ALBERT

Notes: A numerical study has been carried out to predict the indoor air quality in a newly painted partitioned office and to assess the effect of ventilation rate and partition layout on the pre-ventilation time required to allow the contaminant concentration level to drop to an acceptable level. The air-flow pattern, the time history of the average contaminant concentration level in the occupied zone, and the pre-ventilation time were computed by a CFD code with a K-ε turbulence model.A displacement ventilation system, with different operating conditions, was used to remove contaminants in the office. The VB emission model, developed by Guo and Tichenor (1992), has been improved to include the influence of non-uniform concentration distribution on contaminant emission rate from the paints. The average contaminant (VOC) concentration levels in the occupied zone and in each chamber were recorded hourly until the average concentrations in the office were less then 0.0005 g/m3.It has been found that the non-uniform concentration distri- bution greatly influences the decay rate of VOC emissions. The time required for the average concentration in each chamber to reach the threshold level is different, since they are non-uniform. The time differences between the chambers having the highest and lowest concentrations were 3 to 8 hours. The results also show that the time required to reduce the concentration in the occupied zone to the threshold level is dependent on the partition layout. For the same ventilation rate, the required time is approximately 4-8 hours longer when using a side layout than when using a central layout.

Notes: The performance of sub-slab-ventilation (SSV) systems has been parametrically studied with a numerical model that was earlier compared successfully with experiment (Bonnefous et al., 1992). The model distinguishes between the sub-slab gravel and the underlying soil. It is used w examine system performance for the following system parameters: the permeability of the soil and of the sub-slab gravel, the magnitude of pressurization (or depressurization) applied by the SSV system, and the mode of SSV application (i.e. pressurization (SSP) or depressurization (SSD)). The mechanisms contributing to the successful performance of SSP and SSD systems are identified. For SSD systems, the mechanisms are (1) the inversion of the pressure gradient across the basement slab, and (2) the reduction of the radon concentration in the soil. For SSP systems, the mechanisms are (1) the elimination of convective flow of soil-gas from the soil into the sub-slab gravel by pressurization of the sub-slab region, (2) the reduction of the radon concentration in the soil, and (3) the suppression of diffusion of soil-gas from the soil into the sub-slab gravel by advective flow of air from the gravel bed into the subgravel soil. Numerical modeling demonstrates that placement of a sub-slab gravel layer substantially improves the SSV system performance. Except in the case of highly permeable soils, SSD systems are predicted to perform better than SSP systems. This prediction is consistent with reported field experience. The numerical model is used to elucidate the reasons for this difference in performance.

Notes: Deciding between the different policy approaches available for reducing human exposures to indoor pollutants is an exceptionally complex task. These options can range from waiting until more definitive information is available to enacting regulatory standards, with many variations in between. This paper presents some of the factors policy-makers must consider in establishing indoor air quality policies, and the role researchers should play in ensuring that indoor air policies are based on the best available scientific information.

Notes: We tested nasal detection thresholds for airborne chemicals in a group of anosmics (i.e., subjects lacking a functional sense of smell) and in a group of age-, gender-, and smoking-status-matched normosmics (i.e., subjects with normal olfaction). Anosmics provided odor unbiased nasal pungency (irritation) thresholds. Normosmics provided odor thresholds. Homologous series of alcohols, acetates, and ketones served as stimuli. Eye irritation thresholds were also measured for selected acetates. Most substances evoked pungency (i.e., were detected by the anosmics). All sensory thresholds decreased systematically with carbon chain length. The gap between pungency and odor grew larger with increasing carbon chain length. Pungency thresholds-but not odor thresholds-showed a uniform linear relationship of slope close to unity with saturated vapor concentration, irrespective of chemical functionality or carbon chain length. This suggests that pungency from nonreactive airborne chemicals rests heavily on a relatively unspecific physical interaction with a susceptible biophase. Of relevance to indoor environments, such an interaction opens the possibility for a high degree of sensory addition of pungency from individual components of complex mixtures resulting in noticeable irritation even when each component is at a level well below threshold value.

Notes: A health and housing questionnaire was administered to children, ages 9-11, living in 24 communities in the United States and Canada. Logistic regression analysis examined the relationship between respiratory health symptoms (bronchitic, asthmatic and lower respiratory) and housing factors. The health risks (expressed as relative odds) were controlled for gender, parental asthma, parental chronic obstructive pulmonary disease and parental education, as well as between-city differences. Lower respiratory symptoms had significantly higher odds ratios reported in older homes (1.12), homes with smokers (1.24), air conditioners (1.14), air cleaners (1.37), and humidifiers (1.47). Home dampness (1.48) and the individual mold and water variables were all significantly associated with increased symptoms. Similar results were reported for bronchitic and asthmatic symptoms. While air conditioners and air cleaners were confounded with symptoms, humidifiers remained significant after controlling for childhood atopy.

Notes: In two case-referent studies the associations between questionnaire symptom reports, expressed as SBS (Sick Building Syndrome) in office workers or facial skin symptoms among VDT-workers, and physical data from offices in 160 buildings were investigated. The results show that low outdoor airflow rate and presence of certain pollution sources, such as copying machines, tended to be associated with an elevated prevalence of SBS. Buildings built or remodeled between 1977 and 1986, low-rise buildings with a horizontal roof and a foundation of the type “concrete slab on the ground”, as well as rooms with flourescent tube lighting with metal shields were also associated with higher SBS risks. A number of factors were associated with an overrepresentation of skin symptoms among VDT-workers such as type of foundation (concrete slab on the ground and crawlspace), the frequency of floor cleaning and type of lighting (fluorescent tubes with glass/plastic shields). It has not been possible to establish conclusive explanations for these associations. The difference in associations between building factors and S B S, and between building factors and skin symptoms among VD Tworkers points to different etiologies.

Notes: Background. In the Danish Town Hall Study" it has previously been shown that the sick building syndrome is a widespread phenomenon. This has given rise to speculations as to whether biologically active components in dust or whether absorbed organic gases and vapours in the indoor climate may be partly responsible for the sick building syndrome. Therefore, we wished to study whether qualitative conditions in dust, of a physical, chemical, and biological nature, are related to the prevalence of symptoms of the sick building syndrome. Material and methods. The study included 12 town halls in the Copenhagen area. A total of 870 persons participated, 584 women and 286 men. All the participants filled out a questionnaire regarding health and working conditions, and dust samples were collected with a special vacuum cleaner in the working environment of the participants, after which the contents of inorganic and organic particles as well as of human source fragments the (hair, nails, skin) and various fibres were determined. Results. There was a significant correlation (P〈0.05) between the prevalence of gram-negative bacteria in the indoor climate dust, and general symptoms (fatigue, heavy-headedness, headache, dizziness, concentration problems) (corr.coeff.=0.73), as well as symptoms from the mucous membranes of the upper respiratory tract (corr.coeff.=0.76). Also, there was a significant relation between the prevalence of particles in the dust and the prevalence of symptoms from the mucous membranes (corr.coeff.=0.81). There was a strong and significant correlation between the total amount of volatile organic components (TVOC) and lack of concentration (corr.coeff. =0.85) and feeling heavy-headed (corr.coeff.=0.72). Macromolecular dust (potentially allergenetic material) was significantly correlated to the prevalence of headache and general malaise/dizziness (corr.coeff.=0.66), while the ability of the dust to liberate histamine was significantly related to the prevalence of general malaise, dizziness (corr.coeff.=0.65) and lack of concentration (corr.coeff. =0.58). Further analyses including a number of potential confounders did not change the results of the above analyses. Conclusion. The results of this study support the hypothesis that qualitative properties of dust are important to the sick building syndrome. The study was based on relatively few buildings, but nevertheless strong correlations were found. In perspective, epidemiological intervention studies should be carried out to investigate whether minimizing the amount of both dust and bacteria in the indoor climate affect the prevalence of sick building syndrome.

