Immunotherapeutic role of Ag85B as an adjunct to antituberculous chemotherapy

Background

Immunotherapy to enhance the efficiency of the immune response in tuberculosis patients and to eliminate the persisters could be an additional valuable strategy to complement anti-mycobacterial chemotherapy. This study was designed to assess the immunotherapeutic potential of Ag85B as an adjunct to chemotherapy and its effect against active and persister bacteria left after therapy in mouse model of tuberculosis.

Methods

6-8 week old female Balb/c mice were infected with Mycobacterium tuberculosis and treated with chemotherapy or immunotherapy. Protective efficacy was measured in terms of bacterial counts in lungs and spleen. Immune correlates of protection in terms of Th1 and Th2 cytokines were measured by ELISA.

Results

Therapeutic effect of Ag85B was found to be comparable to that of short term dosage of antituberculous drugs (ATDs). The therapeutic effect of ATDs was augmented by the simultaneous treatment with rAg85B and moreover therapy with this protein allowed us to reduce ATD dosage. This therapy was found to be effective even in case of drug persisters. The levels of antigen specific IFNγ and IL-12 were significantly increased after immunotherapy as compared to the basal levels; moreover antigen specific IL-4 levels were depressed on immunotherapy with Ag85B.

Conclusion

We demonstrated in this study that the new combination approach using immunotherapy and concurrent chemotherapy should offer several improvements over the existing regimens to treat tuberculosis. The therapeutic effect is associated not only with initiating a Th1 response but also with switching the insufficient Th2 immune status to the more protective Th1 response.     

Formulation of a killed whole cell pneumococcus vaccine - effect of aluminum adjuvants on the antibody and IL-17 response

Background

Streptococcus pneumoniae causes widespread morbidity and mortality. Current vaccines contain free polysaccharides or protein-polysaccharide conjugates, and do not induce protection against serotypes that are not included in the vaccines. An affordable and broadly protective vaccine is very desirable. The goal of this study was to determine the optimal formulation of a killed whole cell pneumococcal vaccine with aluminum-containing adjuvants for intramuscular injection.

Methods

Four aluminium-containing adjuvants were prepared with different levels of surface phosphate groups resulting in different adsorptive capacities and affinities for the vaccine antigens. Mice were immunized three times and the antigen-specific antibody titers and IL-17 responses in blood were analyzed.

Results

Although all adjuvants induced significantly higher antibody titers than antigen without adjuvant, the vaccine containing aluminum phosphate adjuvant (AP) produced the highest antibody response when low doses of antigen were used. Aluminum hydroxide adjuvant (AH) induced an equal or better antibody response at high doses compared with AP. Vaccines formulated with AH, but not with AP, induced an IL-17 response. The vaccine formulated with AH was stable and retained full immunogenicity when stored at 4°C for 4 months.

Conclusions

Antibodies are important for protection against systemic streptococcal disease and IL-17 is critical in the prevention of nasopharyngeal colonization by S. pneumoniae in the mouse model. The formulation of the whole killed bacterial cells with AH resulted in a stable vaccine that induced both antibodies and an IL-17 response. These experiments underscore the importance of formulation studies with aluminium containing adjuvants for the development of stable and effective vaccines.     

Immunization with genetically attenuated P52-deficient Plasmodium berghei sporozoites induces a long-lasting effector memory CD8+ T cell response in the liver

Background

The induction of sterile immunity and long lasting protection against malaria has been effectively achieved by immunization with sporozoites attenuated by gamma-irradiation or through deletion of genes. For mice immunized with radiation attenuated sporozoites (RAS) it has been shown that intrahepatic effector memory CD8⁺ T cells are critical for protection. Recent studies have shown that immunization with genetically attenuated parasites (GAP) in mice is also conferred by liver effector memory CD8⁺ T cells.

Findings

In this study we analysed effector memory cell responses after immunization of GAP that lack the P52 protein. We demonstrate that immunization with p52 ^-GAP sporozoites also results in a strong increase of effector memory CD8⁺ T cells, even 6 months after immunization, whereas no specific CD4⁺ effector T cells response could be detected. In addition, we show that the increase of effector memory CD8⁺ T cells is specific for the liver and not for the spleen or lymph nodes.

