Determining when the absolute state complexity of a Hermitian code achieves its DLP bound

Let g be the genus of the Hermitian function field H/F(q)2 and let C-L(D,mQ(infinity)) be a typical Hermitian code of length n. In [Des. Codes Cryptogr., to appear], we determined the dimension/length profile (DLP) lower bound on the state complexity of C-L(D,mQ(infinity)). Here we determine when this lower bound is tight and when it is not. For m less than or equal to n-2/2 or m greater than or equal to n-2/2 + 2g, the DLP lower bounds reach Wolf's upper bound on state complexity and thus are trivially tight. We begin by showing that for about half of the remaining values of m the DLP bounds cannot be tight. In these cases, we give a lower bound on the absolute state complexity of C-L(D,mQ(infinity)), which improves the DLP lower bound. Next we give a good coordinate order for C-L(D,mQ(infinity)). With this good order, the state complexity of C-L(D,mQ(infinity)) achieves its DLP bound (whenever this is possible). This coordinate order also provides an upper bound on the absolute state complexity of C-L(D,mQ(infinity)) (for those values of m for which the DLP bounds cannot be tight). Our bounds on absolute state complexity do not meet for some of these values of m, and this leaves open the question whether our coordinate order is best possible in these cases. A straightforward application of these results is that if C-L(D,mQ(infinity)) is self-dual, then its state complexity (with respect to the lexicographic coordinate order) achieves its DLP bound of n /2 - q(2)/4, and, in particular, so does its absolute state complexity.

Reasoning about real-time repetitions: terminating and nonterminating

It is common for a real-time system to contain a nonterminating process monitoring an input and controlling an output. Hence, a real-time program development method needs to support nonterminating repetitions. In this paper we develop a general proof rule for reasoning about possibly nonterminating repetitions. The rule makes use of a Floyd-Hoare-style loop invariant that is maintained by each iteration of the repetition, a Jones-style relation between the pre- and post-states on each iteration, and a deadline specifying an upper bound on the starting time of each iteration. The general rule is proved correct with respect to a predicative semantics. In the case of a terminating repetition the rule reduces to the standard rule extended to handle real time. Other special cases include repetitions whose bodies are guaranteed to terminate, nonterminating repetitions with the constant true as a guard, and repetitions whose termination is guaranteed by the inclusion of a fixed deadline. (C) 2002 Elsevier Science B.V. All rights reserved.

Minimum-order stable recursive filter design via the genetic algorithm approach

In this paper, the minimum-order stable recursive filter design problem is proposed and investigated. This problem is playing an important role in pipeline implementation sin signal processing. Here, the existence of a high-order stable recursive filter is proved theoretically, in which the upper bound for the highest order of stable filters is given. Then the minimum-order stable linear predictor is obtained via solving an optimization problem. In this paper, the popular genetic algorithm approach is adopted since it is a heuristic probabilistic optimization technique and has been widely used in engineering designs. Finally, an illustrative example is sued to show the effectiveness of the proposed algorithm.

But what if I don't want to wait forever?

We present an abstract model of the leader election protocol used in the IEEE 1394 High Performance Serial Bus standard. The model is expressed in the probabilistic Guarded Command Language. By formal reasoning based on this description, we establish the probability of the root contention part of the protocol successfully terminating in terms of the number of attempts to do so. Some simple calculations then allow us to establish an upper bound on the time taken for those attempts.

A review of drainage and spontaneous rupture in free standing thin films with tangentially immobile interfaces