Notes: Settled household dust samples were collected from twelve dwellings in urban areas during an annual winter heating period. Emission of compounds from settled household dust was analyzed under simulated hot surface conditions with a temperature range of 50–300°C. The compounds were analyzed and identified by thermal desorption—gas chromatographic-mass spectrometric technique. The organic emission from household dust was relatively low at temperatures below 70° C, increased appreciably above 100°C, and gained in strength at temperatures above 200°C. Desorption of adsorbed compounds is the main contribution to emissions, but at higher temperatures the thermal degradation seems to affect also the quantity and the quality of the emissions. The organic composition of household dust was found to be equal in quality at different sampling sites; the emissions consist of mainly aliphatic aldehydes (C6—C13), aliphatic carboxylic acids and their esters (C8 C18, C6–C30) and phthalates. Phosphate esters, branched alkanes, n-alkenes, n-alkanones, monoterpenes, aromatic hydrocarbons, and aromatic and aliphatic alcohols were also well represented groups in household dust samples. The potential sources of identified compounds are discussed.

Notes: A procedure is developed for assessing the health effects of the emissions from building products. The procedure is based on:〈list xml:id="l1" style="custom"〉•emission rates measured in environment test chambers•a fixed standard room with fixed standard conditions•a maximum acceptable concentration in the indoor air of each of the chemical compounds emitted, Iv a maximum permissible contribution to Iv from building products.The procedure has two elements: evaluation of the emitted compound alone and evaluation of the compound together with other compounds and indoor air factors. The evaluation includes odour and health effects of the compounds.The procedure has been applied to the emission test results for two building products: a rubber floor covering, and a water-borne acrylic watt paint.Maximum acceptable indoor air concentrations are listed fin-selected chemical compounds emitted by these two materials.

Notes: Heat, mass and momentum transfer takes place simultaneously in ventilated rooms. For accurate predictions of the indoor environment, all the environmental parameters that influence these transport phenomena should be taken into consideration. This paper introduces a method for a full assessment of indoor thermal comfort using computational fluid dynamics in conjunction with comfort models. A computer program has been developed which can be used for predicting thermal comfort indices such as thermal sensation and draught risk. The sensitivity of predicted comfort indices to environmental parameters is analysed for a mechanically ventilated office. It was found that when the mean radiant temperature was considered uniform in the office, the error in the predicted percentage of dissatisfied (PPD) could be as high as 7.5%. The prediction became worse when the mean radiant temperature was taken to be the same as air temperature point by point in the space. Moreover, disregarding the variation of vapour pressure in the space resulted in an error in PPD of abour 4% near the source of moisture generation.The importance of evaluating both thermal sensation and draught risk is also examined. It is concluded that in spaces with little air movement only the thermal sensation is needed for evaluation of indoor thermal comfort whereas in spaces with air movement induced by mechanical vantilation or air-conditioning systems both thermal sensation and draught risk should be evaluated.

Notes: The filtration efficiency of ventilation air cleaners is highly particle-size dependent over the 0.01 to 3 μm diameter size range. Current standardized test methods, which determine only overall efficiencies for ambient aerosol or other test aerosols, provide data of limited utility. Because particles in this range are respirable and can remain airborne for prolonged time periods, measurement of air cleaner fractional efficiency is required for application to indoor air quality issues. The objectives of this work have been to 1) develop a test apparatus and procedure to quantify the fractional filtration efficiency of air cleaners over the 0.01 to 3 μm diameter size range and 2) quantify the fractional efficiency of several induct air cleaners typical of those used in residential and office ventilation systems.Results show that efficiency is highly dependent on particle size, flow rate, and dust load present on the air cleaner. A minimum in efficiency was often observed in the 0.1 to 0.5 μm diameter size range. The presence of a dust load frequently increased an air cleaner's efficiency; however, some air cleaners showed little change or a decrease in efficiency with dust loading. The common furnace filter had fractional efficiency values of less than 10% over much of the measurement size range.

Notes: The objective of this study was to test the effectiveness of individual commercially available portable indoor air cleaning units in removing dust particulates, tobacco smoke particulate and vapor phase constituents (nicotine and vinyl pyridine), viable and total fungal spores, pollen, and gaseous contaminants (carbon monoxide[CO], nitrogen dioxide[NO2], and formaldehyde[HCHO]), in a clean air test chamber. The air cleaner chamber results presented here represent initial-use results. In general, High Efficiency Particulate Air (HEPA) and electrostatic precipitator systems demonstrated the highest efficiencies with respect to particulate, contaminants, followed closely by electret filter systems. Ionizers and ozone generators were least effective in particulate removal. Systems which included sufficient sorbent material (i.e. activated carbon or potassium permanganate) were marginally effective at gaseous contaminant removal. None of the systems tested were effective at carbon monoxide removal.Sensory testing was conducted to discern potential correlation between human perceptive response and measured air cleaner performance (with respect to tobacco smoke removal). An electret filter (EF) loaded with carbon sorbent received the best ratings with respect to odor strength, nasal irritation, eye irritation, and overall air acceptability.

Notes: The indoor concentrations of contaminants originating from outdoor sources have been measured and calculated under transient conditions. The results show that contaminants that are supplied to an office building via the ventilation system can reach considerably high concentration levels. The indoor/outdoor concentration ratio and time lag are dependent on the air change rate. In buildings with low air change rates the indoor concentration variations are smoothed out compared to buildings with high air change rates. The results from the theoretical model are compared to the results from both laboratory and field measurements and the model is verified for well mixed conditions in a 20 m3 test chamber. The model can be used to simulate different control strategies for reduction of indoor contaminant concentrations related to outdoor sources. One such control strategy is based on reduction of the outdoor air change rate during periods with peak outdoor contaminant concentrations.

Notes: A WHO/EURO working group met in Eilat, Israel, from 28 March to 4 April 1993, to assess the significance of risks to health associated with indoor radon, to develop a unified approach to control radon exposure, and to advise on the communication of associated health risks. A summary of the deliberations of this working group and its conclusions and recommendations are presented in this paper.

Notes: Indoor air quality models are commonly based on the assumption of instantaneous and complete air mixing within a zone. Such an assumption is not appropriate for all circumstances, such as investigating the utility of segregating smokers to reduce nonsmoker exposure to environmental tobacco smoke. This experimental study characterizes quantitatively the rate at which smoke from a cigarette disperses within an unoccupied, 31-m3, low air-exchange rate room under natural convection flow conditions. Sidestream smoke from a smoldering cigarette was simulated with a pulsed release of a tracer gas – a neutrally buoyant mixture of sulfur hexafluoride (SF6) in helium – above an electrically heated coil. During each experimental run, sequential air samples were collected remotely, using gas-tight syringes, from 41 locations within the room. After each run, these samples were analyzed for SF6 content using a gas chromatograph with an electron-capture detector. Duplicate runs were conducted under three conditions: nearly isothermal surfaces; convection from a 500–watt heater; and convection from incoming solar radiation. Characteristic mixing times ranged from 7–10 minutes for the solar radiation case to 80–100 minutes for the nearly isothermal case.

Notes: A review is presented of investigations of volatile organic compound (VOC) concentrations in indoor air of buildings of different classifications (dwellings, offices, schools, hospitals) and categories (established, new and complaint buildings). Measured concentrations obtained from the published literature and from research in progress overseas were pooled so that VOC concentration profiles could be derived for each building classification/category. Mean concentrations of individual compounds in established buildings were found to be generally below 50 μg/m3, with most below 5 μg/m3. Concentrations in new buildings were much greater, often by an order of magnitude or more, and appeared to arise from construction materials and building contents. The nature of these sources and approaches to reduce indoor air concentrations by limiting source VOC emissions is discussed. Total VOC (TVOC) concentrations were substantially higher than concentrations of any individual VOCs in all situations, reflecting the large number of compounds present, but interpretation of such measurements was limited by the lack of a common definition for TVOC relevant to occupant exposure.

