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Articles 39991 - 40020 of 45733
Full-Text Articles in Entire DC Network
The Upper Interval Topology, Property M, And Compactness, Jimmie Lawson
The Upper Interval Topology, Property M, And Compactness, Jimmie Lawson
Faculty Publications
The use of intrinsic topology such as interval topology and order topology that were typically symmetric was discussed. The theory of continuous lattices provided strong motivation for the consideration of such topologies such as the Scott topology or the hull-kernel topology which were not symmetric. Another approach to the study of topology on ordered structures was to begin with a set X equipped both with a partial order ≤ and a topology. The results show that these orders were called as closed order and the resulting ordered topological space was called as pospace, when the assumption was satisfied.
Principal Component Mapping Applied To Raman Microspectroscopy Of Fiber-Reinforced Polymer Composites, C. M. Stellman, K. S. Booksh, A. R. Muroski, M. P. Nelson, Michael L. Myrick
Principal Component Mapping Applied To Raman Microspectroscopy Of Fiber-Reinforced Polymer Composites, C. M. Stellman, K. S. Booksh, A. R. Muroski, M. P. Nelson, Michael L. Myrick
Faculty Publications
We describe the development and implementation of a spectroscopic Raman imaging system using Principal Component data analysis. Raman microspectroscopy followed by multivariate data analysis and principal component mapping has been used to investigate the spatial variations of chemical and physical properties at interfaces in glass-reinforced composites on the micrometer scale. A protocol for monitoring chemical and physical variances via multivariate statistics has been developed and a preliminary study of a "real world" glass-reinforced composite is presented. It is demonstrated that multivariate Raman imaging is more precisely interpretable than traditional univariate methods and that by appropriately choosing distinct spectral regions (such …
The Evolution Of Probability Functions In An Inelasticly Deforming Two-Phase Medium, Brent L. Adams, H. Garmestani, S. Lin
The Evolution Of Probability Functions In An Inelasticly Deforming Two-Phase Medium, Brent L. Adams, H. Garmestani, S. Lin
Faculty Publications
A formulation is introduced here for the evolution of correlation functions in an inelastically deforming two phase medium. Probability functions play a major role in describing the statistical distribution of different phases in a heterogeneous medium in the development of statistical continuum theory. Proper formulation of statistical continuum model for inelastic deformation requires better understanding of the evolution of the corresponding probability functions. A two point probability function representation is used to approximate the statistical correlation functions. The evolution of these functions requires the information from higher order probability functions, in this case, a three point probability function. A decomposition …
What Can Humor And Advertising Teach Us About Legal Drafting?, Dallin D. Oaks, Jeremy Lewis
What Can Humor And Advertising Teach Us About Legal Drafting?, Dallin D. Oaks, Jeremy Lewis
Faculty Publications
In his book Legal Drafting in a Nutshell, Haggard includes a useful chapter of nearly 50 pages in which he lists various lexical and structural elements and explains how these can lead to ambiguous writing. The kind of inventory approach that he presents is helpful and reveals that ambiguity doesn't just happen but often results from the careless use of identifiable structures or particular words.
A Recursive Green's Function Method For Boundary Integral Analysis Of Inhomogeneous Domains, Jim D. Freeze, Michael A. Jensen
A Recursive Green's Function Method For Boundary Integral Analysis Of Inhomogeneous Domains, Jim D. Freeze, Michael A. Jensen
Faculty Publications
The recursive Green's function method (RGFM) for computation of fields scattered by two-dimensional (2-D) inhomogeneous dielectric bodies is presented. The algorithm efficiently constructs the Green's function for the inhomogeneous region by recursively combining known Green's functions from smaller subdomains. The fields on the scatterer surface are then computed using a boundary integral formulation. Proper implementation of the RGFM results in computational and storage complexities which scale as N1.5 and N, respectively, where N is the total number of discrete cells in a domain. Comparisons of results obtained using the RGFM with those computed from moment method and exact solutions show …
Growing Up Poor: Home, School And Street In London 1870-1914, L. Margaret Barnett
Growing Up Poor: Home, School And Street In London 1870-1914, L. Margaret Barnett
Faculty Publications
No abstract provided.
