The average inter-crossing number of equilateral random walks and polygons

In this paper, we study the average inter-crossing number between two random walks and two random polygons in the three-dimensional space. The random walks and polygons in this paper are the so-called equilateral random walks and polygons in which each segment of the walk or polygon is of unit length. We show that the mean average inter-crossing number ICN between two equilateral random walks of the same length n is approximately linear in terms of n and we were able to determine the prefactor of the linear term, which is a = (3 In 2)/(8) approximate to 0.2599. In the case of two random polygons of length n, the mean average inter-crossing number ICN is also linear, but the prefactor of the linear term is different from that of the random walks. These approximations apply when the starting points of the random walks and polygons are of a distance p apart and p is small compared to n. We propose a fitting model that would capture the theoretical asymptotic behaviour of the mean average ICN for large values of p. Our simulation result shows that the model in fact works very well for the entire range of p. We also study the mean ICN between two equilateral random walks and polygons of different lengths. An interesting result is that even if one random walk (polygon) has a fixed length, the mean average ICN between the two random walks (polygons) would still approach infinity if the length of the other random walk (polygon) approached infinity. The data provided by our simulations match our theoretical predictions very well.

An LMI approach to H∞ synchronization of second-order neutral master-slave systems

The H∞ synchronization problem of the master and slave structure of a second-order neutral master-slave systems with time-varying delays is presented in this paper. Delay-dependent sufficient conditions for the design of a delayed output-feedback control are given by Lyapunov-Krasovskii method in terms of a linear matrix inequality (LMI). A controller, which guarantees H∞ synchronization of the master and slave structure using some free weighting matrices, is then developed. A numerical example has been given to show the effectiveness of the method

Regional abundance of on-premise outlets and drinking patterns among Swiss young men: District level analyses and geographic adjustments.

INTRODUCTION AND AIMS: This study investigated the associations of alcohol outlet density with specific alcohol outcomes (consumption and consequences) among young men in Switzerland and assessed the possible geographically related variations. DESIGN AND METHODS: Alcohol consumption and drinking consequences were measured in a 2010-2011 study assessing substance use risk factors (Cohort Study on Substance Use Risk Factors) among 5519 young Swiss men. Outlet density was based on the number of on- and off-premise outlets in the district of residence. Linear regression models were run separately for drinking level, heavy episodic drinking (HED) and drinking consequences. Geographically weighted regression models were estimated when variations were recorded at the district level. RESULTS: No consistent association was found between outlet density and drinking consequences. A positive association between drinking level and HED with on-premise outlet density was found. Geographically weighted regressions were run for drinking level and HED. The predicted values for HED were higher in the southwest part of Switzerland (French-speaking part). DISCUSSION AND CONCLUSIONS: Among Swiss young men, the density of outlets and, in particular, the abundance of bars, clubs and other on-premise outlets was associated with drinking level and HED, even when drinking consequences were not significantly affected. These findings support the idea that outlet density needs to be considered when developing and implementing regional-based prevention initiatives. [Astudillo M, Kuendig H, Centeno-Gil A, Wicki M, Gmel G. Regional abundance of on-premise outlets and drinking patterns among Swiss young men: District level analyses and geographic adjustments. Drug Alcohol Rev 2014;33:526-33].

Tightness of random knotting.

Long polymers in solution frequently adopt knotted configurations. To understand the physical properties of knotted polymers, it is important to find out whether the knots formed at thermodynamic equilibrium are spread over the whole polymer chain or rather are localized as tight knots. We present here a method to analyze the knottedness of short linear portions of simulated random chains. Using this method, we observe that knot-determining domains are usually very tight, so that, for example, the preferred size of the trefoil-determining portions of knotted polymer chains corresponds to just seven freely jointed segments.

Linear response functions for a vibrational configuration interaction state

Linear response functions are implemented for a vibrational configuration interaction state allowing accurate analytical calculations of pure vibrational contributions to dynamical polarizabilities. Sample calculations are presented for the pure vibrational contributions to the polarizabilities of water and formaldehyde. We discuss the convergence of the results with respect to various details of the vibrational wave function description as well as the potential and property surfaces. We also analyze the frequency dependence of the linear response function and the effect of accounting phenomenologically for the finite lifetime of the excited vibrational states. Finally, we compare the analytical response approach to a sum-over-states approach

Orthotropic active strain models for the numerical simulation of cardiac biomechanics