Notes: The development of odor emission rates from EU6 classified glass fiber bag filters was studied in four air-handling units (AHU), and emissions from the same kind of filters with EU3 classified polyester prefilters were studied in two units. The filters were loaded in six AHU in downtown Helsinki. The pressure drop was measured, and the odors of the filters were evaluated by a trained panel under laboratory conditions (T = 20°C, face velocity 1.0 m/s) every sixth week. The odor emissions of simultaneous atmospheric dust samples were also studied. The odor emissions of the filters rose during the first three months to a level where every third person would be dissatisfied. The emissions from coarse prefilters were similar to those from the more efficient filters without prefilters, and the emissions of the main filters were significantly lower if used with prefilters. This result indicates that the prefilters effectively protected the fine filters from odor-causing particles. The results of tests made with atmospheric samples agree with this result. Relative odor emissions were the highest in coarse fractions (〉 10.0 μm). The pressure drop increased with the particle mass collected on the ventilation filter, but it did not correlate well with the odor emission of the filter. Thus, pressure drop alone is not an adequate criterion for changing supply air filters when hygienic aspects are a concern.

Notes: To test the reproducibility of a questionnaire previously used to study the association between respiratory symptoms and home dampness/mold, it was sent to the parents of 1,596 children twice, with an interval of one month between distributions. A total of 770 respondents completed the questionnaire both times and were entered into an analysis. For exposure variables, percentages of agreement between the two administrations ranged from 87% for visible mold growth in the home to 95% for basement flooding. Respective kappa scores ranged from 73% to 82%. Percentage agreements for the adults' symptoms variables ranged from 80% for upper respiratory symptoms, to 99% for physician-diagnosed asthma. Percentage agreements for children's symptoms ranged from 81% for upper respiratory symptoms to 97% for current asthma. For all symptoms kappas ranged from 59% to 90% indicating moderate to high reproducibility. Future research should now concentrate on validating the questionnaire as an indicator of mold growth.

Notes: There are few data sets appropriate for characterizing the indoor concentrations of air pollutants over the long term. An understanding of the variability in indoor pollutant levels is particulurly relevant to the design of epidemiologic investigations: misclassifiation of exposure due to the inaccuracy of exposure estimates tends to weaken the association of exposure with health outcome. This paper uses a series of indoor NO2 measurements collected at two-week intervals over 18-month periods between 1988 and 1991 to describe the seasonal and year-to-year variability in indoor NO2,. The data show that there can be large year-to-year differences in both the sample distribution of indoor NO2 as well as the household average. For homes with gas ranges with continuously-burning pilot lights, the average bedroom NO2 concentration was 25% higher in the winter of 1990-1991 than in the winter of 1989-1990 but only 4% higher during the winter of 1988-1989 than during the winter of 1989-1990. The winter-to-winter correlations within homes ranged from a low of 0.53 to a high of 0.88. The year-to-year differences in mean indoor concentrations were not related to temperature patterns. Occupant behaviors that influence air exchange rate and/or source use are hypothesized to be the major determinant of the observed pattern. Exposure data collected during a single year should be cautiously extrapolated to other years. However, in Albuquerque homes, the data suggest that the year-to-year variability in household NO2 levels will not have a strong impact on classifying exposure into broad categories.

Notes: Indoor and outdoor aerosol sampling was conducted in two New York State Counties, Suffolk and Onondaga, during the period of January 6 and April 15, 1986. Week-long fine particle mass samples were collected indoors and outdoors for a total of 596 samples taken in 394 homes. The aerosol samples were analyzed by X-ray fluorescence for the following elements: Si, S, Cl, K, Ca, V, Mn, Fe, Ni, Cu, Zn, As, Se, Br, Cd, and Pb. Lastly, aerosol mass concentrations were determined gravimetrically.Homes included in this study had one or more of the following sources: cigarette smoking, kerosene heaters, wood burning and gas stoves. Homes with none of the above sources were also included. Comparisons between mass and elemental concentrations among the different home groups allowed the investigation of the elemental profiles and importance of the indoor sources. From the five investigated sources, cigarette smoking was found to be the most important, and to a lesser extent, kerosene heaters. Finally, gas stoves did not contribute to the observed indoor aerosol mass and elemental concentrations, but other unknown indoor sources did contribute to indoor aerosol concentrations.Room-to-room differences in mass and elemental concentrations were also investigated. The results of these analyses suggested that concentrations measured in the living area and kitchen are identical, within analytical errors. Therefore, the indoor environment can be characterized as well mixed.

Notes: Local age of air and air change effectiveness were determined in two office buildings using tracer gas techniques to study the applicability of the associated measurement procedures in mechanically ventilated office buildings. Measurement issues examined include the establishment of a uniform tracer gas concentration at the start of the test and the relationship of ventilation system configuration and system operation to the test procedure. Air change effectiveness was determined at locations in the occupied space based on the local age of air at that location and the age of air in the corresponding ventilation system return duct. Values of the air change effectiveness in the occupied space were generally close to one, which is consistent with good mixing of the Ventilation air within the occupied space. Deviations from 1.0, on the order of 10%, did occur, but given the limited experience with these measurement procedures in the field it is not clear whether these deviations are significant. These tests provide data on air change effectiveness to supplement the limited database on mechanically ventilated office buildings in the US. In addition, the experience obtained with the measurement procedures will assist in the development of a standardized approach to measuring air change effectiveness in the field.

Notes: Full-scale residential house tests were conducted to evaluate the effects of organic emissions from a wood finishing product – wood stain – on indoor air quality (IAQ). The test house concentrations of three alkane species, nonane, decane, and undecane, were measured as a function of time after the application of the wood stain. It was found that the test house concentrations can be simulated by an integrated IAQ model which takes into consideration source, sink and ventilation effects. The alkane emissions were controlled by an evaporation-like process. Data analysis indicated that there were significant sink effects in the test house. Different sink strengths were estimated by the model for the three alkane species. An inverse relationship between the test house sink strength and the alkane volatility was found.

Notes: A test chamber has been developed in order to provide a small and simple emission testing facility capable of testing construction products in a climate where the important climatic parameters such as temperature, ventilation rate and air velocity can be varied independently around typical indoor values. The test chamber CLIMPAQ is made of panes of window glass. Other main surface materials are stainless steel and eloxated aluminium. The chamber has a volume of 50.9 litres and is designed to meet the requirements for quantifying air pollution. In this investigation human subjects acted as air pollution judges, and chemical characterization of the air pollution was carried out. Carpet, linoleum, wall paint and seal- ant were tested simultaneously in the CLIMPAQ and in four other chambers ranging from a full-scale chamber of 28 m3 to a field and laboratory emission cell of 3.5· 10−5m3. Product ranking is the same in all chambers for the sensory measurements. Emission rates based on sensory measurements differ for all products less than 100 % except for tests in a 3-litre chamber where emission rates were higher. Chemical measurements differ up to approximately 10 times for the same product in different chambers. Deviations appear to be the result of different environmental parameters in the various chambers. Low air concentrations or high specific ventilation rates seem to increase emissions, while differences in air velocities and sink properties may also be the cause of differences in emission rates.

Notes: Microbial content in dusts such as bacteria, endotoxins and fungal spores are thought to be important causative agents for the symptoms in organic dust-related diseases. Micro-organism-induced mediator release was therefore examined in human cells. Bacteria were found to trigger the release of histamine and leurotriene B4 from bronchoalveolar cells, and in suspensions of dispersed lung and tonsillar cells they induce the release of histamine and prostaglandin D2. Basophil histamine release was triggered by both bacteria and their endotxins. Furthermore, histamine release caused by allergic as well as non-allergic reactions was enhanced by bacteria, endotoxins and fungal spores of mould. These effects of dust components may be crucial for the symptoms in q a n i c dust-related diseases, since the mediators are of key importance to the broncho-obstructive and inflammatory events in these disorders.

