Spectral moment sum rules for the retarded Green's function and self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and nonequilibrium

We derive exact expressions for the zeroth and the first three spectral moment sum rules for the retarded Green's function and for the zeroth and the first spectral moment sum rules for the retarded self-energy of the inhomogeneous Bose-Hubbard model in nonequilibrium, when the local on-site repulsion and the chemical potential are time-dependent, and in the presence of an external time-dependent electromagnetic field. We also evaluate these expressions for the homogeneous case in equilibrium, where all time dependence and external fields vanish. Unlike similar sum rules for the Fermi-Hubbard model, in the Bose-Hubbard model case, the sum rules often depend on expectation values that cannot be determined simply from parameters in the Hamiltonian like the interaction strength and chemical potential but require knowledge of equal-time many-body expectation values from some other source. We show how one can approximately evaluate these expectation values for the Mott-insulating phase in a systematic strong-coupling expansion in powers of the hopping divided by the interaction. We compare the exact moment relations to the calculated moments of spectral functions determined from a variety of different numerical approximations and use them to benchmark their accuracy. DOI: 10.1103/PhysRevA.87.013628

Toll-Like Receptors 7, 8, and 9 Expression and Function in Primary Human Cervical Cancer Langerhans Cells Evidence of Anergy

Objective: Human papillomavirus oncoproteins E6 and E7 down modulate Toll-like receptor (TLR) 9 expression in infected keratinocytes. We explored the status of expression and function of TLR7, TLR8, and TLR9 in primary human Langerhans cells (LCs) isolated from cervical tumors. Methodology: Single-cell suspensions were made from fresh tissues of squamous cell carcinoma (International Federation of Gynecology and Obstetrics stage IB2); myeloid dendritic cells were purified using CD1c magnetic activated cell separation kits. Langerhans cells were further flow sorted into CD1a(+)CD207(+) cells. Acute monocytic leukemia cell line THP-1-derived LCs (moLCs) formed the controls. mRNA from flow-sorted LCs was reverse transcribed to cDNA and TLR7, TLR8, and TLR9 amplified. Monocyte-derived Langerhans cells and cervical tumor LCs were stimulated with TLR7, TLR8, and TLR9 ligands. Culture supernatants were assayed for interleukin (IL) 1 beta, IL-6, IL-10, IL-12p70, interferon (IFN) alpha, interferon gamma, and tumor necrosis factor (TNF) alpha by Luminex multiplex bead array. Human papillomavirus was genotyped. Results: We have for the first time demonstrated that the acute monocytic leukemia cell line THP-1 can be differentiated into LCs in vitro. Although these moLCs. expressed all the 3 TLRs, tumor LCs expressed TLR7 and TLR8, but uniformly lacked TLR9. Also, moLCs secreted IL-6, IL-1 beta, and tumor necrosis factor alpha to TLR8 ligand and interferon alpha in response to TLR9 ligand; in contrast, tumor LCs did not express any cytokine to any of the 3 TLR ligands. Human papillomavirus type 16 was one of the common human papillomavirus types in all cases. Conclusions: Cervical tumor LCs lacked TLR9 expression and were functionally anergic to all the 3: TLR7, TLR8, and TLR9 ligands, which may play a crucial role in immune tolerance. The exact location of block(s) in TLR7 and TLR8 signaling needs to be investigated, which would have important immunotherapeutic implications.

A nested linear codes approach to distributed function computation over subspaces

In this paper, we consider a distributed function computation setting, where there are m distributed but correlated sources X1,...,Xm and a receiver interested in computing an s-dimensional subspace generated by [X1,...,Xm]Γ for some (m × s) matrix Γ of rank s. We construct a scheme based on nested linear codes and characterize the achievable rates obtained using the scheme. The proposed nested-linear-code approach performs at least as well as the Slepian-Wolf scheme in terms of sum-rate performance for all subspaces and source distributions. In addition, for a large class of distributions and subspaces, the scheme improves upon the Slepian-Wolf approach. The nested-linear-code scheme may be viewed as uniting under a common framework, both the Korner-Marton approach of using a common linear encoder as well as the Slepian-Wolf approach of employing different encoders at each source. Along the way, we prove an interesting and fundamental structural result on the nature of subspaces of an m-dimensional vector space V with respect to a normalized measure of entropy. Here, each element in V corresponds to a distinct linear combination of a set {Xi}im=1 of m random variables whose joint probability distribution function is given.

Point Spread Function Engineering for Super-Resolution Single-Photon and Multiphoton Fluorescence Microscopy

Super-resolution imaging techniques are of paramount interest for applications in bioimaging and fluorescence microscopy. Recent advances in bioimaging demand application-tailored point spread functions. Here, we present some approaches for generating application-tailored point spread functions along with fast imaging capabilities. Aperture engineering techniques provide interesting solutions for obtaining desired system point spread functions. Specially designed spatial filters—realized by optical mask—are outlined both in a single-lens and 4Pi configuration. Applications include depth imaging, multifocal imaging, and super-resolution imaging. Such an approach is suitable for fruitful integration with most existing state-of-art imaging microscopy modalities.