An active strain formulation for orthotropic constitutive laws arising in cardiac mechanics modeling is introduced and studied. The passive mechanical properties of the tissue are described by the Holzapfel-Ogden relation. In the active strain formulation, the Euler-Lagrange equations for minimizing the total energy are written in terms of active and passive deformation factors, where the active part is assumed to depend, at the cell level, on the electrodynamics and on the specific orientation of the cardiac cells. The well-posedness of the linear system derived from a generic Newton iteration of the original problem is analyzed and different mechanical activation functions are considered. In addition, the active strain formulation is compared with the classical active stress formulation from both numerical and modeling perspectives. Taylor-Hood and MINI finite elements are employed to discretize the mechanical problem. The results of several numerical experiments show that the proposed formulation is mathematically consistent and is able to represent the main key features of the phenomenon, while allowing savings in computational costs.

Development of Abutment Design Standards for Local Bridge Designs, Volume 1 of 3, Development of Design Methodology, August 2004

Several superstructure design methodologies have been developed for low volume road bridges by the Iowa State University Bridge Engineering Center. However, to date no standard abutment designs have been developed. Thus, there was a need to establish an easy to use design methodology in addition to generating generic abutment standards and other design aids for the more common substructure systems used in Iowa. The final report for this project consists of three volumes. The first volume (this volume) summarizes the research completed in this project. A survey of the Iowa County Engineers was conducted from which it was determined that while most counties use similar types of abutments, only 17 percent use some type of standard abutment designs or plans. A literature review revealed several possible alternative abutment systems for future use on low volume road bridges in addition to two separate substructure lateral load analysis methods. These consisted of a linear and a non-linear method. The linear analysis method was used for this project due to its relative simplicity and the relative accuracy of the maximum pile moment when compared to values obtained from the more complex non-linear analysis method. The resulting design methodology was developed for single span stub abutments supported on steel or timber piles with a bridge span length ranging from 20 to 90 ft and roadway widths of 24 and 30 ft. However, other roadway widths can be designed using the foundation design template provided. The backwall height is limited to a range of 6 to 12 ft, and the soil type is classified as cohesive or cohesionless. The design methodology was developed using the guidelines specified by the American Association of State Highway Transportation Officials Standard Specifications, the Iowa Department of Transportation Bridge Design Manual, and the National Design Specifications for Wood Construction. The second volume introduces and outlines the use of the various design aids developed for this project. Charts for determining dead and live gravity loads based on the roadway width, span length, and superstructure type are provided. A foundation design template was developed in which the engineer can check a substructure design by inputting basic bridge site information. Tables published by the Iowa Department of Transportation that provide values for estimating pile friction and end bearing for different combinations of soils and pile types are also included. Generic standard abutment plans were developed for which the engineer can provide necessary bridge site information in the spaces provided. These tools enable engineers to design and detail county bridge substructures more efficiently. The third volume provides two sets of calculations that demonstrate the application of the substructure design methodology developed in this project. These calculations also verify the accuracy of the foundation design template. The printouts from the foundation design template are provided at the end of each example. Also several tables provide various foundation details for a pre-cast double tee superstructure with different combinations of soil type, backwall height, and pile type.

Development of Abutment Design Standards for Local Bridge Designs, Volume 3 of 3, Verification of Design Methodology, August 2004

Several superstructure design methodologies have been developed for low volume road bridges by the Iowa State University Bridge Engineering Center. However, to date no standard abutment designs have been developed. Thus, there was a need to establish an easy to use design methodology in addition to generating generic abutment standards and other design aids for the more common substructure systems used in Iowa. The final report for this project consists of three volumes. The first volume summarizes the research completed in this project. A survey of the Iowa County Engineers was conducted from which it was determined that while most counties use similar types of abutments, only 17 percent use some type of standard abutment designs or plans. A literature review revealed several possible alternative abutment systems for future use on low volume road bridges in addition to two separate substructure lateral load analysis methods. These consisted of a linear and a non-linear method. The linear analysis method was used for this project due to its relative simplicity and the relative accuracy of the maximum pile moment when compared to values obtained from the more complex non-linear analysis method. The resulting design methodology was developed for single span stub abutments supported on steel or timber piles with a bridge span length ranging from 20 to 90 ft and roadway widths of 24 and 30 ft. However, other roadway widths can be designed using the foundation design template provided. The backwall height is limited to a range of 6 to 12 ft, and the soil type is classified as cohesive or cohesionless. The design methodology was developed using the guidelines specified by the American Association of State Highway Transportation Officials Standard Specifications, the Iowa Department of Transportation Bridge Design Manual, and the National Design Specifications for Wood Construction. The second volume introduces and outlines the use of the various design aids developed for this project. Charts for determining dead and live gravity loads based on the roadway width, span length, and superstructure type are provided. A foundation design template was developed in which the engineer can check a substructure design by inputting basic bridge site information. Tables published by the Iowa Department of Transportation that provide values for estimating pile friction and end bearing for different combinations of soils and pile types are also included. Generic standard abutment plans were developed for which the engineer can provide necessary bridge site information in the spaces provided. These tools enable engineers to design and detail county bridge substructures more efficiently. The third volume (this volume) provides two sets of calculations that demonstrate the application of the substructure design methodology developed in this project. These calculations also verify the accuracy of the foundation design template. The printouts from the foundation design template are provided at the end of each example. Also several tables provide various foundation details for a pre-cast double tee superstructure with different combinations of soil type, backwall height, and pile type.