Reading Lives: Reconstructing Childhood, Books And Schools In Britain, 1870-1920, L. Margaret Barnett
Reading Lives: Reconstructing Childhood, Books And Schools In Britain, 1870-1920, L. Margaret Barnett
Faculty Publications
No abstract provided.
Seasonal Patterns And Controls On Net Ecosystem Co2 Exchange In A Boreal Peatland Complex, Jill L. Bubier, Patrick M. Crill, Tim R. Moore, Kathleen Savage, Ruth K. Varner
Seasonal Patterns And Controls On Net Ecosystem Co2 Exchange In A Boreal Peatland Complex, Jill L. Bubier, Patrick M. Crill, Tim R. Moore, Kathleen Savage, Ruth K. Varner
Faculty Publications
We measured seasonal patterns of net ecosystem exchange (NEE) of CO2 in a diverse peatland complex underlain by discontinuous permafrost in northern Manitoba, Canada, as part of the Boreal Ecosystems Atmosphere Study (BOREAS). Study sites spanned the full range of peatland trophic and moisture gradients found in boreal environments from bog (pH 3.9) to rich fen (pH 7.2). During midseason (July‐August, 1996), highest rates of NEE and respiration followed the trophic sequence of bog (5.4 to −3.9 μmol CO2 m−2 s−1) < poor fen (6.3 to −6.5 μmol CO2 m−2 s−1) < intermediate fen (10.5 to −7.8 μmol CO2 m−2 s−1) < rich fen (14.9 to −8.7 μmol CO2m−2 s−1). The sequence changed during spring (May‐June) and fall (September‐October) when ericaceous shrub (e.g., Chamaedaphne calyculata) bogs and sedge (Carex spp.) communities in poor to intermediate fens had higher maximum CO2 fixation rates than deciduous shrub‐dominated (Salix spp. and Betula spp.) rich fens. Timing of snowmelt and differential rates of peat surface thaw in microtopographic hummocks and hollows controlled the onset of carbon uptake in spring. Maximum photosynthesis and respiration were closely correlated throughout the growing season with a ratio of approximately 1/3 ecosystem respiration to maximum carbon uptake at all sites across the trophic gradient. Soil temperatures above the water table and timing of surface thaw and freeze‐up in the spring and fall were more important to net CO2 exchange than deep soil warming. This close coupling of maximum CO2 uptake and respiration to easily measurable variables, such as trophic status, peat temperature, and water table, will improve models of wetland carbon exchange. Although trophic status, aboveground net primary productivity, and surface temperatures were more important than water level in predicting respiration on a daily basis, the mean position of the water table was a good predictor (r2 = 0.63) of mean respiration rates across the range of plant community and moisture gradients. Q10 values ranged from 3.0 to 4.1 from bog to rich fen, but when normalized by above ground vascular plant biomass, the Q10 for all sites was 3.3.
Aveux Incités Par Les Officiers Chargés De L’Application De La Loi, L’Expérience Des Etats-Unis, Paul Marcus
Aveux Incités Par Les Officiers Chargés De L’Application De La Loi, L’Expérience Des Etats-Unis, Paul Marcus
Faculty Publications
No abstract provided.
A Work Minimization Approach To Image Morphing, Peisheng Gao, Thomas W. Sederberg
A Work Minimization Approach To Image Morphing, Peisheng Gao, Thomas W. Sederberg
Faculty Publications
An algorithm is presented for morphing two images, often with little or no user interaction. For two similar images (such as different faces against a neutral background) the algorithm generally can create a pleasing morph completely automatically. The algorithm seeks the minimum work to deform one image into the other, where work is a function of the amount of warping and recoloration. A hierarchical method for finding a minimal work solution is invoked. Anchor point constraints are satisfied by imposing penalties on deformations that disobey these constraints. Good results can be obtained in less than ten seconds for 256 x …
Vassiliev Invariants: A New Framework For Quantum Gravity, Rodolfo Gambini, Jorge Griego, Jorge Pullin
Vassiliev Invariants: A New Framework For Quantum Gravity, Rodolfo Gambini, Jorge Griego, Jorge Pullin
Faculty Publications
We show that Vassiliev invariants of knots, appropriately generalized to the spin network context, are loop differentiable in spite of being diffeomorphism invariant. This opens the possibility of defining rigorously the constraints of quantum gravity as geometrical operators acting on the space of Vassiliev invariants of spin nets. We show how to explicitly realize the diffeomorphism constraint on this space and present proposals for the construction of Hamiltonian constraints. © 1998 Published by Elsevier Science B.V.
