(Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap

We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass dependence) are transmuted into expansions in 1/F, where $F \sim 1/g(m)$ for $m \gg \Lambda$ while $F \sim (m/\Lambda)^\alpha$ for m \lsim \Lambda, $\Lambda$ being the basic scale and $\alpha$ given by renormalization group coefficients. (Borel) convergence holds in a range of $F$ which corresponds to reach unambiguously the strong coupling infrared regime near $m\to 0$, which can define certain "non-perturbative" quantities, such as the mass gap, from a resummation of this alternative expansion. Convergence properties can be further improved, when combined with $\delta$ expansion (variationally improved perturbation) methods. We illustrate these results by re-evaluating, from purely perturbative informations, the O(N) Gross-Neveu model mass gap, known for arbitrary $N$ from exact S matrix results. Comparing different levels of approximations that can be defined within our framework, we find reasonable agreement with the exact result.Comment: 33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording corrections, 2 references added. To appear in Phys. Rev.

Asymptotically Improved Convergence of Optimized Perturbation Theory in the Bose-Einstein Condensation Problem

We investigate the convergence properties of optimized perturbation theory, or linear $\delta$ expansion (LDE), within the context of finite temperature phase transitions. Our results prove the reliability of these methods, recently employed in the determination of the critical temperature T_c for a system of weakly interacting homogeneous dilute Bose gas. We carry out the explicit LDE optimized calculations and also the infrared analysis of the relevant quantities involved in the determination of $T_c$ in the large-N limit, when the relevant effective static action describing the system is extended to O(N) symmetry. Then, using an efficient resummation method, we show how the LDE can exactly reproduce the known large-N result for $T_c$ already at the first non-trivial order. Next, we consider the finite N=2 case where, using similar resummation techniques, we improve the analytical results for the nonperturbative terms involved in the expression for the critical temperature allowing comparison with recent Monte Carlo estimates of them. To illustrate the method we have considered a simple geometric series showing how the procedure as a whole works consistently in a general case.Comment: 38 pages, 3 eps figures, Revtex4. Final version in press Phys. Rev.

Identification of New SRF Binding Sites in Genes Modulated by SRF Over-Expression in Mouse Hearts

Background To identify in vivo new cardiac binding sites of serum response factor (SRF) in genes and to study the response of these genes to mild over-expression of SRF, we employed a cardiac-specific, transgenic mouse model, with mild over-expression of SRF (Mild-O SRF Tg). Methodology Microarray experiments were performed on hearts of Mild-O-SRF Tg at 6 months of age. We identified 207 genes that are important for cardiac function that were differentially expressed in vivo. Among them the promoter region of 192 genes had SRF binding motifs, the classic CArG or CArG-like (CArG-L) elements. Fifty-one of the 56 genes with classic SRF binding sites had not been previously reported. These SRF-modulated genes were grouped into 12 categories based on their function. It was observed that genes associated with cardiac energy metabolism shifted toward that of carbohydrate metabolism and away from that of fatty acid metabolism. The expression of genes that are involved in transcription and ion regulation were decreased, but expression of cytoskeletal genes was significantly increased. Using public databases of mouse models of hemodynamic stress (GEO database), we also found that similar altered expression of the SRF-modulated genes occurred in these hearts with cardiac ischemia or aortic constriction as well. Conclusion and significance SRF-modulated genes are actively regulated under various physiological and pathological conditions. We have discovered that a large number of cardiac genes have classic SRF binding sites and were significantly modulated in the Mild-O-SRF Tg mouse hearts. Hence, the mild elevation of SRF protein in the heart that is observed during typical adult aging may have a major impact on many SRF-modulated genes, thereby affecting Cardiac structure and performance. The results from our study could help to enhance our understanding of SRF regulation of cellular processes in the aged heart

Stability robustness to unstructured uncertainties of linear systems controlled on the basis of the multirate sampling of the plant output

The stability robustness of stable feedback loops designed on the basis of multirate-output controllers (MROCs) is analysed in this paper. For MROC-based feedback loops, designed to achieve stabilization through pole placement or deterministic linear-quadratic (LQ) optimal regulation, we characterize additive or multiplicative norm-bounded perturbations of the loop transfer-function matrix that do not destabilize the closed-loop system. New sufficient stability conditions in terms of the elementary MROC matrices are presented, for both static and (stable) dynamic MROCs. Moreover, lower bounds for the minimum singular values of the return-difference and of the inverse return-difference matrices are suggested for all cases of the aforementioned MROC-based stable feedback designs. Also suggested are guaranteed stability margins for MROC-based pole placers and LQ optimal regulators. A comparison between the suggested stability margins for static and (stable) dynamic MROCs is presented, while the superiority of these margins over known stability margins for deterministic LQ optimal regulators is identified. Finally, an analysis of the deficiency of the aforementioned stablity margins is presented for cases where the MROC feedback gains become very large, and useful guidelines are suggested for the choice of the sampling period and of the output multiplicities of the sampling to avoid this deficiency

A matrix-pencil-based interpretation of inconsistent initial conditions and system properties of generalized state-space systems