Conclusions

These results indicate that immunization of mice with P. berghei p52 ^-GAP results in immune responses that are comparable to those induced by RAS or GAP lacking expression of UIS3 or UIS4, with an important role implicated for intrahepatic effector memory CD8⁺ T cells. The knowledge of the mediators of protective immunity after immunization with different GAP is important for the further development of vaccines consisting of genetically attenuated sporozoites.     

Development of the time course for processing conflict: an event-related potentials study with 4 year olds and adults

Background

The neurological complications of HIV infection remain poorly understood. Clinically, in vivo ¹H magnetic resonance spectroscopy (MRS) demonstrates brain injury caused by HIV infection even when the MRI is normal. Our goal was to undertsand the dynamics of cerebral injury by performing a longitudinal in vivo ¹H MRS study of the SIV/macaque model of neuroAIDS.

Results

Eight rhesus macaques were infected with SIVmac251 and serially imaged with MRI and ¹H MRS to terminal AIDS or the endpoint of 2 years. During acute infection, there were stereotypical brain MRS changes, dominated by a significant elevation of the Cho/Cr ratio in the frontal cortex. Subsequently, brain metabolic patterns diverged between animals. There was an elevation of basal ganglia Cho/Cr four weeks post-inoculation in 2 animals that developed SIV encephalitis (p = 0.022). Metabolite ratios averaged across all 8 animals were not significantly different from baseline at any time point after 2 weeks post inoculation. However, linear regression analysis on all 8 animals revealed a positive correlation between a change in frontal lobe Cho/Cr and plasma viral load (P < 0.001, R = 0.80), and a negative correlation between NAA/Cr in the basal ganglia and the plasma viral load (P < 0.02, R = -0.73). No MRI abnormalities were detected at any time.

Conclusions

After infection with SIV, macaque brain metabolism changes in a complex manner that is dependent on brain region, host factors and viral load. An elevation of basal ganglia Cho/Cr 4 weeks after SIV infection may be marker of a propensity to develop SIV encephalitis. Elevations of Cho/Cr, often observed in CNS inflammation, were associated with increased plasma viral load during acute and chronic infection. Evidence of neuronal injury in the basal ganglia was associated with increased plasma viral load in the chronic stage of infection. These observations support the use of drugs capable of controlling the viral replication and trafficking of virus into the CNS, and may help explain the reduction in incidence of HIV-associated dementia in the era of HAART despite the inability of most of those drugs to effectively enter the CNS.     

Physics beyond the Standard Model through b → s μ ?+? μ ? transition

A comprehensive study of the impact of new-physics operators with different Lorentz structures on decays involving the b ?? s ?? ^?+? ?? ^? transition is performed. The effects of new vector?Caxial vector (VA), scalar?Cpseudoscalar (SP) and tensor (T) interactions on the differential branching ratios, forward?Cbackward asymmetries (A _FB??s), and direct CP asymmetries of ${\bar B}_{\rm s}^0 \to \mu^+ \mu^-$ , ${\bar B}_{\rm d}^0 \to$ $ X_{\rm s} \mu^+ \mu^-$ , ${\bar B}_{\rm s}^0 \to \mu^+ \mu^- \gamma$ , ${\bar B}_{\rm d}^0 \to {\bar K} \mu^+ \mu^-$ , and ${\bar B}_{\rm d}^0\to {\bar{K}^*} \mu^+ \mu^-$ are examined. In ${\bar B}_{\rm d}^0\to {\bar{K}^*} \mu^+ \mu^-$ , we also explore the longitudinal polarization fraction f _L and the angular asymmetries $A_{\rm T}^{(2)}$ and A _LT, the direct CP asymmetries in them, as well as the triple-product CP asymmetries $A_{\rm T}^{\rm (im)}$ and $A^{\rm (im)}_{\rm LT}$ . While the new VA operators can significantly enhance most of the observables beyond the Standard Model predictions, the SP and T operators can do this only for A _FB in ${\bar B}_{\rm d}^0 \to {\bar K} \mu^+ \mu^-$ .     