Insulator-Metal Crossover Near Optimal Doping In Pr22xcexcuo4: Anomalous Normal-State Low Temperature Resistivity, P. Fournier, P. Mohanty, E. Maiser, S. Darzens, T. Venkatesan, C. J. Lobb, G. Czjzek, Richard A. Webb, R. L. Greene
Insulator-Metal Crossover Near Optimal Doping In Pr22xcexcuo4: Anomalous Normal-State Low Temperature Resistivity, P. Fournier, P. Mohanty, E. Maiser, S. Darzens, T. Venkatesan, C. J. Lobb, G. Czjzek, Richard A. Webb, R. L. Greene
Faculty Publications
Normal-state resistivity measurements at high fields and low temperatures in electron-doped Pr2-xCexCuO4 thin films reveal an insulator-metal crossover near a doping level x≈0.15, similar to a previous report on hole-doped La2-xSrxCuO4. The temperature dependence of the resistivity of insulatinglike samples is sublogarithmic, while for metallic samples (with x = 0.17) the resistivity is linear from 40 mK to 40 K. This surprising latter observation suggests an unusual contribution to the scattering processes at low temperature in these materials. We conclude that the ground state at x = 0.15, corresponding …
Activation Of Signal Transducers And Activators Of Transcription 1 And 3 By Leukemia Inhibitory Factor, Oncostatin-M, And Interferon-Γ In Adipocytes, Jacqueline M. Stephens, Steven J. Lumpkin, Jordan B. Fishman
Activation Of Signal Transducers And Activators Of Transcription 1 And 3 By Leukemia Inhibitory Factor, Oncostatin-M, And Interferon-Γ In Adipocytes, Jacqueline M. Stephens, Steven J. Lumpkin, Jordan B. Fishman
Faculty Publications
We have recently demonstrated that signal transducers and activators of transcription (STATs) 1, 3, 5A, 5B, and 6 are expressed in both cultured and native adipocytes. Our current studies have focused on the activation of STATs 1 and 3 by leukemia inhibitory factor (LIF), oncostatin-M (OSM), and interferon-γ, (IFNγ) in 3T3-L1 adipocytes. IFNγ is shown to be a potent activator of STAT 1 as indicated by both tyrosine phosphorylation and nuclear translocation. However, LIF and OSM, which are potent inducers of STAT 3, are less potent activators of STAT 1 as measured by both tyrosine phosphorylation and nuclear translocation. Both …
Analytical Solution Of The Generalized Discrete Poisson Equation, G. Y. Hu, Jai Yon Ryu, R. F. O'Connell
Analytical Solution Of The Generalized Discrete Poisson Equation, G. Y. Hu, Jai Yon Ryu, R. F. O'Connell
Faculty Publications
We present an analytical solution to the generalized discrete Poisson equation, a matrix equation which has a tridiagonal matrix with fringes having an arbitrary value for the diagonal elements. The results are of relevance to a variety of physical problems, which require the numerical solution of the Poisson equation. As examples, the formula has been applied to the solution of the electrostatic problem of tunnelling junction arrays with two and three rows.
Ecosystem Metabolism In A Subtropical Seagrass-Dominated Lagoon, Susan Ziegler, Ronald Benner
Ecosystem Metabolism In A Subtropical Seagrass-Dominated Lagoon, Susan Ziegler, Ronald Benner
Faculty Publications
Measurements of ecosystem gross primary production (GPP) and respiration (R) were made for 2 to 3 consecutive days on 10 occasions from February 1996 through June 1997 in the seagrass-dominated Laguna Madre (Texas, USA). Ecosystem GPP and R were quantified using 3 independent measurements including the open-water technique using dissolved oxygen (DO) and dissolved inorganic carbon (DIC) and the summation of discrete measurements of the water column and benthos. Diel curves of DIC were often influenced by water movement while the impact of water movement on DO was not apparent. This was attributed to the longer turnover time of DIC …
Life In The World To Come: How Real Will It Be?, Samuele Bacchiocchi
Life In The World To Come: How Real Will It Be?, Samuele Bacchiocchi
Faculty Publications
No abstract provided.
