reaction. Salinomycin coordinates with cadmium(II) ions as a bidentate monoanionic ligand through the deprotonated carboxylic moiety and one of the hydroxyl groups to yield <b>1</b>. Two salinomycin anions occupy the equatorial plane of the Cd(II) center, while two water molecules take the axial positions of the inner coordination sphere of the metal(II) cation. Complex <b>2 </b>consists of monoanionic salinomycin acting in polydentate coordination mode in a molar ratio of 1: 1 to the metal ion with one nitrate ion for charge compensation.</p> <p>Conclusion</p> <p>The formation of the salinomycin heavy metal(II) complexes indicates a possible antidote activity of the ligand in case of chronic/acute intoxications likely to occur in the stock farming.</p

Effects of Ionomycin on Egg Activation and Early Development in Starfish

Ionomycin is a Ca2+-selective ionophore that is widely used to increase intracellular Ca2+ levels in cell biology laboratories. It is also occasionally used to activate eggs in the clinics practicing in vitro fertilization. However, neither the precise molecular action of ionomycin nor its secondary effects on the eggs' structure and function is well known. In this communication we have studied the effects of ionomycin on starfish oocytes and zygotes. By use of confocal microscopy, calcium imaging, as well as light and transmission electron microscopy, we have demonstrated that immature oocytes exposed to ionomycin instantly increase intracellular Ca2+ levels and undergo structural changes in the cortex. Surprisingly, when microinjected into the cells, ionomycin produced no Ca2+ increase. The ionomycin-induced Ca2+ rise was followed by fast alteration of the actin cytoskeleton displaying conspicuous depolymerization at the oocyte surface and in microvilli with concomitant polymerization in the cytoplasm. In addition, cortical granules were disrupted or fused with white vesicles few minutes after the addition of ionomycin. These structural changes prevented cortical maturation of the eggs despite the normal progression of nuclear envelope breakdown. At fertilization, the ionomycin-pretreated eggs displayed reduced Ca2+ response, no elevation of the fertilization envelope, and the lack of orderly centripetal translocation of actin fibers. These alterations led to difficulties in cell cleavage in the monospermic zygotes and eventually to a higher rate of abnormal development. In conclusion, ionomycin has various deleterious impacts on egg activation and the subsequent embryonic development in starfish. Although direct comparison is difficult to make between our findings and the use of the ionophore in the in vitro fertilization clinics, our results call for more defining investigations on the issue of a potential risk in artificial egg activation

On Traces of d-stresses in the Skeletons of Lower Dimensions of Piecewise-linear d-manifolds

We show how a d-stress on a piecewise-linear realization of an oriented (non-simplicial, in general) d-manifold in R d naturally induces stresses of lower dimensions on this manifold, and discuss implications of this construction to the analysis of self-stresses in spatial frameworks. The mappings we construct are not linear, but polynomial. In the 1860–70s J. C. Maxwell described an interesting relationship between self-stresses in planar frameworks and vertical projections of polyhedral 2-surfaces. We offer a spatial analog of Maxwell’s correspondence based on our polynomial mappings. By applying our main result we derive a class of three-dimensional spider webs similar to the two-dimensional spider webs described by Maxwell. We also conjecture an important property of our mappings that is Author: based on the lower bound theorem (g2(d +1) = dim Stress2 ≥ 0) for d-pseudomanifolds generically realized in R d+1 [12]

Severity of age-related hearing loss is associated with impaired activities of daily living

Background: age-related hearing loss is a common chronic condition; hence, it is important to understand its influence on the functional status of older adults. We assessed the association between hearing impairment with activity limitations as assessed by the activities of daily living (ADL) scale. Methods: a total of 1,952 Blue Mountains Hearing Study participants aged ≥60 years had their hearing levels measured using pure-tone audiometry. A survey instrument with questions on functional status as determined by the Older Americans Resources and Services ADL scale was administered. Results: one hundred and sixty-four (10.4%) participants reported ADL difficulty. A higher proportion of hearing impaired than non-impaired adults reported difficulties in performing three out of the seven basic ADL and six out of the seven instrumental ADL tasks. After multivariable adjustment, increased severity of hearing loss was associated with impaired ADL (Ptrend = 0.001). Subjects with moderate to severe hearing loss compared with those without, had a 2.9-fold increased likelihood of reporting difficulty in ADL, multivariate-adjusted odds ratio (OR): 2.87 [95% confidence interval (CI): 1.59–5.19]. Participants aged <75 years with hearing loss compared with those without, had 2-fold higher odds of impaired ADL. Having worn or wearing a hearing aid was also associated with a 2-fold increased likelihood of impaired ADL. Conclusion: functional status as measured by a common ADL scale is diminished in older hearing impaired adults. Our findings suggest that severely diminished hearing could make the difference between independence and the need for formal support services or placement.6 page(s

Incidence and predictors of hearing aid use and ownership among older adults with hearing loss

Purpose: The reasons are not clear as to why people who need hearing aids and possess them do not use them. We aimed to describe the incidence and predictors of hearing aid ownership and use among older adults. Methods: We included 2,015 Blue Mountains Hearing Study participants aged ≥55 years who were examined between 1997 and 1999 and 2002 and 2004. Hearing levels were measured with pure-tone audiometry. Results: The 5-year incidence of hearing aid use and ownership was 8.1% and 8.5%, respectively. Age was associated with incident hearing aid ownership and use, multivariable-adjusted odds ratio (OR) per decade increase in age of 1.79 (95% confidence interval [CI], 1.21-2.64) and of 1.66 (95% CI, 1.15-2.40), respectively. Any level of hearing loss (HL) at baseline predicted a 2.8-fold increased likelihood of using a hearing aid at follow-up. Hearing handicap was associated with 7% increased likelihood of incident aid use. Key reasons provided for not obtaining/using a hearing aid were: not recommended one (8.0%), its high cost (1.7%), and believing that they did not need one (9.0%). Conclusions: Incident hearing aid ownership and usage was relatively low among hearing impaired adults. Age, question-defined hearing handicap, and measured HL were significant predictors of incident hearing aid use/ownership.10 page(s