A proof of the unitarity ofS-matrix in a nonlocal quantum field theory

Using the formfactors which are entire analytic functions in a momentum space, nonlocality is introduced for a wide class of interaction Lagrangians in the quantum theory of one-component scalar field φ(x). We point out a regularization procedure which possesses the following features:

1. The regularizedS ^δ matrix is defined and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} S^\delta = S.$$
2. The Green positive-frequency functions which determine the operation of multiplication in \(S \cdot S^ + \mathop = \limits_{Df} S \circledast S^ + \) can be also regularized ?^δ and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} \circledast ^\delta = \circledast \equiv .$$
3. The operator \(J(\delta _1 ,\delta _2 ,\delta _3 ) = S^{\delta _1 } \circledast ^{\delta _2 } S^{\delta _3 + } \) is continuous at the point δ₁=δ₂=δ₃=0.
4. $$S^\delta \circledast ^\delta S^{\delta + } \equiv 1at\delta > 0.$$ Consequently, theS-matrix is unitary, i.e. $$S \circledast S^ + = S \cdot S^ + = 1.$$

     

Parametric study of EEG sensitivity to phase noise during face processing

Background

The zitter (zi/zi) rat, a loss-of-function mutant of the glycosylated transmembrane protein attractin (atrn), exhibits widespread age-dependent spongiform degeneration, hypomyelination, and abnormal metabolism of reactive oxygen species (ROS) in the brain. To date, the mechanisms underlying these phenotypes have remained unclear.

Results

Here, we show differentiation defects in zi/zi oligodendrocytes, accompanied by aberrant extension of cell-processes and hypomyelination. Axonal bundles were relatively preserved during postnatal development. With increasing in age, the injured oligodendrocytes in zi/zi rats become pathological, as evidenced by the accumulation of iron in their cell bodies. Immunohistochemical analysis revealed that atrn expression was absent from an oligodendrocyte lineage, including A2B5-positive progenitors and CNPase-positive differentiated cells. The number and distribution of Olig2-positive oligodendrocyte progenitors was unchanged in the zi/zi brain. Furthermore, an in vitro differentiation assay of cultured oligodendrocyte progenitors prepared from zi/zi brains revealed their normal competence for proliferation and differentiation into mature oligodendrocytes. Interestingly, we demonstrated the accelerated recruitment of ED1-positive macrophages/microglia to the developing zi/zi brain parenchyma prior to the onset of hypomyelination. Semiquantitative RT-PCR analysis revealed a significant up-regulation of CD26 and IL1-β in the zi/zi brain during this early postnatal stage.

Conclusion

We demonstrated that the onset of the impairment of oligodendrocyte differentiation occurs in a non-cell autonomous manner in zi/zi rats. Hypomyelination of oligodendrocytes was not due to a failure of the intrinsic program of oligodendrocytes, but rather, was caused by extrinsic factors that interrupt oligodendrocyte development. It is likely that macrophage/microglial activation in the zi/zi CNS leads to disturbances in oligodendrocyte differentiation via deleterious extrinsic factors, such as the cytokine IL1-β or ROS. Atrn might be involved in the activation of brain macrophages/microglia by suppressing excessive migration of monocytes into the CNS, or by accelerating the transformation of brain monocytes into resting microglia. Understanding the pathogenesis of the zi/zi rat may provide novel insights into the developmental interaction betweens macrophages/microglia and cells of an oligodendrocyte lineage.     

Approximation and Equidistribution of Phase Shifts: Spherical Symmetry

Consider a semiclassical Hamiltonian $$H_{V, h} := h^{2} \Delta + V - E,$$ where h > 0 is a semiclassical parameter, Δ is the positive Laplacian on ${\mathbb{R}^{d}, V}$ is a smooth, compactly supported central potential function and E > 0 is an energy level. In this setting the scattering matrix S _h (E) is a unitary operator on ${L^2(\mathbb{S}^{d-1})}$ , hence with spectrum lying on the unit circle; moreover, the spectrum is discrete except at 1. We show under certain additional assumptions on the potential that the eigenvalues of S _h (E) can be divided into two classes: a finite number ${\sim c_d (R\sqrt{E}/h)^{d-1}}$ , as ${h \to 0}$ , where B(0, R) is the convex hull of the support of the potential, that equidistribute around the unit circle, and the remainder that are all very close to 1. Semiclassically, these are related to the rays that meet the support of, and hence are scattered by, the potential, and those that do not meet the support of the potential, respectively. A similar property is shown for the obstacle problem in the case that the obstacle is the ball of radius R.     