Ubiquitous Molecular Substrates For Associative Learning And Activity-Dependent Neuronal Facilitation., Louis D. Matzel, Andrew C. Talk, Isabel A. Muzzio, Ronald F. Rogers
Ubiquitous Molecular Substrates For Associative Learning And Activity-Dependent Neuronal Facilitation., Louis D. Matzel, Andrew C. Talk, Isabel A. Muzzio, Ronald F. Rogers
Faculty Publications
Recent evidence suggests that many of the molecular cascades and substrates that contribute to learning-related forms of neuronal plasticity may be conserved across ostensibly disparate model systems. Notably, the facilitation of neuronal excitability and synaptic transmission that contribute to associative learning in Aplysia and Hermissenda, as well as associative LTP in hippocampal CA1 cells, all require (or are enhanced by) the convergence of a transient elevation in intracellular Ca2+ with transmitter binding to metabotropic cell-surface receptors. This temporal convergence of Ca2+ and G-protein-stimulated second-messenger cascades synergistically stimulates several classes of serine/threonine protein kinases, which in turn modulate receptor function or …
Isolation Of A Highly Active Photosystem Ii Preparation From Synechocystis 6803 Using A Histidine-Tagged Mutant Of Cp 47, Terry M. Bricker, Jason Morvant, Najy Masri, Holly M. Sutton, Laurie K. Frankel
Isolation Of A Highly Active Photosystem Ii Preparation From Synechocystis 6803 Using A Histidine-Tagged Mutant Of Cp 47, Terry M. Bricker, Jason Morvant, Najy Masri, Holly M. Sutton, Laurie K. Frankel
Faculty Publications
Site-directed mutagenesis was used to produce a Synechocystis mutant containing a histidine tag at the C terminus of the CP 47 protein of Photosystem II. This mutant cell line, designated HT-3, exhibited slightly above normal rates of oxygen evolution and appeared to accumulate somewhat more Photosystem II reaction centers than a control strain. A rapidly isolatable (<7 >h) oxygen-evolving Photosystem II preparation was prepared from HT-3 using dodecyl-β-d-maltoside solubilization and Co2+ metal affinity chromatography. This histidine-tagged Photosystem II preparation stably evolved oxygen at a high rate (2440 μmol O2 (mg chl)-1 h-1), exhibited an α-band absorption maximum at 674 nm, …7>
Determination Of Chloride Concentration Using Capillary Zone Electrophoresis: An Instrumental Analysis Chemistry Laboratory Experiment, Michael A. Janusa
Determination Of Chloride Concentration Using Capillary Zone Electrophoresis: An Instrumental Analysis Chemistry Laboratory Experiment, Michael A. Janusa
Faculty Publications
Capillary zone electrophoresis (CZE) has received a great deal of attention as a tool for the separation and detection of low-molecular-mass inorganic ions. CZE is a fast growing analytical technique that uses a low-volume sample accompanied by a high detection efficiency. Since this is a fairly new analytical technique that shows tremendous promise, it should be introduced to students at the undergraduate level. We have developed a CZE experiment that is well suited for an instrumental analysis chemistry laboratory and can be modified for other species or substances.