A matrix-pencil-based approach is presented to interpret transition matrices, inconsistent initial conditions, and systems properties of regular generalized state-space (GSS) systems. On the basis of the well known Weierstrass canonical form of a regular pencil, several definitions of transition matrices for GSS systems are given. Convolution forms of the forced state evolution of GSS systems are also established, both for the case of consistent and of inconsistent initial conditions. Moreover, a fundamental interpretation of inconsistent initial conditions of GSS systems is outlined. Finally, the notion of several types of controllability and observability Gramians of GSS systems is introduced. Relations of these Gramians to the respective controllability and observability properties of GSS systems are examined, and simple and easily checked algebraic criteria based on these Gramians, are established. It is pointed out that these results appear to be first in the field of GSS systems

Stability robustness of LQ optimal regulators based on multirate sampling of plant output

The stability robustness of stable feedback loops, designed on the basis of multirate-output controllers (MROCs), is analyzed in this paper. For MROC-based feedback loops, designed in order to achieve LQ optimal regulation, we characterize additive and multiplicative norm-bounded perturbations of the loop transfer function matrix which do not destabilize the closed-loop system. New sufficient conditions for stability robustness, in terms of elementary MROC matrices, are presented. Moreover, guaranteed stability margins for MROC-based LQ optimal regulators are suggested for the first time. These margins are obtained on the basis of a fundamental spectral factorization equality, called the modified return difference equality, and are expressed directly in terms of elementary cost and system matrices. Sufficient conditions in order to guarantee the suggested stability margins are established. Finally, the connection between the suggested stability margins and the selection of cost weighting matrices is investigated and useful guidelines for choosing proper weighting matrices are presented

Multirate technique for adaptive LQ optimal tracking

In this paper, the certainty equivalence principle is used to combine the identification method with a control structure derived from the linear quadratic (LQ) optimal tracking problem. The proposed LQ optimal trackers are based on multirate-output controllers (MROCs). MROCs contain a sampling mechanism in which the system output is detected many times over one sampling period, and its sampled-data over this period are appropriately used for feedback. Such a control strategy provides the possibility for the output of the sampled closed-loop system to `track' the output of a given reference model subject to a quadratic cost criterion, without making assumptions on the plant other than controllability, observability and known order. A simple indirect adaptive control scheme is derived, which estimates the unknown plant parameters (and consequently the controller parameters) on-line, from sequential data of the inputs and the outputs of the plant, which are recursively updated within the time limit imposed by a fundamental sampling period. On the basis of the proposed technique, the adaptive LQ optimal tracking problem considered, is reduced to the determination of a fictitious static state feedback controller, due to the merits of MROC based LQ optimal trackers. Known indirect adaptive techniques for LQ optimal tracking usually resort to the computation of full order adaptive state observers, thus introducing high order exogenous dynamics in the control loop. In contrast, the dynamics introduced by the proposed multirate technique are of low order. Moreover, persistency of excitation and therefore parameter convergence, of the continuous and the discretized plant under control, is provided without making assumptions either on the existence of specific convex sets in which the estimated parameters belong or on the coprimeness of the polynomials describing the ARMA model, as compared to known adaptive LQ optimal control schemes

A new multirate sampled-data technique for adaptive pole positioning in linear systems

The adaptive pole placement problem for linear systems is solved using a new class of multirate controllers, called two-point multirate controllers. In such a type of controller, the control is constrained to a certain piecewise constant signal, while the controlled plant output is detected many times over a fundamental sampling period. On the basis of the proposed strategy, the original problem is reduced to an associate discrete pole placement problem, for which a fictitious static-state feedback controller is needed to be computed. This control strategy allows us to assign the poles of the sampled closed-loop system arbitrarily in desired locations, and does not make assumptions on the plant other than controllability and observability of the continuous and the sampled system, and known order. The controller determination relies on a closed-form formula, which can be thought as the extension of the Ackerman formula for multi-input/multi-output (MIMO) systems. Known indirect adaptive pole placement techniques require the solution of matrix polynomial Diophantine equations, which, in many cases, might yield an unstable controller. Moreover, the proposed adaptive scheme is readily applicable to non-minimum phase systems, and to systems which do not possess the parity interlacing property. Finally, persistency of excitation and, therefore, parameter convergence, of the continuous-time plant is provided without making assumptions either on the existence of specific convex sets in which the estimated parameters belong or on the coprimeness of the polynomials describing the ARMA model, or finally on the richeness of the reference signals, as compared to known adaptive pole placement schemes

Guaranteed stability margins and singular value properties of the discrete-time linear quadratic optimal regulator

Useful singular value properties for the state feedback discrete linear quadratic (LQ) optimal regulator are established. In particular, new lower bounds for the minimum singular value of the regulator's return difference matrix are suggested. On the basis of these bounds, new guaranteed stability margins for such a type of LQ regulator are established. These margins are more relaxed than the guaranteed stability margins proposed in the literature. Furthermore, our investigation provides guaranteed stability margins in cases where known techniques fail. Moreover, it is verified that, in contrast to what happens in the continuous-time case, the singular values of the closed-loop transfer function of the discrete LQ regulator can be, in general, greater than the singular values of the open-loop transfer function. Moreover, in the case of the output-weighted cost function, the singular values of the closed-loop transfer function of the discrete LQ regulator can be, in general, greater than the output-weighting parameter. In this respect, new results relating the singular values of the closed-loop and the open-loop transfer functions of the discrete LQ regulator, are also established