A review of spontaneous rupture in thin films with tangentially immobile interfaces is presented that emphasizes the theoretical developments of film drainage and corrugation growth through the linearization of lubrication theory in a cylindrical geometry. Spontaneous rupture occurs when corrugations from adjacent interfaces become unstable and grow to a critical thickness. A corrugated interface is composed of a number of waveforms and each waveform becomes unstable at a unique transition thickness. The onset of instability occurs at the maximum transition thickness, and it is shown that only upper and lower bounds of this thickness can be predicted from linear stability analysis. The upper bound is equivalent to the Freakel criterion and is obtained from the zeroth order approximation of the H-3 term in the evolution equation. This criterion is determined solely by the film radius, interfacial tension and Hamaker constant. The lower bound is obtained from the first order approximation of the H-3 term in the evolution equation and is dependent on the film thinning velocity A semi-empirical equation, referred to as the MTR equation, is obtained by combining the drainage theory of Manev et al. [J. Dispersion Sci. Technol., 18 (1997) 769] and the experimental measurements of Radoev et al. [J. Colloid Interface Sci. 95 (1983) 254] and is shown to provide accurate predictions of film thinning velocity near the critical thickness of rupture. The MTR equation permits the prediction of the lower bound of the maximum transition thickness based entirely on film radius, Plateau border radius, interfacial tension, temperature and Hamaker constant. The MTR equation extrapolates to Reynolds equation under conditions when the Plateau border pressure is small, which provides a lower bound for the maximum transition thickness that is equivalent to the criterion of Gumerman and Homsy [Chem. Eng. Commun. 2 (1975) 27]. The relative accuracy of either bound is thought to be dependent on the amplitude of the hydrodynamic corrugations, and a semiempirical correlation is also obtained that permits the amplitude to be calculated as a function of the upper and lower bound of the maximum transition thickness. The relationship between the evolving theoretical developments is demonstrated by three film thickness master curves, which reduce to simple analytical expressions under limiting conditions when the drainage pressure drop is controlled by either the Plateau border capillary pressure or the van der Waals disjoining pressure. The master curves simplify solution of the various theoretical predictions enormously over the entire range of the linear approximation. Finally, it is shown that when the Frenkel criterion is used to assess film stability, recent studies reach conclusions that are contrary to the relevance of spontaneous rupture as a cell-opening mechanism in foams. (C) 2003 Elsevier Science B.V. All rights reserved.

Configurations in 4-cycle systems

A 4-cycle system of order n, denoted by 4CS(n), exists if and only if nequivalent to1 (mod 8). There are four configurations which can be formed by two 4-cycles in a 4CS(n). Formulas connecting the number of occurrences of each such configuration in a 4CS(n) are given. The number of occurrences of each configuration is determined completely by the number d of occurrences of the configuration D consisting of two 4-cycles sharing a common diagonal. It is shown that for every nequivalent to1 (mod 8) there exists a 4CS(n) which avoids the configuration D, i.e. for which d=0. The exact upper bound for d in a 4CS(n) is also determined.

Entanglement measure for rank-2 mixed states

We provide an easily computable formula for a bipartite mixed-state entanglement measure. Our formula can be applied to readily calculate the entanglement for any rank-2 mixed state of a bipartite system. We use this formula to provide a tight upper bound for the entanglement of formation for rank-2 states of a qubit and a qudit. We also outline situations where our formula could be applied to study the entanglement properties of complex quantum systems.

Bounding the stability and rupture condition of emulsion and foam films

A scaling law is presented that provides a complete solution to the equations bounding the stability and rupture of thin films. The scaling law depends on the fundamental physicochemical properties of the film and interface to calculate bounds for the critical thickness and other key film thicknesses, the relevant waveforms associated with instability and rupture, and film lifetimes. Critical thicknesses calculated from the scaling law are shown to bound the values reported in the literature for numerous emulsion and foam films. The majority of critical thickness values are between 15 to 40% lower than the upper bound critical thickness provided by the scaling law.

Maximal triangle trades with foundation 5 (mod 6) - the final case

The maximum possible volume of a simple, non-Steiner (v, 3, 2) trade was determined for all v by Xhosrovshahi and Torabi (Ars Combinatoria 51 (1999), 211-223), except that in the-case v equivalent to 5 (mod 6), v >= 23, they were only able to provide an upper, bound on the volume. In this paper we construct trades with volume equal to that bound for all v equivalent to 5 (mod 6), thus completing the problem.

Investigations into an optimal transmission scheme for a MIMO system operating in a ricain fading environment

This paper describes investigations into an optimal transmission scheme for a multiple input multiple output (MIMO) system operating in a Rician fading environment. The considerations are reduced to determining a covariance matrix of transmitted signals which maximizes the MIMO capacity under the condition that the receiver has perfect knowledge of the channel while the transmitter has the information about selected statistical quantities which are measured at the receiver. An optimal covariance matrix, which requires information of the Rice factor and the signal to noise ratio, is determined. The transmission scheme relying on the choice of the proposed covariance matrix outperforms the other transmission schemes which were reported earlier in the literature. The proposed scheme realizes an upper bound limit for the MIMO capacity under arbitrary Rician fading conditions. ©2005 IEEE

Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.