Development of Abutment Design Standards for Local Bridge Designs, Volume 2 of 3, Design Manual, August 2004

Several superstructure design methodologies have been developed for low volume road bridges by the Iowa State University Bridge Engineering Center. However, to date no standard abutment designs have been developed. Thus, there was a need to establish an easy to use design methodology in addition to generating generic abutment standards and other design aids for the more common substructure systems used in Iowa. The final report for this project consists of three volumes. The first volume summarizes the research completed in this project. A survey of the Iowa County Engineers was conducted from which it was determined that while most counties use similar types of abutments, only 17 percent use some type of standard abutment designs or plans. A literature review revealed several possible alternative abutment systems for future use on low volume road bridges in addition to two separate substructure lateral load analysis methods. These consisted of a linear and a non-linear method. The linear analysis method was used for this project due to its relative simplicity and the relative accuracy of the maximum pile moment when compared to values obtained from the more complex non-linear analysis method. The resulting design methodology was developed for single span stub abutments supported on steel or timber piles with a bridge span length ranging from 20 to 90 ft and roadway widths of 24 and 30 ft. However, other roadway widths can be designed using the foundation design template provided. The backwall height is limited to a range of 6 to 12 ft, and the soil type is classified as cohesive or cohesionless. The design methodology was developed using the guidelines specified by the American Association of State Highway Transportation Officials Standard Specifications, the Iowa Department of Transportation Bridge Design Manual, and the National Design Specifications for Wood Construction. The second volume (this volume) introduces and outlines the use of the various design aids developed for this project. Charts for determining dead and live gravity loads based on the roadway width, span length, and superstructure type are provided. A foundation design template was developed in which the engineer can check a substructure design by inputting basic bridge site information. Tables published by the Iowa Department of Transportation that provide values for estimating pile friction and end bearing for different combinations of soils and pile types are also included. Generic standard abutment plans were developed for which the engineer can provide necessary bridge site information in the spaces provided. These tools enable engineers to design and detail county bridge substructures more efficiently. The third volume provides two sets of calculations that demonstrate the application of the substructure design methodology developed in this project. These calculations also verify the accuracy of the foundation design template. The printouts from the foundation design template are provided at the end of each example. Also several tables provide various foundation details for a pre-cast double tee superstructure with different combinations of soil type, backwall height, and pile type.

Genometrics as an essential tool for the assembly of whole genome sequences: the example of the chromosome of Bifidobacterium longum NCC2705.

BACKGROUND: Analysis of the first reported complete genome sequence of Bifidobacterium longum NCC2705, an actinobacterium colonizing the gastrointestinal tract, uncovered its proteomic relatedness to Streptomyces coelicolor and Mycobacterium tuberculosis. However, a rapid scrutiny by genometric methods revealed a genome organization totally different from all so far sequenced high-GC Gram-positive chromosomes. RESULTS: Generally, the cumulative GC- and ORF orientation skew curves of prokaryotic genomes consist of two linear segments of opposite slope: the minimum and the maximum of the curves correspond to the origin and the terminus of chromosome replication, respectively. However, analyses of the B. longum NCC2705 chromosome yielded six, instead of two, linear segments, while its dnaA locus, usually associated with the origin of replication, was not located at the minimum of the curves. Furthermore, the coorientation of gene transcription with replication was very low. Comparison with closely related actinobacteria strongly suggested that the chromosome of B. longum was misassembled, and the identification of two pairs of relatively long homologous DNA sequences offers the possibility for an alternative genome assembly proposed here below. By genometric criteria, this configuration displays all of the characters common to bacteria, in particular to related high-GC Gram-positives. In addition, it is compatible with the partially sequenced genome of DJO10A B. longum strain. Recently, a corrected sequence of B. longum NCC2705, with a configuration similar to the one proposed here below, has been deposited in GenBank, confirming our predictions. CONCLUSION: Genometric analyses, in conjunction with standard bioinformatic tools and knowledge of bacterial chromosome architecture, represent fast and straightforward methods for the evaluation of chromosome assembly.

