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

The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r^4) scaling

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral (ERI) tensor and the two-particle excitation amplitudes used in the parametric reduced density matrix (pRDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r4), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the traditional pRDM algorithm, somewhere between that of CCSD and CCSD(T).Comment: 11 pages, 1 figur

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

Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo

Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in imaginary time independently from the first, and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality, and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation.Comment: 11 page

Semirelativistic stability of N-boson systems bound by 1/r pair potentials

We analyze a system of self-gravitating identical bosons by means of a semirelativistic Hamiltonian comprising the relativistic kinetic energies of the involved particles and added (instantaneous) Newtonian gravitational pair potentials. With the help of an improved lower bound to the bottom of the spectrum of this Hamiltonian, we are able to enlarge the known region for relativistic stability for such boson systems against gravitational collapse and to sharpen the predictions for their maximum stable mass.Comment: 11 pages, considerably enlarged introduction and motivation, remainder of the paper unchange

Running towards amblyopia recovery

Amblyopia is a neurodevelopmental disorder of the visual cortex arising from abnormal visual experience early in life which is a major cause of impaired vision in infants and young children (prevalence around 3.5%). Current treatments such as eye patching are ineffective in a large number of patients, especially when applied after the juvenile critical period. Physical exercise has been recently shown to enhance adult visual cortical plasticity and to promote visual acuity recovery. With the aim to understand the potentialities for translational applications, we investigated the effects of voluntary physical activity on recovery of depth perception in adult amblyopic rats with unrestricted binocular vision; visual acuity recovery was also assessed. We report that three weeks of voluntary physical activity (free running) induced a marked and long-lasting recovery of both depth perception and visual acuity. In the primary visual cortex, ocular dominance recovered both for excitatory and inhibitory cells and was linked to activation of a specific intracortical GABAergic circuit

Investigating the role of Armadillo-related proteins in early land plants

Mosses evolved approximately 500 million years ago and were among the earliest plants to make the transition from water to land. Mosses are therefore placed at an ideal evolutionary position in which to understand how plant physiology and development has evolved from simple unicellular aquatic organisms to generate the huge diversity of complex modern day flowering plants. The moss Physcomitrella has the unique ability among known land plants to carry out homologous recombination at a similar efficiency to the yeast Saccharyomyces cerevisiae. Armadillo-related proteins play important roles in cellular processes both in animals and plants. In Arabidopsis, ARABIDILLO1 and ARABIDILLO2 control root system architecture. ARABIDILLO-like proteins have been identified extensively throughout the plant kingdom, including early-evolving moss and agriculturally important crops such as rice and maize. Three Physcomitrella ARABIDILLO homologues have been identified; PHYSCODILLO1A, PHYSCODILLO1B and PHYSCODILLO2. Cloning, sequencing and Southern blotting approaches confirmed that PHYSCODILLO2 was a single copy gene, whereas full-length PHYSCODILLO1A and PHYSCODILLO1B genes were 100% identical and exist in a tail-to-tail orientation with 8kb separating their stop codons. A number of physcodillo deletion mutants have been generated. Phenotypic analyses revealed that PHYSCODILLO proteins appear to play important roles during early developmental processes, including growth of filaments from protoplasts and spore germination.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Interleukin-9 regulates macrophage activation in the progressive multiple sclerosis brain.

BACKGROUND: Multiple sclerosis (MS) is an immune-mediated, chronic inflammatory, and demyelinating disease of the central nervous system (CNS). Several cytokines are thought to be involved in the regulation of MS pathogenesis. We recently identified interleukin (IL)-9 as a cytokine reducing inflammation and protecting from neurodegeneration in relapsing-remitting MS patients. However, the expression of IL-9 in CNS, and the mechanisms underlying the effect of IL-9 on CNS infiltrating immune cells have never been investigated. METHODS: To address this question, we first analyzed the expression levels of IL-9 in post-mortem cerebrospinal fluid of MS patients and the in situ expression of IL-9 in post-mortem MS brain samples by immunohistochemistry. A complementary investigation focused on identifying which immune cells express IL-9 receptor (IL-9R) by flow cytometry, western blot, and immunohistochemistry. Finally, we explored the effect of IL-9 on IL-9-responsive cells, analyzing the induced signaling pathways and functional properties. RESULTS: We found that macrophages, microglia, and CD4 T lymphocytes were the cells expressing the highest levels of IL-9 in the MS brain. Of the immune cells circulating in the blood, monocytes/macrophages were the most responsive to IL-9. We validated the expression of IL-9R by macrophages/microglia in post-mortem brain sections of MS patients. IL-9 induced activation of signal transducer and activator of transcription (STAT)1, STAT3, and STAT5 and reduced the expression of activation markers, such as CD45, CD14, CD68, and CD11b in inflammatory macrophages stimulated in vitro with lipopolysaccharide and interferon (IFN)-γ. Similarly, in situ the number of activated CD68+ macrophages was significantly reduced in areas with high levels of IL-9. Moreover, in the same conditions, IL-9 increased the secretion of the anti-inflammatory cytokine, transforming growth factor (TGF)-β. CONCLUSIONS: These results reveal a new cytokine expressed in the CNS, with a role in the context of MS. We have demonstrated that IL-9 and its receptor are both expressed in CNS. Moreover, we found that IL-9 decreases the activation state and promotes the anti-inflammatory properties of human macrophages. This mechanism may contribute to the beneficial effects of IL-9 that are observed in MS, and may be therapeutically potentiated by modulating IL-9 expression in MS

Selective Disruption of Perineuronal Nets in Mice Lacking Crtl1 is Sufficient to Make Fear Memories Susceptible to Erasure

The ability to store, retrieve, and extinguish memories of adverse experiences is an essential skill for animals' survival. The cellular and molecular factors that underlie such processes are only partially known. Using chondroitinase ABC treatment targeting chondroitin sulfate proteoglycans (CSPGs), previous studies showed that the maturation of the extracellular matrix makes fear memory resistant to deletion. Mice lacking the cartilage link protein Crtl1 (Crtl1-KO mice) display normal CSPG levels but impaired CSPG condensation in perineuronal nets (PNNs). Thus, we asked whether the presence of PNNs in the adult brain is responsible for the appearance of persistent fear memories by investigating fear extinction in Crtl1-KO mice. We found that mutant mice displayed fear memory erasure after an extinction protocol as revealed by analysis of freezing and pupil dynamics. Fear memory erasure did not depend on passive loss of retention; moreover, we demonstrated that, after extinction training, conditioned Crtl1-KO mice display no neural activation in the amygdala (Zif268 staining) in comparison to control animals. Taken together, our findings suggest that the aggregation of CSPGs into PNNs regulates the boundaries of the critical period for fear extinction