The effects of stress management on symptoms of upper respiratory tract infection, secretory immunoglobulin A, and mood in young adults

Objective: To investigate the efficacy of a stress management programme on symptoms of colds and influenza in 27 university students before and after the examination period. Method: The incidence of symptoms, levels of negative affect, and secretion rate of secretory immunoglobulin A (sIgA) were recorded for 5 weeks before treatment, for the 4 weeks of treatment, and for 8 weeks after treatment in treated subjects and in 25 others who did not participate in stress management. Results: Symptoms decreased in treated subjects but not in controls during and after the examination period. Although sIgA secretion rate increased significantly after individual sessions of relaxation, resting secretion rate of sIgA did not increase over the course of the study. Negative affect decreased after examinations in both groups, but was not affected by treatment. Conclusion: Stress management reduced days of illness independently of negative affect and sIgA secretion rate. Although the component of treatment responsible for this effect has yet to be identified, psychological interventions may have a role in reducing symptoms of upper respiratory tract infection. (C) 2001 Elsevier Science Inc. All rights reserved.

The reliability of immunohistochemistry as a prescreening method for the diagnosis of hereditary nonpolyposis colorectal cancer (HNPCC) - Results of an international collaborative study

Hereditary nonpolyposis colorectal cancer syndrome (HNPCC) is an autosomal dominant condition accounting for 2–5% of all colorectal carcinomas as well as a small subset of endometrial, upper urinary tract and other gastrointestinal cancers. An assay to detect the underlying defect in HNPCC, inactivation of a DNA mismatch repair enzyme, would be useful in identifying HNPCC probands. Monoclonal antibodies against hMLH1 and hMSH2, two DNA mismatch repair proteins which account for most HNPCC cancers, are commercially available. This study sought to investigate the potential utility of these antibodies in determining the expression status of these proteins in paraffin-embedded formalin-fixed tissue and to identify key technical protocol components associated with successful staining. A set of 20 colorectal carcinoma cases of known hMLH1 and hMSH2 mutation and expression status underwent immunoperoxidase staining at multiple institutions, each of which used their own technical protocol. Staining for hMSH2 was successful in most laboratories while staining for hMLH1 proved problematic in multiple labs. However, a significant minority of laboratories demonstrated excellent results including high discriminatory power with both monoclonal antibodies. These laboratories appropriately identified hMLH1 or hMSH2 inactivation with high sensitivity and specificity. The key protocol point associated with successful staining was an antigen retrieval step involving heat treatment and either EDTA or citrate buffer. This study demonstrates the potential utility of immunohistochemistry in detecting HNPCC probands and identifies key technical components for successful staining.

Total Daily Energy Expenditure and Incidence of Upper Respiratory Tract Infection Symptoms in Young Females

A group of 31 young females, tennis players and non-athletes, aged 16 2 years (range: 14 - 21 years), with a wide range of physical activity levels was used to investigate the relationship between total daily energy expenditure and the incidence of upper respiratory tract infection symptoms. Methods: During a 12 week winter period, habitual daily activity (excluding training) was evaluated using a 3-day physical activity record. Tennis training was quantified using a validated method of estimating energy expenditure during play. Total daily energy expenditure was calculated from the sum of daily training plus mean habitual daily activity energy expenditures. The total group of subjects was divided in quartiles for total daily energy expenditure. A validated symptom checklist was used to assess the incidence and severity of upper respiratory tract infections, on a daily basis. Results: The girls in the highest quartile of total daily energy expenditure (greater than or equal to 17322 kJ/day) and in the lowest quartile (less than or equal to 10 047 kJ/day) had the greatest incidence of URTI symptomatology, although the moderately active girls in quartile three (12290-16410 kJ/day) presented the lowest incidence. Significant differences in number of upper respiratory tract infection episodes, sickness days and symptomatology index were found between quartiles three and one (p < 0.05) and quartiles three and four (p < 0.01). Peak severity of symptoms was significantly lower in quartile three compared with all other quartiles (p < 0.05).

Application of the maximum entropy method to the (2 + 1)D four-fermion model

We investigate spectral functions extracted using the maximum entropy method from correlators measured in lattice simulations of the (2+1)-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma, and massive pseudoscalar meson; our results confirm the Goldstone nature of the π and permit an estimate of the meson binding energy. We have, however, seen no signal of σ→ππ decay as the chiral limit is approached. In the symmetric phase we observe a resonance of nonzero width in qualitative agreement with analytic expectations; in addition the ultraviolet behavior of the spectral functions is consistent with the large nonperturbative anomalous dimension for fermion composite operators expected in this model.