Notes: One hundred and eighty eight Volatile organic compound (VOCs) were identified from dust emission, dust headspace, and in air sampling in a residence by sampling on Tenax TA followed by thermal desorption and HRGC/MS. Of these, 83 compounds were found in dust headspace. Aliphatic aldehydes (C4-8 and octane were major contributors to headspace gas chromatograms while the total ion current response for desorbed VOCs (120° C) was dominated by n-alkanes (C7-16), n- and branched alkanals (C4-10 and alkanoic acids (C2-14). Many of the identified VOCs could be products of microbial or human metabolism. Dust volatiles resulting from desorption were compared w dust headspace VOC analyses and found to be comparable considering the temperature difference. A method for determination of total VOC (TVOC-dust) emission at 120°C, was developed. Variation in desorption TVOC analyses was mainly due to sample heterogeneity.

Notes: The development of standardized non-culture-based approaches capable of assessing microbial contarnination of airborne dust is sorely needed. Direct chemical analysis has previously been successfully used for measuring components unique to Gram-negative bacteria. In the present study, dust from primary filters of hospital air-conditioning intake systems (which filter incoming outdoor and recirculated air) and dust from secondary room filters (filtering primarily indoor air) were analyzed. Dust from home air-condition-ing filters (which also filter outdoor air, with recirculation) were also analyzed. Muramic acid is an aminosugar present in Gram-positive and Gram-negative bacterial cell walls and can serve as a measure of bacterial contamination in dust. Samples were analyzed by gas chromatography-mass spectrometry after hydrolysis and conversion of released sugars (including muramic acid) to alditol acetates. Primary hospital filters contained 26.3 ± 10.0 ng of muramic acid/mg dust while secondary filters contained 5.3 ± 5.4 ng/mg. The level of inuramic acid in home air-conditioner dust was 31.7 ± 13.4 ng/mg. This study of dust collected from air-conditioners demonstrates the feasibility of chemical assessment of the microbial contamination of indoor air.

Notes: Ozone concentrations were measured in indoor and outdoor residential air during the summer of 1992. Six homes located in a New Jersey suburban area were chosen for analysis, and each home was monitored for 6 days under different ventilation and indoor combustion conditions. The 5-hour average ozone concentration outdoors over the monitoring period was 95 ± 36 ppbv. One third of the days exceeded the National Ambient Air Quality Standard (NAAQS), one-hour maximum concentration of 120 ppb. The mean indoor to outdoor (I/O) ratios of ozone concentration ranged from 0.22 ± 0.09 to 0.62 ± 0.11, depending upon ventilation rate and indoor gas combustion. The presence of indoor gas combustion can significantly decrease the I/O ratio. Because of the great amount of time that people spend indoors, the indoor residential exposures were estimated to account for 57% of the total residential exposures. One type of the possible gas-phase reactions for indoor ozone, the reaction of ozone with a volatile organic compound containing unsaturated carbon-carbon bonds, is discussed with some supporting evidence provided in the study.

Notes: Abstract More than 20 years after its proposal, Keller and Segel's model (1971,J. theor. Biol.,30, 235–248) remains by far the most popular model for chemical control of cell movement. However, before the Keller-Segel equations can be applied to a particular system, appropriate functional forms must be specified for the dependence on chemical concentration of the cell transport coefficients and the chemical degradation rate. In the vast majority of applications, these functional forms have been chosen using simple intuitive criteria. We focus on the particular case of eukaryotic cell movement, and derive an approximation to the detailed model of Sherrattet al. (1993,J. theor. Biol.,162, 23–40). The approximation consists of the Keller-Segel equations, with specific forms predicted for the cell transport coefficients and chemical degradation rate. Moreover, the parameter values in these functional forms can be directly measured experimentally. In the case of the much studied neutrophil-peptide system, we test our approximation using both the Boyden chamber and under-agarose assays. Finally, we show that for other cell-chemical interactions, a simple comparison of time scales provides a rapid check on the validity of our Keller-Segel approximation.

Notes: Abstract The formal structure of evolutionary theory is based upon the dynamics of alleles, individuals and populations. As such, the theory must assume the prior existence of these entities. This existence problem was recognized nearly a century ago, when DeVries (1904,Species and Varieties: Their Origin by Mutation) stated. “Natural selection may explain the survival of the fittest, but it cannot explain the arrival of the fittest.” At the heart of the existence problem is determining how biological organizations arise in ontogeny and in phylogeny. We develop a minimal theory of biological organization based on two abstractions from chemistry. The theory is formulated using λ-calculus, which provides a natural framework capturing (i) the constructive feature of chemistry, that the collision of molecules generates specific new molecules, and (ii) chemistry's diversity of equivalence classes, that many different reactants can yield the same stable product. We employ a well-stirred and constrained stochastic flow reactor to explore the generic behavior of large numbers of applicatively interacting λ-expressions. This constructive dynamical system generates fixed systems of transformation characterized by syntactical and functional invariances. Organizations are recognized and defined by these syntactical and functional regularities. Objects retained within an organization realize and algebraic structure and possess a grammar which is invariant under the interaction between objects. An organization is self-maintaining, and is characterized by (i) boundaries established by the invariances, (ii) strong self-repair capabilities responsible for a robustness to perturbation, and (iii) a center, defined as the smallest kinetically persistent and self-maintaining generator set of the algebra. Imposition of different boundary conditions on the stochastic flow reactor generates different levels of organization, and a diversity of organizations within each level. Level 0 is defined by selfcopying objects or simple ensembles of copying objects. Level 1 denotes a new object class, whose objects are self-maintaining organizations made of Level 0 objects, and Level 2 is defined by self-maintaining metaorganizations composed of Level 1 organizations. These results invite analogy to the history of life, that is, to the progression from self-replication to self-maintaining procaryotic organizations to ultimately yield self-maintaining eucaryotic organizations. In our system self-maintaining organizations arise as a generic consequence of two features of chemistry, without appeal to natural selection. We hold these findings as calling for increased attention to the structural basis of biological order.

Notes: Abstract A model is developed to describe neuronal elongation as a result of the polymerization of microtubules and elastic stretching of the neurites by force produced by the growth cone. The model for a single segment with a single growth cone revealed a constant elongation rate, while the concentration of tubulin in the soma rises, and the concentration of tubulin becomes constant in the growth cone. Extending the model to a neurite with a single branch point and two growth cones revealed the same results. When the assembly or the disassembly rate of microtubules is unequal in both growth cones, transient retraction of one of the terminal segments occurs, which results in complete retraction of the segment when the difference in (dis)assembly rate between the two growth cones is large enough. When the model is applied to large trees, a maximal sustainable number of terminal segments as a function of the production rate of tubulin appears. Mechanisms to stop outgrowth are discussed in relation to the establishment of synaptical contacts between cells.

Notes: Abstract We have developed a new model describing the relationship between plasma and red cell tracers flowing through the lung. The model is the result of an analysis of the transport of radiolabeled plasma albumin between two flowing phases and shows that differences between red cell and plasma tracer curves are related to microvascular hematocrit. The model was tested in an isolated, blood-perfused dog lung preparation in which we injected51Cr-labeled red cells and125I-labeled plasma albumin into the pulmonary artery. From the tracer concentration-time curves at the venous outflow, we calculatedh r, the ratio of microvascular hematocrit to large-vessel hematocrit. In 18 baseline experiments,h r=0.92±0.01 (mn±sem) at a blood flow rate of 10.7±0.3 ml s−1. We determined the effects of (a) glass bead embolization, (b) alloxan, and (c) lobe ligation onh r. Embolization attenuated the separation between plasma and red cells (increasedh r), probably as a consequence of passive vasodilation. Alloxan enhanced separation of plasma and red cells (decreasedh r), possibly as a result of arteriolar vasoconstriction. Ligation of a fraction of the perfused tissue at constant flow did not cause significant change inh r in the remaining perfused tissue. The model assumes that large-vessel transit times are uniform and that all dispersion occurs in the microvasculature. A theoretical analysis apportioning dispersion between large and small vessels disclosed that the error associated with these assumptions is likely to be less than 15% of the measuredh r. We conclude from this study that the microvascular hematocrit model describes experimental plasma and red cell curves. The results imply thath r can be readily deduced from tagged red cells and plasma and can be accounted for in calculating permeability-surface area in diffusing tracer experiments.