Predictability and chaotic nature of daily streamflow

The predictability of a chaotic series is limited to a few future time steps due to its sensitivity to initial conditions and the exponential divergence of the trajectories. Over the years, streamflow has been considered as a stochastic system in many approaches. In this study, the chaotic nature of daily streamflow is investigated using autocorrelation function, Fourier spectrum, correlation dimension method (Grassberger-Procaccia algorithm) and false nearest neighbor method. Embedding dimensions of 6-7 obtained indicates the possible presence of low-dimensional chaotic behavior. The predictability of the system is estimated by calculating the system’s Lyapunov exponent. A positive maximum Lyapunov exponent of 0.167 indicates that the system is chaotic and unstable with a maximum predictability of only 6 days. These results give a positive indication towards considering streamflow as a low dimensional chaotic system than as a stochastic system.

Clusters of bound particles in the derivative delta-function Bose gas

In this paper we discuss a novel procedure for constructing clusters of bound particles in the case of a quantum integrable derivative delta-function Bose gas in one dimension. It is shown that clusters of bound particles can be constructed for this Bose gas for some special values of the coupling constant, by taking the quasi-momenta associated with the corresponding Bethe state to be equidistant points on a single circle in the complex momentum plane. We also establish a connection between these special values of the coupling constant and some fractions belonging to the Farey sequences in number theory. This connection leads to a classification of the clusters of bound particles associated with the derivative delta-function Bose gas and allows us to study various properties of these clusters like their size and their stability under the variation of the coupling constant. (C) 2013 Elsevier B.V. All rights reserved.

A novel Q-learning algorithm with function approximation for constrained Markov decision processes

We present a novel multi-timescale Q-learning algorithm for average cost control in a Markov decision process subject to multiple inequality constraints. We formulate a relaxed version of this problem through the Lagrange multiplier method. Our algorithm is different from Q-learning in that it updates two parameters - a Q-value parameter and a policy parameter. The Q-value parameter is updated on a slower time scale as compared to the policy parameter. Whereas Q-learning with function approximation can diverge in some cases, our algorithm is seen to be convergent as a result of the aforementioned timescale separation. We show the results of experiments on a problem of constrained routing in a multistage queueing network. Our algorithm is seen to exhibit good performance and the various inequality constraints are seen to be satisfied upon convergence of the algorithm.

Influence of system size on spatiotemporal dynamics of a model for plastic instability: Projecting low-dimensional and extensive chaos

This work is a continuation of our efforts to quantify the irregular scalar stress signals from the Ananthakrishna model for the Portevin-Le Chatelier instability observed under constant strain rate deformation conditions. Stress related to the spatial average of the dislocation activity is a dynamical variable that also determines the time evolution of dislocation densities. We carry out detailed investigations on the nature of spatiotemporal patterns of the model realized in the form of different types of dislocation bands seen in the entire instability domain and establish their connection to the nature of stress serrations. We then characterize the spatiotemporal dynamics of the model equations by computing the Lyapunov dimension as a function of the drive parameter. The latter scales with the system size only for low strain rates, where isolated dislocation bands are seen, and at high strain rates, where fully propagating bands are seen. At intermediate applied strain rates corresponding to the partially propagating bands, the Lyapunov dimension exhibits two distinct slopes, one for small system sizes and another for large. This feature is rationalized by demonstrating that the spatiotemporal patterns for small system sizes are altered from the partially propagating band types to isolated burst type. This in turn allows us to reconfirm that low-dimensional chaos is projected from the stress signals as long as there is a one-to-one correspondence between the bursts of dislocation bands and the stress drops. We then show that the stress signals in the regime of partially to fully propagative bands have features of extensive chaos by calculating the correlation dimension density. We also show that the correlation dimension density also depends on the system size. A number of issues related to the system size dependence of the Lyapunov dimension density and the correlation dimension density are discussed.

Proportional navigation with delayed line-of-sight rate

This brief discusses the convergence analysis of proportional navigation (PN) guidance law in the presence of delayed line-of-sight (LOS) rate information. The delay in the LOS rate is introduced by the missile guidance system that uses a low cost sensor to obtain LOS rate information by image processing techniques. A Lyapunov-like function is used to analyze the convergence of the delay differential equation (DDE) governing the evolution of the LOS rate. The time-to-go until which decreasing behaviour of the Lyapunov-like function can be guaranteed is obtained. Conditions on the delay for finite time convergence of the LOS rate are presented for the linearized engagement equation. It is observed that in the presence of line-of-sight rate delay, increasing the effective navigation constant of the PN guidance law deteriorates its performance. Numerical simulations are presented to validate the results.