Average temperature and multiplicities ofe + e − annihilation

Hadron temperatures ofe ⁺ e ^?→h \(\bar h\) from PEP experiments at 29 GeV are estimated using theP _⊥ distribution; rather small fluctuations are found for temperatures of π,K,..., Ξ with respect to the average \(\bar T = 196 \pm 7\) MeV. A semi-empirical formula including quark content ofh is proposed to account for multiplicities of π,K, ..., Δ in terms of a unique temperature \(\bar T\) . The formula is further extended to charmed particlesD, F, J/Ψ andΛ _c without free parameters. The property \(\bar T\) ~E _cm ^1/4 holds for other experiments of DESY andCESR.     

Vaccine based on a ubiquitous cysteinyl protease and streptococcal pyrogenic exotoxin A protects against Streptococcus pyogenes sepsis and toxic shock

Background

The gram-positive bacterium Streptococcus pyogenes is a common pathogen of humans that causes invasive infections, toxic-shock syndrome, rheumatic fever, necrotizing fasciitis and other diseases. Detection of antibiotic resistance in clinical isolates has renewed interest in development of new vaccine approaches for control S. pyogenes sepsis. In the study presented, a novel protein vaccine was examined. The vaccine was based on a recombinant protein fusion between streptococcal pyrogenic exotoxin B (SpeB), a cysteinyl protease expressed by all clinical isolates, and streptococcal pyrogenic exotoxin A (SpeA), a superantigen produced by a large subset of isolates.

Results

A novel protein was produced by mutating the catalytic site of SpeB and the receptor binding surface of SpeA in a fusion of the two polypeptides. Vaccination of HLA-DQ8 transgenic mice with the SpeA-SpeB fusion protein protected against a challenge with the wild-type SpeA that was lethal to naïve controls, and vaccinated mice were protected from an otherwise lethal S. pyogenes infection.

Conclusion

These results suggest that the genetically attenuated SpeA-SpeB fusion protein may be useful for controlling S. pyogenes infections. Vaccination with the SpeA-SpeB fusion protein described in this study may potentially result in protective immunity against multiple isolates of S. pyogenes due to the extensive antibody cross-reactivity previously observed among all sequence variants of SpeB and the high frequency of SpeA-producing strains.     

Strangeness enhancement in sulphur—Nucleus collisions at 200 A GeV/c

The NA35 experiment used several independent methods to determine the strange particle production in p+S and S+A collisions. The different techniques show consistent results. Strangeness conservation in full phase space is used as an additional check of the consistency of the data. On the base of the analysis in full phase space it could be shown that strangeness conservation is fullfilled. The NA35K _S ⁰ in S+S and S+Ag are consistent with the NA44 results forK ⁺ andK ^?. The results of the NA36 collaboration for S+Pb collisions were extrapolated to full phase space. The comparison with the NA35 results shows more than two times lower yields. The ratio of Λ to $\bar \Lambda $ at midrapidity of NA36 is inconsistent with the high baryon density determind by NA35. The strange particle production is compared to the abundance of non strange particles, especially negatively charged pions which are measured in full phase space in the same experiment. A clear enhanced strange hadron production relative to σ^? is observed in S+Ag collisions compared to p+S reactions at the same energy. TheK _S ⁰ multiplicity in full phase space per negative hadron (h ^?) in S+S, S+Ag and Pb+Pb is enhanced by about a factor 1.6 compared to N+N and p+S collisions. The NA36 result for theK _S ⁰ multiplicity perh ^? in S+Pb is below the N+N value.     

Antiproton-proton annihilation at rest intoπ + π − η ′ andπ + π − η from atomicS andP states