Notes: Abstract We present a mathematical model of the cytotoxic T lymphocyte response to the growth of an immunogenic tumor. The model exhibits a number of phenomena that are seenin vivo, including immunostimulation of tumor growth, “sneaking through” of the tumor, and formation of a tumor “dormant state”. The model is used to describe the kinetics of growth and regression of the B-lymphoma BCL1 in the spleen of mice. By comparing the model with experimental data, numerical estimates of parameters describing processes that cannot be measuredin vivo are derived. Local and global bifurcations are calculated for realistic values of the parameters. For a large set of parameters we predict that the course of tumor growth and its clinical manifestation have a recurrent profile with a 3- to 4-month cycle, similar to patterns seen in certain leukemias.

Notes: Abstract We present a new, practical algorithm to resolve the experimental data in restriction site analysis, which is a common technique for mapping DNA. Specifically, we assert that multiple digestions with a single restriction enzyme can provide sufficient information to identify the positions of the restriction sites with high probability. The motivation for the new approach comes from combinatorial results on the number of mutually homeometric sets in one dimension, where two sets ofn points are homeometric if the multiset ofn(n−1)/2 distances they determine are the same. Since experimental data contain errors, we propose algorithms for reconstructing sets from noisy interpoint distances, including the possibility of missing fragments. We analyse the performance of these algorithms under a reasonable probability distribution, establishing a relative error limit ofr=Θ(1/n 2) beyond which our technique becomes infeasible. Through simulations, we establish that our technique is robust enough to reconstruct data with relative errors of up to 7.0% in the measured fragment lengths for typical problems, which appears sufficient for certain biological applications.

Notes: Abstract A simple chemical model of the idiotypic network of immune systems, namely the AB model, has been developed by De Boeret al. The complexity of the system, such as the steady states, periodic oscillations and chaotic motions, has been examined by the authors mentioned above. In the present paper, the periodic motions and chaotic behaviours exhibited by the system are intuitively described. To clarify in which parameter domains concerned the system exhibits periodic oscillations and in which parameter domains the system demonstrates chaotic behaviours the Lyapounov exponent is explored. To characterize the strangeness of the attractors, the fractal dimension problem is worked out.

Notes: Abstract We consider a stochastic mechanism of the loss of resistance of cancer cells to cytotoxic agents, in terms of unstable gene amplification. Two models being different versions of a time-continuous branching random walk are presented. Both models assume strong dependence in replication and segregation of the extrachromosomal elements. The mathematical part of the paper includes the expression for the expected number of cells with a given number of gene copies in terms of modified Bessel functions. This adds to the collection of rare explicit solutions to branching process models. Original asymptotic expansions are also demonstrated. Fitting the model to experimental data yields estimates of the probabilities of gene amplification and deamplification. The thesis of the paper is that purely stochastic mechanisms may explain the dynamics of reversible drug resistance of cancer cells. Various stochastic approaches and their limitations are discussed.

Notes: Abstract Dextran has been the most commonly employed test molecule for probing the selectivity of glomerular filtration to macromolecules of varying size. The usual theories for hindered transport of solid spheres through pores have limited utility in interpreting clearance data for dextran or other linear polymers because such polymers in solution more closely resemble random, solvent-filled coils than solid spheres. To provide a model for glomerular filtration of random-coil macromolecules, the equilibrium partitioning of random coils between cylindrical pores and bulk solution was simulated using Monte Carlo calculations, and those results were combined with a hydrodynamic theory for restricted motion of solvent-filled polymer coils in pores. The rates of transport predicted for either neutral random coils or for solid spheres of the same Stokes-Einstein radius were significantly lower than observed transport rates of dextran through the glomerular capillary wall or across synthetic porous membranes. This facilitation of dextran transport was modeled by postulating weak, attractive interactions between dextran monomers and the pore wall. The random-coil model with attractive interactions, modeled using a short-range, square-well potential, was found to adequately represent dextran sieving data in normal rats. Various limitations of this approach are discussed.

Notes: Abstract Method-dependent mechanisms that may affect dynamic numerical solutions of a hyperbolic partial differential equation that models concentration profiles in renal tubules are described. Some numerical methods that have been applied to the equation are summarized, and ways by which the methods may misrepresent true solutions are analysed. Comparison of these methods demonstrates the need for thoughtful application of computational mathematics when simulating complicated time-dependent phenomena.

Notes: Abstract The regulation of the interactions between the actin binding proteins and the actin filaments are known to affect the cytoskeletal structure of F-actin. We develop a model depicting the formation of actin cytoskeleton, bundles and orthogonal networks, via activation or inactivation of different types of actin binding proteins. It is found that as the actin filament density increases in the cell, a spontaneous tendency to organize into bundles or networks occurs depending on the active actin binding protein concentration. Also, a minute change in the relative binding affinity of the actin binding proteins in the cell may lead to a major change in the actin cytoskeleton. Both the linear stability analysis and the numerical results indicate that the structures formed are highly sensitive to changes in the parameters, in particular to changes in the parameter ϕ, denoting the relative binding affinity and concentration of the actin binding proteins.

Notes: Abstract To investigate morphogenesis and in particular circularization mechanisms in young mycelia, we observe cultures of the zygomyceteMucor spinosus and develop discrete models of two-dimensional filamental branching growth. The models are based on the hypothesis that the fungus secretes a regulatory substance that diffuses into the surrounding medium and is detected by the growing hyphae. We also present a simple Markovian growth model without such a feedback, but yielding to analytical computations.

Notes: Abstract In vivo volume growth of two murine tumor cell lines was compared by mathematical modeling to their volume growth as multicellular spheroids. Fourteen deterministic mathematical models were studied. For one cell line, spheroid growth could be described by a model simpler than needed for description of growthin vivo. A model that explicitly included the stimulatory role for cell-cell interactions in regulation of growth was always superior to a model that did not include such a role. The von Bertalanffy model and the logistic model could not fit the data; this result contradicted some previous literature and was found to depend on the applied least squares fitting method. By the use of a particularly designed mathematical method, qualitative differences were discriminated from quantitative differences in growth dynamics of the same cells cultivated in two different three-dimensional systems.

Notes: Abstract This paper develops and applies a dynamic mathematical model for optimal scheduling of nitrogen fertilization and irrigation that minimizes nitrogen leaching subject to a target level of yield. The analysis assumes a single crop grown during a single growing season of a given length. It is shown that substitution of water for nitrogen along a given plant growth path decreases nitrogen leaching and, therefore, groundwater contamination. It is proved that a minimum leaching solution to the optimization problem is obtained with a single nitrogen application at the beginning of the season and irrigation scheduling that maintains a wet soil throughout the growing period. A numerical example utilizing experimental data for an irrigated summer corn in Israel confirms and quantifies the analytical findings.

Notes: Abstract We analyse the stochastic properties of dynamical systems with finite populations of a few differentreplicator species. Our main interest is to evaluate the typicallifetime, i.e. the time for the extinction of the first species in the network, for different catalytic structures, as a function of the population size.

Notes: Abstract The capacity of a model immune network in terms of the number of different antigens that can be vaccinated against without any memory lost is computed and tested by numerical simulations. We also investigate memory loss and failure to vaccinate due to overcrowding the network with too many antigens. The computations are done for two different strategies for proliferation, one implying all the antigen specific clones and the second one being more thrifty.

Notes: Abstract The technique of model-building a protein of known sequence but unknown tertiary structure from the structures of homologous proteins is probably so far the most reliable means of mapping from primary to tertiary structure. A key step towards the realization of the aim is to develop ways of aligning three-dimensional structures of homologus proteins, thereby deriving the rules useful for protein modelling. We have developed a generalized differential-geometric representation of protein local conformation for use in a protein comparison program which aligns protein sequences on the basis of their sequence and conformational knowledge. Because the differetial-geometric distance measure between local conformations is independent of the coordinate frame and remains chirality information, the comparison program is easily implemented, relatively rational and reasonably fast. The utility of this program for aligning closely and distantly related homologous proteins is demonstrated by multiple alignment of globins, serine proteinases and aspartic proteinase domains. Particularly, the method has reached the rational alignment between the mammalian and microbial serine proteinases as compared with many published alignment programs.