Evaluation of Virtual Reality Snowplow Simulator Training, January 2007

Each winter, Iowa Department of Transportation (Iowa DOT) maintenance operators are responsible for plowing snow off federal and state roads in Iowa. Drivers typically work long shifts under treacherous conditions. In addition to properly navigating the vehicle, drivers are required to operate several plowing mechanisms simultaneously, such as plow controls and salt spreaders. There is little opportunity for practicing these skills in real-world situations. A virtual reality training program would provide operators with the opportunity to practice these skills under realistic yet safe conditions, as well as provide basic training to novice or less-experienced operators. In order to provide such training to snowplow operators in Iowa, the Iowa DOT purchased a snowplow simulator. The Iowa DOT commissioned a study through Iowa State University designed to (1) assess the use of this simulator as a training tool and (2) examine personality and other characteristics associated with being an experienced snowplow operator. The results of this study suggest that Iowa DOT operators of all ages and levels of experience enjoyed and seemed to benefit from virtual reality snowplow simulator training. Simulator sickness ratings were relatively low, implying that the simulator is appropriate for training a wide range of Iowa DOT operators. Many reported that simulator training was the most useful aspect of training for them.

On prediction of individual sequences

Sequential randomized prediction of an arbitrary binary sequence isinvestigated. No assumption is made on the mechanism of generating the bit sequence. The goal of the predictor is to minimize its relative loss, i.e., to make (almost) as few mistakes as the best ``expert'' in a fixed, possibly infinite, set of experts. We point out a surprising connection between this prediction problem and empirical process theory. First, in the special case of static (memoryless) experts, we completely characterize the minimax relative loss in terms of the maximum of an associated Rademacher process. Then we show general upper and lower bounds on the minimaxrelative loss in terms of the geometry of the class of experts. As main examples, we determine the exact order of magnitude of the minimax relative loss for the class of autoregressive linear predictors and for the class of Markov experts.

A new compact linear programming formulation for choice network revenue management

The choice network revenue management model incorporates customer purchase behavioras a function of the offered products, and is the appropriate model for airline and hotel networkrevenue management, dynamic sales of bundles, and dynamic assortment optimization.The optimization problem is a stochastic dynamic program and is intractable. A certainty-equivalencerelaxation of the dynamic program, called the choice deterministic linear program(CDLP) is usually used to generate dyamic controls. Recently, a compact linear programmingformulation of this linear program was given for the multi-segment multinomial-logit (MNL)model of customer choice with non-overlapping consideration sets. Our objective is to obtaina tighter bound than this formulation while retaining the appealing properties of a compactlinear programming representation. To this end, it is natural to consider the affine relaxationof the dynamic program. We first show that the affine relaxation is NP-complete even for asingle-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a newcompact linear program that approximates the dynamic programming value function betterthan CDLP, provably between the CDLP value and the affine relaxation, and often comingclose to the latter in our numerical experiments. When the segment consideration sets overlap,we show that some strong equalities called product cuts developed for the CDLP remain validfor our new formulation. Finally we perform extensive numerical comparisons on the variousbounds to evaluate their performance.