We have measured the branching ratios for \(\bar pp\) annihilation at rest intoπ ⁺ π ^? η andπ ⁺ π ^? η′ in hydrogen gas in two data samples that have different fractions ofS-wave andP-wave initial states. The branching ratios are derived from a comparison with the topological branching ratio for \(\bar pp\) annihilations into four charged pions of (49±4)% and the branching ratio intoπ ⁺ π ^? π ⁺ π ^? π ⁰ of (18.7±1.6)%. We find a significant reduction of the branching ratios fromP-states for \(\bar pp \to \pi ^ + \pi ^ - \eta \) andπ ⁺ π ^? η′ in comparison toS-state annihilation. $$\begin{gathered} BR(S - wave \to \pi ^ + \pi ^ - \eta ) = (13.7 \pm 1.46) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta ) = (3.35 \pm 0.84) \cdot 10^{ - 3} \hfill \\ BR(S - wave \to \pi ^ + \pi ^ - \eta ') = (3.46 \pm 0.67) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta ') = (0.61 \pm 0.33) \cdot 10^{ - 3} . \hfill \\ \end{gathered} $$ In a partial wave analysis of theπ ⁺ π ^? η Dalitz plot we find the following contributions: Phase space, \(a_2^ + (1320)\pi ^ \mp \) ,ηρ⁰ andf ₂(1270)η: $$\begin{gathered} BR(S - wave \to \pi ^ + \pi ^ - \eta PS) = (6.31 \pm 1.22) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta PS) = (0.47 \pm 0.26) \cdot 10^{ - 3} \hfill \\ BR(^1 S_0 \to a_2^ \pm (1320)\pi ^ \mp ) = (2.59 \pm 0.73) \cdot 10^{ - 3} \hfill \\ BR(^3 S_1 \to a_2^ \pm (1320)\pi ^ \mp ) = (1.31 \pm 0.48) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to a_2^ \pm (1320)\pi ^ \mp ) = (1.31 \pm 0.69) \cdot 10^{ - 3} \hfill \\ BR(^3 S_1 \to \rho \eta ) = (3.29 \pm 0.90) \cdot 10^{ - 3} \hfill \\ BR(^1 P_1 \to \rho \eta ) = (0.94 \pm 0.53) \cdot 10^{ - 3} \hfill \\ BR(^1 S_0 \to f_2 (1270)\eta ) = (0.083 \pm 0.086) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to f_2 (1270)\eta ) = (0.64 \pm 0.26) \cdot 10^{ - 3} . \hfill \\ \end{gathered} $$ We find a 2 σ effect for the reaction \(\bar pp \to a_0^ \pm (980)\pi ^ \mp \) , \(a_0^ \pm \to \eta \pi ^ \pm \) , with a branching ratio of (0.13±0.07)·10^?3. For η' production we give a branching ratio of \(\bar pp \to \rho \eta '\) of (1.81±0.44)·10^?3 from³ S ₁. We estmate a contribution of about 0.3·10^?3 for ρη' fromP-states. The ratio of ρη and ρη' rpoduction is used to test the validity of the quark line rule. In theπ ⁺ π ^? π ⁺ π ^? γ final state we do not observe the reaction \(\bar pp \to \pi ^ + \pi ^ - \omega \) , ω→π ⁺ π ^? λ and derive an upper limit of 3·10^?3 for decay modeω→π ⁺ π ^? λ.     

Differential expression of Cathepsin S and X in the spinal cord of a rat neuropathic pain model

Background

Proteoglycan (PG) in the extracellular matrix (ECM) of the central nervous system (CNS) may act as a barrier for neurite elongation in a growth tract, and regulate other characteristics collectively defined as structural neural plasticity. Proteolytic cleavage of PGs appears to alter the environment to one favoring plasticity and growth. Brevican belongs to the lectican family of aggregating, chondroitin sulfate (CS)-bearing PGs, and it modulates neurite outgrowth and synaptogenesis. Several ADAMTSs (a disintegrin and metalloproteinase with thrombospondin motifs) are glutamyl-endopeptidases that proteolytically cleave brevican. The purpose of this study was to localize regions of adult CNS that contain a proteolytic-derived fragment of brevican which bears the ADAMTS-cleaved neoepitope sequence. These regions were compared to areas of Wisteria floribunda agglutin (WFA) reactivity, a common reagent used to detect "perineuronal nets" (PNNs) of intact matrix and a marker which is thought to label regions of relative neural stability.

Results

WFA reactivity was found primarily as PNNs, whereas brevican and the ADAMTS-cleaved fragment of brevican were more broadly distributed in neuropil, and in particular regions localized to PNNs. One example is hippocampus where the ADAMTS-cleaved brevican fragment is found surrounding pyramidal neurons, in neuropil of stratum oriens/radiatum and the lacunosum moleculare. The fragment was less abundant in the molecular layer of the dentate gyrus. Mostly PNNs of scattered interneurons along the pyramidal layer were identified by WFA. In lateral thalamus, the reticular thalamic nucleus stained abundantly with WFA whereas ventral posterior nuclei were markedly immunopositive for ADAMTS-cleaved brevican. Using Western blotting techniques, no common species were reactive for brevican and WFA.