Notes: Abstract New formulas for deriving the sensitivities of stable stage structures and reproductive values to changes in vital rates are presented. They enable comparison of the sensities to changes of different elements in the projection matrix; in other words, comparison of partial derivatives of the eigenvectors. These kinds of sensitivities can be used in applied problems such as an analysis of the effect of harvesting on the population structure. However, in this paper, we examine the application of the sensitivities in a more general ecological context. We investigate why the stable stage structure of the mustard aphid,Lipaphis erysimi, changes very little in the temperature interval 10–30°C. The sensitivities of the stable stage structure at 15°C and 25°C were derived. The character of the sensitivites were the same in both temperatures although the stage structure was more sensitive to changes at 15°C than at 25°C. The sensitivity analysis also revealed that the temperature variation results in changes in fecundity and developmental rate that have a counteractive effect on the population structure.

Notes: Abstract Plankton populations undergo dramatic surges. Rapid increases and decreases by a factor of 10 or more are observed, often separated by relatively stable interludes. We propose a description of plankton communities as excitable systems. In particular, we present a model for the evolution of phytoplankton and zooplankton populations which resembles models for the behaviour of excitable media. The parameter dependency of the various “excitable” phenomena, trigger mechanism, threshold, and slow recovery, is clear, and permits ready investigation of the influence of properties of the physical environment, including variations in nutrient fluxes, temperature or pollution levels.

Notes: Abstract Analysis schemes for the classification of synergism and antagonism for mixed agents operate on the discrepancies between observed and calculated results. As such they cannot be confirmed by experiments and therefore have to be tested in terms of mathematical and logical self-consistency. The concept of independent action is close to the literal meaning of the term “non-interaction”. Since this concept does not depend on the mechanisms of actions nor on the type of effect scale used, it is suitable as one of the basic criterion for the definition of synergism and antagonism. A general mathematical framework of independent action is presented in this paper based on the concept of “relative effect” as used in the literature. The, different equations for independent action currently used in various areas are shown to be manifestations, of a general formula under different sets of boundary conditions, which are the natural limiting values of the effects of the corresponding system observed at low and at high doses of the agents. The framework can, be generalized to the combined action ofn-agents as well as to the interaction of an agent with itself. In addition, the differential form of the formula for independent action is derived. This framework of systematic definitions and derived equations enable a more in-depth study of the implications of the concept of independent action and its relation to other concepts of non-interaction.

Notes: Abstract We model how auto-reactiveB cells are kept under control by an idiotypic network. Autoimmunity occurs when the control is broken by an infection or not achieved through an abnormal ontogenetic evolution. We describe the idiotypic network, viz., the central immune system, by idiotype-anti-idiotype pairs which are coupled to a set of highly connected clones, which interact with each clone of the network. Some clones of the central immune system recognize self-antigen. We find a huge variety of fixed points which can be classified as tolerant, autoimmune, and neutral states according to the concentration of the auto-reactive antibody. Most significant are auto-reactive clones which are a member of an idiotype-anti-idiotype pair. In a healthy individual, an autoimmune disease is induced by an antigen infection which triggers a transition from a tolerant to an autoimmune state. Autoimmunity is induced more readily by an antigen coupling to theanti-idiotype than by one interacting with the auto-reactive clone itself. We indicate a possible therapy which simply reverses the processes that have lead to the autoimmune disease. In the early development of the central immune system its highly connected, core part serves to draw the more specific clones of idiotype-anti-idiotype pairs into the network. In order to avoid autoimmunity in ontogenetic evolution the anti-idiotype of an auto-reactive clone must be formed in advance by a sufficiently long period of time. Thus, a well ordered succession of the appearance of the more specific clones is required.

Notes: Abstract A method of dimensionless time-scaling based on extrinsic expectation of life at birth but intrinsic to a system generating a survival distribution is introduced. Such scaling allows the survival fraction function and its associated mortality function to serve as Green's functions for their generalized equivalents. i.e. a “population” function and a “death” function. The analytical mechanics of utilizing these concepts are formulated, applied to the classical Gompertz and Weibull survival models, and discussed with respect to biological relevance.

Notes: Abstract It is now widely accepted that localized high concentrations of Ca2+ (Ca2+ domains) play a major role in controlling the time course of neurotransmitter release. In the present work we calculate the magnitude and the time course of Ca2+ domains that evolve in the vicinity of a Ca2+ channel and an adjacent release site. In the calculations we consider a accurately dimensioned Ca2+ channel. Moreover, the Ca2+ current is continuously adjusted with regard to the accumulated intracellular Ca2+ and, in addition, endogenous buffers are considered. The calculations, carried out by the software FIDAP, based on finite element method, show that the Ca2+ concentrations achieved near the release sites are significantly lower than claimed by other investigators. Furthermore, we present arguments indicating that the Ca2+ domains, regardless of their magnitude, do not play a role in controlling the time course of release of neurotransmitter.

Notes: Abstract Mammalian white blood cells are known to bias the direction of their movement along concentration gradients of specific chemical stimuli, a phenomenon called chemotaxis. Chemotaxis of leukocyte cells is central to the acute inflammatory response in living organisms and other critical physiological functions. On a molecular level, these cells sense the stimuli termed chemotactic factor (CF) through specific cell surface receptors that bind CF molecules. This triggers a complex signal transduction process involving intracellular biochemical pathways and biophysical events, eventually leading to the observable chemotactic response. Several investigators have shown theoretically that statistical fluctuations in receptor binding lead to “noisy” intracellular signals, which may explain the observed imperfect chemotactic response to a CF gradient. The most recent dynamic model (Tranquillo and Lauffenburger,J. Math. Biol. 25, 229–262. 1987) couples a scheme for intracellular signal transduction and cell motility response with fluctuations in receptor binding. However, this model employs several assumptions regarding receptor dynamics that are now known to be oversimplifications. We extend the earlier model by accounting for several known and speculated chemotactic receptor dynamics, namely, transient G-protein signaling, cytoskeletal association, and receptor internalization and recycling, including statistical fluctuations in the numbers of receptors among the various states. Published studies are used to estimate associated constants and ensure the predicted receptor distribution is accurate. Model analysis indicates that directional persistence in uniform CF concentrations is enhanced by increasing rate constants for receptor cytoskeletal inactivation, ternary complex dissociation, and binary complex dissociation, and by decreasing rate constants for receptor internalization and recycling. For most rate constants, we have detected an optimal range that maximizes orientation bias in CF gradients. We have also examined different desensitization and receptor recycling mechanisms that yield experimentally documented orientation behavior. These yield novel insights into the relationship between receptor dynamics and leukocyte chemosensory movement behavior.

Notes: Abstract Given two independent sequences of letters, we seek the probability distribution of the length of the longest matching word. This word can be in different positions in the two sequences and we consider both perfect and nearly perfect matching. We derive bounds and approximations for the probability and compare them with other bounds and approximations. The results can be applied to DNA sequences in molecular biology and generalized matching between two independent random sequences.

Notes: Abstract A basic control engineer's adage-the poles of a feedback compensator become zeros of the closed-loop system-admits difficulties of interpretation even in the most simple of cases; that of single-input, single-output. An earlier investigation has provided an analysis of this adage in a module-theoretic context for systems in state space form while avoiding restrictive assumptions on system minimality or squareness. The main result is expressed concisely in terms of an exact sequence of modules which include Ω-zero modules corresponding to the feedback system and the plant. Extended zero modules of Ω-type incorporate both finite invariant zero structure, and generic zero information which occurs when a system fails to be right-invertible. In the case of compensation in the feedback path, this main exact sequence reduces to a mathematically clear expression of the aforementioned adage: the Ω-zero module of the feedback system is precisely the direct sum of the Ω-zero module of the plant and the system pole module of the feedback compensator. This paper extends the previous work in order to avoid assumptions on causality in the plant. Implicit dynamical systems are employed, in lieu of systems in state space form. Once again, it is not assumed that the system is one-to-one or onto; and so the concepts of generic zeros and their modules are brought into the arena of implicit systems. The implicit system itself is assumed in this work to be regular; however, decoupling zeros are permitted. Moreover, input-decoupling zeros and system pole feedback relationships are considered.