Bibliography, Cultural Studies, And Rare Book Librarianship: Tennyson's "Crossing The Bar" And The Cultural Significance Of Unauthoritative Texts, Patrick G. Scott
Bibliography, Cultural Studies, And Rare Book Librarianship: Tennyson's "Crossing The Bar" And The Cultural Significance Of Unauthoritative Texts, Patrick G. Scott
Faculty Publications
For a conference discussion of textual bibliographers and rare book librarians on the topic "Who needs textual studies?," this paper examines three different appearances of Alfred Tennyson's poem "Crossing the Bar": (1) a manuscript facsimile, (ii) its reuse as a hymn and in a giftbook; and (iii) the paperback Armed Services Edition distributed to US troops overseas during World War II, and argues that with the shift from literary studies to cultural studies such later "unauthoritative texts" have a new importance for scholars and students, and deserve increased attention from bibliographers, collectors, and rare book librarians. Originally presented at the …
A Theory Of Satisficing Decisions And Control, Richard L. Frost, Michael A. Goodrich, Wynn C. Stirling
A Theory Of Satisficing Decisions And Control, Richard L. Frost, Michael A. Goodrich, Wynn C. Stirling
Faculty Publications
The existence of an optimal control policy and the techniques for finding it are grounded fundamentally in a global perspective. These techniques can be of limited value when the global behavior of the system is difficult to characterize, as it may be when the system is nonlinear, when the input is constrained, or when only partial information is available regarding system dynamics or the environment. Satisficing control theory is an alternative approach that is compatible with the limited rationality associated with such systems. This theory is extended by the introduction of the notion of strong satisficing to provide a systematic …
Annotated Bibliography Of Research In The Teaching Of English, Deborah Brown, Melissa Whiting, Richard L. Larson
Annotated Bibliography Of Research In The Teaching Of English, Deborah Brown, Melissa Whiting, Richard L. Larson
Faculty Publications
Twice a year, in the May and November issues, RTE publishes a selected bibliography of recent research in the teaching of English. Most of the studies appeared during the six-month period preceding the compilation of the bibliography (January through June, 1998, for the present bibliography), but some studies that appeared earlier are occasionally included. The listing is selective; we make no attempt to include all research and research-related studies that appeared in the period under review. Comments on the bibliography and suggestions about items for inclusion may be directed to the bibliography editors. We encourage you to send your suggestions …
Effects Of Land Cover, Water Redistribution, And Temperature On Ecosystem Processes In The South Platte Basin, Jill S. Baron, Melannie D. Hartman, Timothy G. F. Kittel, Larry E. Band, Dennis S. Ojima, Richard B. Lammers
Effects Of Land Cover, Water Redistribution, And Temperature On Ecosystem Processes In The South Platte Basin, Jill S. Baron, Melannie D. Hartman, Timothy G. F. Kittel, Larry E. Band, Dennis S. Ojima, Richard B. Lammers
Faculty Publications
Over one‐third of the land area in the South Platte Basin of Colorado, Nebraska, and Wyoming, has been converted to croplands. Irrigated cropland now comprises 8% of the basin, while dry croplands make up 31%. We used the RHESSys model to compare the changes in plant productivity and vegetation‐related hydrological processes that occurred as a result of either land cover alteration or directional temperature changes (−2°C, +4°C). Land cover change exerted more control over annual plant productivity and water fluxes for converted grasslands, while the effect of temperature changes on productivity and water fluxes was stronger in the mountain vegetation. …
Successive Galerkin Approximation Algorithms For Nonlinear Optimal And Robust Control, Timothy Mclain, Randal W. Beard
Successive Galerkin Approximation Algorithms For Nonlinear Optimal And Robust Control, Timothy Mclain, Randal W. Beard
Faculty Publications
Nonlinear optimal control and nonlinear H infinity control are two of the most significant paradigms in nonlinear systems theory. Unfortunately, these problems require the solution of Hamilton-Jacobi equations, which are extremely difficult to solve in practice. To make matters worse, approximation techniques for these equations are inherently prone to the so-called 'curse of dimensionality'. While there have been many attempts to approximate these equations, solutions resulting in closed-loop control with well-defined stability and robustness have remained elusive. This paper describes a recent breakthrough in approximating the Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations. Successive approximation and Galerkin approximation methods are combined to derive …
Monte Carlo Simulation Of An Ion-Dipole Mixture As A Model Of An Electrical Double Layer, Douglas Henderson, Dezso Boda, Kwong-Yu Chan
Monte Carlo Simulation Of An Ion-Dipole Mixture As A Model Of An Electrical Double Layer, Douglas Henderson, Dezso Boda, Kwong-Yu Chan
Faculty Publications