Conclusion

In general, a marked discordance was observed in the regional localization between WFA and brevican or the ADAMTS-derived N-terminal fragment of brevican. Functionally, this difference may correspond to regions with varied prevalence for neural stability/plasticity.     

Covariant partition temperature model ande + e − annihilation

The rapidity distributions of inclusive \(e^ + e^ - \to h\bar h + \cdot \cdot \cdot\) of PEP and DESY experiments are analyzed in terms of the covariant partition temperatureT _p model. The estimates ofT _p ^* in the fireball system are comparable to the conventional temperature, the energy dependence follows approximately Stefan's law, the radius of the specific volume ralative to the energy density being ～1.18 fm. In the c.m.s. of collision, \(T_p = AW^a (W = \sqrt s in GeV)\) witha=0.60±0.05 andA=0.256±0.006, it is found \(T_p \cong {W \mathord{\left/ {\vphantom {W {\tfrac{3}{2}\left\langle {n_ \pm } \right\rangle }}} \right. \kern-0em} {\tfrac{3}{2}\left\langle {n_ \pm } \right\rangle }}\) . These properties hold also for \(\bar pp\) collision, but not forpp→π^?+...     

On the number of negative eigenvalues for a Schrödinger operator with magnetic field

We consider the Schrödinger operator with magnetic field $$H = \sum\limits_{j = 1}^n {\left( {\frac{1}{i}\frac{\partial }{{\partial x_j }} - a_j } \right)^2 + Vin\mathbb{R}^n .} $$ Under certain conditions on the magnetic fieldB=curla, we generalize the Fefferman—Phong estimates (Bull. A. M. S.9, 129–206 (1983)) on the number of negative eigenvalues for ?Δ+V to the operatorH. Upper and lower bounds are established. Our estimates incorporate the contribution from the magnetic field. The conditions onB in particular are satisfied if the magnetic potentialsa _j (x) are polynomials.     

New exact travelling wave solutions of bidirectional wave equations

The surface water waves in a water tunnel can be described by systems of the form [Bona and Chen, Physica D116, 191 (1998)] 1 $$ \label{BWE} \left\{ \begin{array}{l} v_t+u_x+(uv)_x+au_{xxx}-bv_{xxt}=0, \\ u_t+v_x+uu_x+cv_{xxx}-du_{xxt}=0, \end{array} \right. $$ where a, b, c and d are real constants. In general, the exact travelling wave solutions will be helpful in the theoretical and numerical study of the nonlinear evolution systems. In this paper, we obtain exact travelling wave solutions of system (1) using the modified $\tanh$ – $\coth$ function method with computerized symbolic computation.     

Positive Lyapunov Exponents for Higher Dimensional Quasiperiodic Cocycles

We consider an m-dimensional analytic cocycle \({\mathbb{T} \times \mathbb{R}^m \ni (x, \vec{\psi}) \mapsto (x + \omega, A (x) \cdot \vec{\psi}) \in \mathbb{T} \times \mathbb{R}^m}\) , where \({\omega \notin \mathbb{Q}}\) and \({A \in C^\omega (\mathbb{T}, \mathrm{Mat}_m (\mathbb{R}))}\) . Assuming that the d × d upper left corner block of A is typically large enough, we prove that the d largest Lyapunov exponents associated with this cocycle are bounded away from zero. The result is uniform relative to certain measurements on the matrix blocks forming the cocycle. As an application of this result, we obtain nonperturbative (in the spirit of Sorets–Spencer theorem) positive lower bounds of the nonnegative Lyapunov exponents for various models of band lattice Schrödinger operators.     