Notes: Abstract When the problem is considered of obtaining a periodic description in state-space form of a linear process which can be modelled by linear difference equations with periodic coefficients, it is natural to ask whether it is possible to preliminarily derive a polynomial equivalent form of such equations, which in the periodic case plays a role similar to the Rosenbrock's polynomial matrix description of a linear time-invariant process. In this paper a polynomial time-invariant description of a linear periodic process is introduced. It is shown that such a polynomial description gives a simple characterization of the dimension of the space of the solutions corresponding to the null input function, i.e., of the order of the periodic model under consideration. In addition, it allows us to introduce a transfer matrix for the computation of the output responses corresponding to null initial conditions, and to deduce conditions for the periodic model to be causal. These results, as well as the possibility of defining strict system equivalence between two periodic models through their time-invariant polynomial descriptions, in a similar sense as in the time-invariant case, show the relevance of such a polynomial time-invariant description for the problem under consideration.

Notes: Abstract An actual sampling process can be modeled as a random process, which consists of the regular (uniform) deterministic sampling process plus an error in the sampling times which constitutes a zero-mean noise (the jitter). In this paper we discuss the problem of estimating the jitter process. By assuming that the jitter process is an i.i.d. one, with standard deviation that is small compared to the regular sampling time, we show that the variance of the jitter process can be estimated from thenth order spectrum of the sampled data,n=2, 3, i.e., the jitter variance can be extracted from the 2nd-order spectrum or the 3rd-order spectrum (the bispectrum) of the sampled data, provided the continuous signal spectrum is known. However when the signal skewness exceeds a certain level, the potential performance of the bispectrum-based estimation is better than that of the spectrum-based estimation. Moreover, the former can also provide jitter variance estimates when the continuous signal spectrum is unknown while the latter cannot. This suggests that the bispectrum of the sampled data is potentially better for estimating any parameter of the sampling jitter process, once the signal skewness is sufficiently large.

Notes: Abstract Functions belonging to various Paley-Wiener spaces have representations in sampling series. When a function does not belong to such a space, the sampling series may converge, not to the object function but to an "alias" of it, and an aliasing error is said to occur. Aliasing error bounds are derived for one- and two-channel sampling series analogous to the Whittaker-Kotel’nikov-Shannon series, and for the multi-band sampling series, and a "derivative" extension of it, due to Dodson, Beaty, et al. The Poisson summation formula is a basic tool throughout. Aliasing in the one-channel case is shown to arise from a transformation with similarities to a projection. Where possible, the sharpness of the error bounds is discussed.

Notes: Abstract This paper is devoted to a study of the Hausdorff-Young theorems from a historical perspective, beginning with the F. Riesz-Fischer theorem. Introduced by W. H. Young (1912), these theorems were considered and extended by F. Hausdorff (1923), F. Riesz (1923), E.C. Titchmarsh (1924), G. H. Hardy and J.E. Littlewood (1926), M. Riesz (1927), and O. Thorin (1939/48). Special emphasis is placed upon the development of the proofs of the two Hausdorff-Young inequalities and their impact upon Fourier analysis as a whole, in particular on the M. Riesz-Thorin convexity theoremand on the interpolation of operators. The golden thread connecting the various extensions and generalizations is the concept of logarithmic convexity, one that goes back to the work of J. Hadamard (1896), A. Liapounoff (1901), J.L.W.V. Jensen (1906), and O. Blumenthal (1907).

Notes: Abstract In this paper we give a further investigation of the method introduced by the author in [1, Frequency-domain bounds for nonnegative unsharply band-limited functions] for proving bounds for functions with nonnegative Fourier transforms. We also dealt with the question of how large the supremum KS of all numbers |f(u)| is with f the Fourier transform of a nonnegative integrable function F and f(0) = 1, |f(ku)| ≤ ε for k ∈ S. Here u 〉 0 and S ⊂ {2, 3, . . .}. This problem was related in [1] to finding the infimum MS of all numbers Mh = maxϑ [(1−h(ϑ))/(1− cos ϑ)] over all 2π-periodic even, smooth functions h whose Fourier cosine coefficients ak vanish for k ∉ S, and it was proved and announced for several cases that MS (1−KS ) = 1. In this paper we prove the results announced in [1]. To that end we generalize the method given in [1] to include Fourier transforms f of probability measures on R and a certain generalized function h, and we show that the numbers KS, MS are assumed as |f(u)|, Mh for certain allowed f,h. Moreover, we establish a fundamental relation between finding the numbers KS, MS and the numbers KT, MT where T = {2, 3, . . .}\S. In particular, we show that MT = 2KS (2KS − 1)−1,KT = 1/2 MS(MS − 1)−1 and that MT (1 − KT) = 1,KSKT = 1/2 , whenever MS (1 − KS) = 1.

Notes: Abstract Finite energy band-limited functions are reconstructed iteratively from nonuniform sample values of the functions and its derivatives. It is shown that the maximum gap allowed between the sampling points increases linearly with the number of derivatives considered. Moreover, a more precise result is presented for the first derivative case and another reconstruction of the functions using the frame algorithm is deduced.

Notes: Abstract In the early 1960s research into radar signal synthesis produced important formulas describing the action of the two-dimensional Fourier transform on auto- and crossambiguity surfaces. When coupled with the Poisson Summation formula, these results become applicable to the theory of Weyl-Heisenberg systems, in the form of lattice sum formulas that relate the energy of the discrete crossambiguity function of two signals f and g over a lattice with the inner product of the discrete autoambiguity functions of f and g over a "complementary" lattice. These lattice sum formulas provide a framework for a new proof of a result of N.J. Munch characterizing tight frames and for establishing an important relationship between l1-summability (condition A) of the discrete ambiguity function of g over a lattice and properties of the Weyl-Heisenberg system of g over the complementary lattice. This condition leads to formulas for upper frame bounds that appear simpler than those previously published and provide guidance in choosing lattice parameters that yield the most snug frame at a stipulated density of basis functions.

Notes: Abstract Let $a〉0, b〉0, ab〈1;$ and let $g\in L^2({\Bbb R}).$ In this paper we investigate the relation between the frame operator $S:f\in L^2({\Bbb R})\rightarrow \sum_{n,m}\,(f,g_{na,mb})\,g_{na,mb}$ and the matrix $H$ whose entries $H_{k,l\,;\,k',l'}$ are given by $(g_{k'/b,l'/a},g_{k/b,l/a})$ for $k,l,k',l'\in{\Bbb Z}.$ Here $f_{x,y}(t)={\rm exp}(2\pi iyt)\,f(t-x),$ $t\in{\Bbb R}$ , for any $f\in L^2({\Bbb R}).$ We show that $S$ is bounded as a mapping of $L^2({\Bbb R})$ into $L^2({\Bbb R})$ if and only if $H$ is bounded as a mapping of $l^2({\Bbb Z}^2)$ into $l^2({\Bbb Z}^2).$ Also we show that $AI\leq S\leq BI$ if and only if $AI\leq\frac{1}{ab}\,H\leq BI,$ where $I$ denotes the identity operator of $L^2({\Bbb R})$ and $l^2({\Bbb Z}^2),$ respectively, and $A\geq 0,$ $B〈\infty.$ Next, when $g$ generates a frame, we have that $(g_{k/b,l/a})_{k,l}$ has an upper frame bound, and the minimal dual function $^{\circ}\gamma$ can be computed as $ab\,\sum_{k,l}\,(H^{-1})_{k,l\,;\,o,o}\,g_{k/b,l/a}.$ The results of this paper extend, generalize, and rigourize results of Wexler and Raz and of Qian, D. Chen, K. Chen, and Li on the computation of dual functions for finite, discrete-time Gabor expansions to the infinite, continuous-time case. Furthermore, we present a framework in which one can show that certain smoothness and decay properties of a $g$ generating a frame are inherited by $^{\circ}\gamma.$ In particular, we show that $^{\circ}\gamma\in{\cal S}$ when $g\in{\cal S}$ generates a frame $({\cal S}$ Schwartz space). The proofs of the main results of this paper rely heavily on a technique introduced by Tolimieri and Orr for relating frame bound questions on complementary lattices by means of the Poisson summation formula.