Expression of apoptosis and survival genes in human memory T cell populations

RESUME Introduction: Les cellules T mémoires humaines sont classées en trois sous-populations sur la base de l'expression d'un marqueur de surface cellulaire, CD45RA, et du récepteur aux chimiokines, CCR7. Ces sous-populations, nommées cellules mémoires centrales (TcM), mémoires effectrices (TEM) et mémoires effectrices terminales (ITEM), ont des rôles fonctionnels distincts, ainsi que des capacités de prolifération et de régénération différentes. Cependant, la génération de ces différences reste encore mal comprise et on ignore les mécanismes moléculaires impliqués. Matériaux et Méthodes: Des cellules mononucléaires humaines du sang périphérique ont été séparées par cytométrie de flux selon leur expression de CD4, CD8, CD45RA et CCR7 en sous-populations de cellules CD4+ ou CD8+ naïves, TcM, TEM ou ITEM. Dans chacune de ces sous-populations, 14 gènes impliqués dans l'apoptose, la survie ou la capacité proliférative des cellules T ont été quantifiés par RT-PCR en temps réel, relativement à l'expression d'un gène de référence endogène. L'ARN provenant de 450 cellules T a été utilisé par gène et par sous-population. Les gènes analysés (cibles) comprenaient des gènes de survie (BAFF, APRIL, BAFF-R, BCMA, TACI, IL-15Rα, IL-7Rα), des gènes anti-apoptotiques (Bcl-2, BclxL, FLIP), des gènes pro-apoptotiques (Bad, Bax, Fast) et le gène anti-prolifératif, Tob. A l'aide de la méthode comparative delta-delta-CT, le taux d'expression des gènes cibles de chaque sous-population des cellules T mémoires CD4+ et CD8+, à été comparée à leur taux d'expression dans les cellules T naïves CD4+ et CD8+. Résultats: Dans les cellules CD8+, les gènes pro-apoptotiques Bax et Fast étaient surexprimés dans toutes les sous-populations mémoires, tandis que l'expression des facteurs anti-apoptotiques et de survie comme Bcl-2, APRIL et BAFF-R, étaient diminués. Ces deux tendances étaient particulièrement accentuées dans les sous-groupes des cellules mémoires TEM et TTEM. A noter que malgré le fait que leur expression était également diminuée dans les autres cellules mémoires, le facteur de survie IL-7Ra, était sélectivement surexprimé dans la sous-population de cellules TcM et l'expression d'IL-15Ra était sélectivement augmentée dans les TEM. Dans les cellules CD4+, le taux d'expression des gènes analysés était plus variable entre les sujets étudiés que dans les cellules CD8+, ne permettant pas de définir un profil d'expression spécifique. L'expression du gène de survie BAFF par contre, a été significativement augmentée dans toutes les sous-populations mémoire CD4+. Il en va de même pour l'expression d' APRIL et de BAFF-R, bien que dans moindre degré. A remarquer que l'expression du facteur anti-apoptotique Fast a été observée uniquement dans la souspopulation des TTEM. Discussion et Conclusions: Cette étude montre une nette différence entre les cellules CD8+ et CD4+, en ce qui concerne les profils d'expression des gènes impliqués dans la survie et l'apoptose des cellules T mémoires. Ceci pourrait impliquer une régulation cellulaire homéostatique distincte dans ces deux compartiments de cellules T mémoires. Dans les cellules CD8+ l'expression d'un nombre de gènes impliqués dans la survie et la protection de l'apoptose semblerait être diminuée dans les populations TEM et TTEM en comparaison à celle des sous-populations naïves et TEM, tandis que l'expression des gènes pro-apoptotiques semblerait être augmentée. Comme ceci paraît être plus accentué dans les TTEM, cela pourrait indiquer une plus grande disposition à l'apopotose dans les populations CCR7- (effectrices) et une perte de survie parallèlement à l'acquisition de capacités effectrices. Ceci parlerait en faveur d'un modèle de différentiation linéaire dans les cellules CD8+. De plus, l'augmentation sélective de l'expression d'IL-7Ra observée dans le sous-groupe de cellules mémoires TEM, et d'IL-15Ra dans celui des TEM, pourrait indiquer un moyen de sélection pour des réponses immunitaires mémoires à long terme par une réponse distincte à ces cytokines. Dans les cellules CD4+ par contre, aucun profil d'expression n'a pu être déterminé; les résultats suggèrent même une résistance relative à l'apoptose de la part des cellules mémoires. Ceci pourrait favoriser l'existence d'un modèle de différentiation plus flexible avec des possibilités d'interaction multiples. Ainsi, la surexpression sélective de BAFF, APRIL et BAFF-R dans les sous-populations individuelles des cellules mémoires pourrait être un indice de l'interaction de ces sous-groupes avec des cellules B. ABSTRACT Introduction: Based on their surface expression of the CD45 isoform and of the CCR7 chemokine receptor, memory T cells have been divided into the following three subsets: central memory (TAM), effector memory (TEM) and terminal effector memory (ITEM). Distinct functional