On the zeta function of a periodic-finite-type shift

Periodic-finite-type shifts (PFT's) are sofic shifts which forbid the appearance of finitely many pre-specified words in a periodic manner. The class of PFT's strictly includes the class of shifts of finite type (SFT's). The zeta function of a PET is a generating function for the number of periodic sequences in the shift. For a general sofic shift, there exists a formula, attributed to Manning and Bowen, which computes the zeta function of the shift from certain auxiliary graphs constructed from a presentation of the shift. In this paper, we derive an interesting alternative formula computable from certain ``word-based graphs'' constructed from the periodically-forbidden word description of the PET. The advantages of our formula over the Manning-Bowen formula are discussed.

Cl-35 NQR frequency and spin lattice relaxation time in 3,4-dichlorophenol as a function of pressure and temperature

The pressure dependences of Cl-35 nuclear quadrupole resonance (NQR) frequency, temperature and pressure variation of spin lattice relaxation time (T-1) were investigated in 3,4-dichlorophenol. T-1 was measured in the temperature range 77-300 K. Furthermore, the NQR frequency and T-1 for these compounds were measured as a function of pressure up to 5 kbar at 300 K. The temperature dependence of the average torsional lifetimes of the molecules and the transition probabilities W-1 and W-2 for the Delta m = +/- 1 and Delta m = +/- 2 transitions were also obtained. A nonlinear variation of NQR frequency with pressure has been observed and the pressure coefficients were observed to be positive. A thermodynamic analysis of the data was carried out to determine the constant volume temperature coefficients of the NQR frequency. An attempt is made to compare the torsional frequencies evaluated from NQR data with those obtained by IR spectra. On selecting the appropriate mode from IR spectra, a good agreement with torsional frequency obtained from NQR data is observed. The previously mentioned approach is a good illustration of the supplementary nature of the data from IR studies, in relation to NQR studies of compounds in solid state.

Synthesis and application of weight function for edge cracked semicircular disk (ECSD)

We analyze the utility of edge cracked semicircular disk (ECSD) for rapid assessment of fracture toughness using compressive loading. Continuing our earlier work on ECSD, a theoretical examination here leads to a novel way for synthesizing weight functions using two distinct form factors. The efficacy of ECSD mode-I weight function synthesized using displacement and form factor methods is demonstrated by comparing with finite element results. Theory of elasticity in conjunction with finite element method is utilized to analyze crack opening potency of ECSD under eccentric compression to explore newer configurations of ECSD for fracture testing.

Case for multiple views of function in design based on a common definition

Functions are important in designing. However, several issues hinder progress with the understanding and usage of functions: lack of a clear and overarching definition of function, lack of overall justifications for the inevitability of the multiple views of function, and scarcity of systematic attempts to relate these views with one another. To help resolve these, the objectives of this research are to propose a common definition of function that underlies the multiple views in literature and to identify and validate the views of function that are logically justified to be present in designing. Function is defined as a change intended by designers between two scenarios: before and after the introduction of the design. A framework is proposed that comprises the above definition of function and an empirically validated model of designing, extended generate, evaluate, modify, and select of state-change, and an action, part, phenomenon, input, organ, and effect model of causality (Known as GEMS of SAPPhIRE), comprising the views of activity, outcome, requirement-solution-information, and system-environment. The framework is used to identify the logically possible views of function in the context of designing and is validated by comparing these with the views of function in the literature. Describing the different views of function using the proposed framework should enable comparisons and determine relationships among the various views, leading to better understanding and usage of functions in designing.

Transverse single spin asymmetry in e plus p(up arrow) -> e plus J/psi plus X and transverse momentum dependent evolution of the Sivers function

We extend our analysis of transverse single spin asymmetry in electroproduction of J/psi to include the effect of the scale evolution of the transverse momentum dependent (TMD) parton distribution functions and gluon Sivers function. We estimate single spin asymmetry for JLab, HERMES, COMPASS, and eRHIC energies using the color evaporation model of charmonium production, using an analytically obtained approximate solution of TMD evolution equations discussed in the literature. We find that there is a reduction in the asymmetry compared with our predictions for the earlier case considered by us, wherein the Q(2) dependence came only from DGLAP evolution of the unpolarized gluon densities and a different parametrization of the TMD Sivers function was used.

Predictability and chaotic nature of daily streamflow

The predictability of a chaotic series is limited to a few future time steps due to its sensitivity to initial conditions and the exponential divergence of the trajectories. Over the years, streamflow has been considered as a stochastic system in many approaches. In this study, the chaotic nature of daily streamflow is investigated using autocorrelation function, Fourier spectrum, correlation dimension method (Grassberger-Procaccia algorithm) and false nearest neighbor method. Embedding dimensions of 6-7 obtained indicates the possible presence of low-dimensional chaotic behavior. The predictability of the system is estimated by calculating the system's Lyapunov exponent. A positive maximum Lyapunov exponent of 0.167 indicates that the system is chaotic and unstable with a maximum predictability of only 6 days. These results give a positive indication towards considering streamflow as a low dimensional chaotic system than as a stochastic system.