Canonical Monte Carlo simulations were performed for a nonprimitive model of an electrical double layer. The ions and the solvent molecules are modeled as charged and dipolar hard spheres, respectively, while the electrode as a hard, impenetrable wall carrying uniform surface charge. We found that the ion-dipole model gives a reasonable description of the double layer for partially charged ions with small to moderate dipole moments, or equivalently for an "effective" dielectric constant. Density, polarization and mean electrostatic potential profiles are reported. Strong layering structure, and at higher charges, charge inversion in the second layer were found. With appropriate choices …
Interior Blowup In A Convection-Diffusion Equation, Christopher P. Grant
Interior Blowup In A Convection-Diffusion Equation, Christopher P. Grant
Faculty Publications
This paper addresses the qualitative behavior of a nonlinear convection-diffusion equation on a smooth bounded domain in Rn, in which the strength of the convection grows superlinearly as the density increases. While the initial-boundary value problem is guaranteed to have a local-in-time solution for smooth initial data, it is possible for this solution to be extinguished in nite time. We demonstrate that the way this may occur is through nite-time "blow up," i.e., the unboundedness of the solution in arbitrarily small neighborhoods of one or more points in the closure of the spatial domain. In special circumstances, such as the …
Exact Relations For Effective Tensors Of Polycrystals. Ii. Applications To Elasticity And Piezoelectricity, Yury Grabovsky, Daniel S. Sage
Exact Relations For Effective Tensors Of Polycrystals. Ii. Applications To Elasticity And Piezoelectricity, Yury Grabovsky, Daniel S. Sage
Faculty Publications
An important necessary condition for an exact relation for effective moduli of polycrystals to hold is stability of that relation under lamination. This requirement is so restrictive that it is possible (if not always feasible) to find all such relations explicitly. In order to do this one needs to combine the results developed in Part I of this paper and the representation theory of the rotation groups SO(2) and SO(3). More precisely, one needs to know all rotationally invariant subspaces of the space of material moduli. This paper presents an algorithm for finding all such subspaces. We illustrate the workings …
A Continuum Analysis Of The Chemotactic Signal Seen By Dictyostelium Discoideum, J. C. Dallon, H. G. Othmer
A Continuum Analysis Of The Chemotactic Signal Seen By Dictyostelium Discoideum, J. C. Dallon, H. G. Othmer
Faculty Publications
We develop a mathematical model of cell-to-cell-signalling in Dictyostelium discoideum that predicts the cAMP signal seen by individual cells in early aggregation. The model employs two cells on a plane and is designed to predict the space-time characteristics of both the extracellular cAMP signal seen by one cell when a nearby cell relays, and the intracellular cAMP response produced by the stimulus in the receiving cell. The effect of membrane bound phosphodiesterase is studied and it is shown that cells can orient effectively even in its absence. Our results give a detailed picture of how the spatio-temporal characteristics of the …
Deriving Of Single Intensive Picosecond Optical Pulses From A High-Power Gain-Switched Laser Diode By Spectral Filtering, S. N. Vainshtein, Grigory Simin, J. T. Kostamovaara
Deriving Of Single Intensive Picosecond Optical Pulses From A High-Power Gain-Switched Laser Diode By Spectral Filtering, S. N. Vainshtein, Grigory Simin, J. T. Kostamovaara
Faculty Publications
Single 25 ps/16 W optical pulses were achieved by spectral filtering from a multiheterostructure gain-switched laser diode with its quasisteady-state modes suppressed by a factor of 103 as compared with the peak power. A significant transient spectrum broadening makes this possible provided that a very high dI/dt rate of the pumping current pulse is used. A simple numerical model is suggested which describes adequately both the spectral and transient features of the observed phenomenon. It follows from the model that single picosecond optical pulses can be obtained from any type of high power semiconductor laser.
Mycobacterium Avium Complex Augments Macrophage Hiv-1 Production And Increases Ccr5 Expression, S. M. Wahl, T. Greenwell-Wild, G. Peng, H. Hale-Donze, T. M. Doherty, D. Mizel, J. M. Orenstein
Mycobacterium Avium Complex Augments Macrophage Hiv-1 Production And Increases Ccr5 Expression, S. M. Wahl, T. Greenwell-Wild, G. Peng, H. Hale-Donze, T. M. Doherty, D. Mizel, J. M. Orenstein
Faculty Publications
Infection with HIV-1 results in pronounced immune suppression and susceptibility to opportunistic infections (OI). Reciprocally, OI augment HIV-1 replication. As we have shown for Mycobacterium avium complex (MAC) and Pneumocystis carinii, macrophages infected with opportunistic pathogens and within lymphoid tissues containing OI, exhibit striking levels of vital replication. To explore potential underlying mechanisms for increased HIV-1 replication associated with coinfection, blood monocytes were exposed to MAC antigens (MAg) or viable MAC and their levels of tumor necrosis factor α (TNFα) and HIV-1 coreceptors monitored. MAC enhanced TNFα production in vitro, consistent with its expression in coinfected lymph nodes. Using a …