roles and different proliferative and regenerative capacities have been attributed to each one of these subpopulations. The molecular mechanisms underlying these differences; however, remain poorly understood. Materials and Methods: According to their expression of CD4, CD8, CD45RA and CCR7, human peripheral blood mononuclear cells were sorted by flow-cytometry into CD4+ or CD8+ naïve, TAM, TEM and ITEM subsets. Using real-time PCR, the expression of 14 genes known to be involved in apoptotis, survival or proliferation of T cells was quantified separately in each individual subset, relative to an endogenous reference gene. The RNA equivalent of 450 T cells was used for each gene and subset. The target gene panel included the survival genes BAFF, APRIL, BAFF-R, BCMA, TACI, IL-15Rα and IL-7Rα, the anti-apoptotic genes Bcl2, Bcl-xL and FLIP, the pro-apoptotic genes Bad, Bax and Fast, as well as the antiproliferative gene Tob. Using the comparative CT-method, the expression of the target genes in the three memory T cell subsets of both CD4+ and CD8+ T cell populations was compared to their expression in the naïve T cells. Results: In CD8+ cells, the pro-apoptotic factors Bax and Fast were found to be upregulated in all memory T cell subsets, whereas the survival and anti-apoptotic factors Bcl-2, APRIL and BAFF-R were downregulated. These tendencies were most accentuated in TEM and TTEM subsets. Even though the survival factor IL-7Rα was also downregulated in these subsets, interestingly, it was selectively upregulated in the CD8+ TAM subset. Similarly, IL-15Rαexpression was shown to be selectively upregulated in the CD8+ TEM subset. In CD4+ cells, the expression levels of the analyzed genes showed a greater inter-individual variability than in CD8+ cells, thus suggesting the absence of any particular expression pattern for CD4+ memory T cells. However, the survival factor BAFF was found to be significantly upregulated in all CD4+ memory T cell subsets, as was also the expression of APRIL and BAFF-R, although to a lesser extent. Furthermore, it was noted that the pro-apoptotic gene Fast was only expressed in the TTEM CD4+ subset. Discussion and Conclusions: Genes involved in apoptosis and survival in human memory T cells have been shown to be expressed differently in CD8+ cells as compared to CD4+ cells, suggesting a distinct regulation of cell homeostasis in these two memory T cell compartments. The present study suggests that, in CD8+ T cells, the expression of various survival and antiapoptotic genes is downregulated in TEM and TTEM subsets, while the expression of proapoptotic genes is upregulated in comparison to the naïve and the TAM populations. These characteristics, potentially translating to a greater susceptibility to apoptosis in the CCR7- (effector) memory populations, are accentuated in the TTEM population, suggesting a loss of survival in parallel to the acquisition of effector capacities. This speaks in favour of a linear differentiation model in CD8+ T memory cells. Moreover, the observed selectively increased expression of IL-7Rα in CD8+ TAM cells - as that of IL-15Rα in CD8+ TEM cells -suggest that differential responsiveness to cytokines could confer a selection bias for distinct long-term memory cell responses. Relative to the results for CD8+ T cells, those for CD4+ T cells seem to indicate a certain resistance of the memory subsets to apoptosis, suggesting the possibility of a more flexible differentiation model with multiple checkpoints and potential interaction of CD4+ memory cells with other cells. Thus, the selective upregulation of BAFF, APRIL and BAFF-R in individual memory subsets could imply an interaction of these subsets with B cells.

Optimization of multiclass queueing networks with changeover times via the achievable region method: Part II, the multi-station case

We address the problem of scheduling a multi-station multiclassqueueing network (MQNET) with server changeover times to minimizesteady-state mean job holding costs. We present new lower boundson the best achievable cost that emerge as the values ofmathematical programming problems (linear, semidefinite, andconvex) over relaxed formulations of the system's achievableperformance region. The constraints on achievable performancedefining these formulations are obtained by formulatingsystem's equilibrium relations. Our contributions include: (1) aflow conservation interpretation and closed formulae for theconstraints previously derived by the potential function method;(2) new work decomposition laws for MQNETs; (3) new constraints(linear, convex, and semidefinite) on the performance region offirst and second moments of queue lengths for MQNETs; (4) a fastbound for a MQNET with N customer classes computed in N steps; (5)two heuristic scheduling policies: a priority-index policy, anda policy extracted from the solution of a linear programmingrelaxation.