An expansion of Hartree-Fock and correlation energies,relativistic corrections and the dipole matrix element in the powers of of 1/Z

Feynman diagrammatic technique was used for the calculation of Hartree-Fock and correlation energies, relativistic corrections, dipole matrix element. The whole energy of atomic system was defined as a polen-electron Green function. Breit operator was used for the calculation of relativistic corrections. The Feynman diagrammatic technique was developed for 〈H_B>. Analytical expressions for the contributions from diagrams were received. The calculations were carried out for the terms of such configurations as 1s² 2sⁿ¹ 2pⁿ² (2 ≧n₁≧ 0, 6≧ n₂ ≧ 0). Numerical results are presented for the energies of the terms in the form $$E = E_0 Z^2 + \Delta {\rm E}_2 + \frac{1}{Z}\Delta {\rm E}_3 + \frac{{\alpha ^2 }}{4}(E_0^r + \Delta {\rm E}_1^r Z^3 )$$ and for fine structure of the terms in the form $$\begin{gathered} \left\langle {1s^2 2s^{n_1 } 2p^{n_2 } LSJ|H_B |1s^2 2s^{n_1 \prime } 2p^{n_2 \prime } L\prime S\prime J} \right\rangle = \hfill \\ = ( - 1)^{\alpha + S\prime + J} \left\{ {\begin{array}{*{20}c} {L S J} \\ {S\prime L\prime 1} \\ \end{array} } \right\}\frac{{\alpha ^2 }}{4}(Z - A)^3 [E^{(0)} (Z - B) + \varepsilon _{co} ] + \hfill \\ + ( - 1)^{L + S\prime + J} \left\{ {\begin{array}{*{20}c} {L S J} \\ {S\prime L\prime 2} \\ \end{array} } \right\}\frac{{\alpha ^2 }}{4}(Z - A)^3 \varepsilon _{cc} . \hfill \\ \end{gathered} $$ Dipole matrix elements are necessary for calculations of oscillator strengths and transition probabilities. For dipole matrix elements two members of expansion by 1/Z have been obtained. Numerical results were presented in the form P(a,a′) = a/Z(1+τ/Z).     

On the free energy of the hopfield model

The general theory of inhomogeneous mean-field systems of Raggio and Werner provides a variational expression for the (almost sure) limiting free energy density of the Hopfield model $$H_{N,p}^{\{ \xi \} } (S) = - \frac{1}{{2N}}\sum\limits_{i,j = 1}^N {\sum\limits_{\mu = 1}^N {\xi _i^\mu \xi _j^\mu S_i S_j } } $$ for Ising spinsS _i andp random patterns ξ^μ=(ξ ₁ ^μ ,ξ ₂ ^μ ,...,ξ _N ^μ ) under the assumption that $$\mathop {\lim }\limits_{N \to \gamma } N^{ - 1} \sum\limits_{i = 1}^N {\delta _{\xi _i } = \lambda ,} \xi _i = (\xi _i^1 ,\xi _i^2 ,...,\xi _i^p )$$ exists (almost surely) in the space of probability measures overp copies of {?1, 1}. Including an “external field” term ?ξ _μ ^p h^μμξ _i=1 ^N ξ _i ^μ S_i, we give a number of general properties of the free-energy density and compute it for (a)p=2 in general and (b)p arbitrary when λ is uniform and at most the two componentsh ^μ1 andh ^μ2 are nonzero, obtaining the (almost sure) formula $$f(\beta ,h) = \tfrac{1}{2}f^{ew} (\beta ,h^{\mu _1 } + h^{\mu _2 } ) + \tfrac{1}{2}f^{ew} (\beta ,h^{\mu _1 } - h^{\mu _2 } )$$ for the free energy, wheref ^cw denotes the limiting free energy density of the Curie-Weiss model with unit interaction constant. In both cases, we obtain explicit formulas for the limiting (almost sure) values of the so-called overlap parameters $$m_N^\mu (\beta ,h) = N^{ - 1} \sum\limits_{i = 1}^N {\xi _i^\mu \left\langle {S_i } \right\rangle } $$ in terms of the Curie-Weiss magnetizations. For the general i.i.d. case with Prob {ξ _i ^μ =±1}=(1/2)±?, we obtain the lower bound 1+4?²(p?1) for the temperatureT _c separating the trivial free regime where the overlap vector is zero from the nontrivial regime where it is nonzero. This lower bound is exact forp=2, or ε=0, or ε=±1/2. Forp=2 we identify an intermediate temperature region between T_*=1?4?² and T_c=1+4?² where the overlap vector is homogeneous (i.e., all its components are equal) and nonzero.T _* marks the transition to the nonhomogeneous regime where the components of the overlap vector are distinct. We conjecture that the homogeneous nonzero regime exists forp≥3 and that T_*=max{1?4?²(p?1),0}.