Notes: Abstract For any ε 〉 0, we construct an orthonormal Schauder basis of C(K) consisting of trigonometric polynomials Tn n = 1, 2, . . . , such that deg(Tn) ≤ (1/2)(1 + ε)n. This is best possible with regard to the degree. The construction uses wavelet techniques.

Notes: Abstract We study the general question of the existence of self-similar lattice tilings of Euclidean space. A necessary and sufficient geometric condition on the growth of the boundary of approximate tiles is reduced to a problem in Fourier analysis that is shown to have an elegant simple solution in dimension one. In dimension two we further prove the existence of connected self-similar lattice tilings for parabolic and elliptic dilations. These results apply to produce Haar wavelet bases and certain canonical number systems.

Notes: Abstract In the spirit of work of Kerman and Sawyer, a condition is given that is necessary and sufficient for the Fourier transform norm inequality $\Big(\int_{{\Bbb R}_d} \vert\hat{f}\vert^q d\mu\Big)^{1/q} \leq C\Big(\int_{{\Bbb R}_d} \vert f\vert^p v\Big)^{1/p}$ provided v is a radial weight for which v−1/p is convexly decreasing and μ is a suitable measure. We also establish alternative conditions for such inequalities by proving corresponding trace type inequalities and maximal function inequalities that underlie the Fourier transform estimates. Our conditions are relatively simple to compute. Among applications we give extensions of a Sobolev restriction theorem.

Notes: Abstract We present two-sided singular value estimates for a class of convolution-product operators related to time-frequency localization.

Notes: Abstract A linear-quadratic (LQ) control problem subject to a standard continuous-time system is called regular if the input weighting matrix is invertible, and singular if this is not the case. Consequently, optimal inputs for regular LQ problems are ordinary functions (state feedbacks), whereas optical controls for singular problems are in general distributions, e.g., impulses. We will show that regularity and singularity in LQ problems subject to ageneral (implicit) system depends not so much on the input weighting matrix, as on the property that the integrand of the cost criterion is a function only if inputs and state trajectories are, as is the case for LQ problems, subject to astandard system. In particular, we will provide a simple criterion for distinguishing between regularity and singularity in LQ problems subject to a general system. Our criterion is expressed in the system coefficients only and reduces to the classical one if the underlying system is standard.

Notes: Abstract Completions of linear time varying singular systems of the formE(t)x′(t)+F(t)x′(t)=f(t) are explicitly computed using recent results on rational matrix functions. The algorithm and the theory behind it are carefully described. Computational issues are discussed.

Notes: Abstract In this paper a spectral method using orthogonal periodic basis functions for the analysis of linear time invariant descriptor systems is discussed, and the case of the trigonometric Fourier functions is investigated in detail. The method is shown to be convergent, in the distributional sense. However, for any finite number of basis functions, the periodicity induced by the chosen basis can give rise to spurious impulsive components in the computed system response, even in the case of correct initial conditions.

Notes: Abstract In this paper we will study topological properties of the class of proper and improperp×m transfer functions of a fixed McMillan degreen. A natural generalization of this class is all autoregressive systems of degreen under external system equivalence. The subset of irreducible systems has in a natural way the structure of a manifold and we show how to extend this topology to the set of all autoregressive systems of degree at mostn. We will describe the subset of systems with fixed Kronecker indicesv=(v1,...,v p ) as an orbit space, which will enable us to calculate the topological dimension for each collection of indicesv. Finally, we will describe the topological closure of those sets in the space of all autoregressive systems.

Notes: Abstract It has been shown in [B.M.90] that non-square implicit differential equations allow for the description of variable structure systems (variable order, variable sign, variable parameters). We combine here the possible control strategy developed in [L.91] for rectangular systems (insuring a unique output behavior for the system compensated with a proportional or proportional and derivative state feedback) with the detector and the observer introduced in [B.M.90] in order to obtain a closed-loop system where the initial structure variation disappears on the output. We also give necessary and sufficient conditions for the free assignment of the associated output dynamics.

Notes: Abstract An exposition of joint cumulants and cumulant spectra is presented. A distinction is emphasized in this paper between the cumulant spectrum of a time series and its stationary version, here called apolyspectrum. The variance and covariance of the sample bispectrum is then derived using a relationship between cumulant spectra of the finite Fourier transform for the 2nd and 4th cumulant function, and the bispectrum and trispectrum of the time series.

Notes: Abstract The detection of a general class of transient (i.e., finite energy) signals in additive stationary interference using the spectral correlation function (second order cumulant spectrum) is presented. Observable features in the two-dimensional spectral correlation function due to properties of signals in the assumed class of transients are exploited to derive a detection statistic. The performance of the proposed detection statistic relative to a conventional power spectral detector is presented.

Notes: Abstract Vibroacoustic signals of rotating machinery are composed of sums of modulated periodicities, broadband random components, and occasionally a set of transient responses. These signals are not ergodic as the modulated periodicities are partially coherent. Progressive wear of the rotating machine causes the nonlinear structure of the received signal to intensify, and nonlinearity results in transfer of energy between harmonics of the signal's periodic components. Statistics developed from bispectrum and second-order cumulant spectrum estimates of the measured signal are combined with power spectrum amplitudes as feature inputs for standard multivariate classifiers. The higher-order statistics measure, respectively, the extent of nonlinearity and intermodulation of the received signal. Classification results of simulated and actual incipient wear data collected from a controlled experiment drilling circuit boards illustrate the potential of this novel statistical signal processing approach.

Notes: Abstract A geometric interpretation of the Lewis Structure Algorithm (LSA) is given in terms of precise projection maps directly defined from the (E, A, B, C) maps of the system. An extended version of LSA is offered which, in addition to this geometric information, also provides in a direct way, and within the same (E, A, B, C) class of models, a left inverse (if any) of the system. An example is given.

Notes: Abstract We consider the problem of control of linear, time-invariant, multivariable descriptor (implicit) systems. In particular we examine the effectiveness of an algorithm (which is a generalization of previous work in state space systems) for the design of an output feedback control giving pole placement in such systems. Conditions are presented which ensure that the algorithm produces the required control. We also address the important issue of uniqueness of solutions.

Notes: Abstract Detecting active sonar returns in multipath media is a central underwater signal processing problem. This paper studies a new approach to active sonar detection using bispectral analysis of sonar data. Its sensitivity to non-stationarities is used to develop a threshold detector that can be applied to broad classes of signals and noise. Precise statistical descriptions of the underwater medium and noise are not required. Theoretical analyses predicting its performance as a function of signal-to-noise ratio and time-bandwidth product are presented. Computer simulation experiments verify the results and show that its performance compares favorably to that of conventional detectors.

Notes: Abstract The noise suppression capability of higher-order moments and spectra has made them attractive when the goal is to extract or reconstruct a signal that is contaminated by multivariate Gaussian noise or certain types of non-Gaussian noise. Two new detectors, one centralized and one distributed, which are based on the third-order moment of the data are proposed. The asymptotic performance of the centralized detector and the asymptotic distribution of the components of the distributed detector are analyzed. Further, the performance of these detectors is simulated and compared to that of the matched filter for three different types of interference: Gaussian noise, Gaussian noise corrupted by a sinusoid with random phase, and Arctic under-ice noise.

Notes: Abstract We investigate the controller design problem for linear systems in which the state and the controls are subject to static linear constraints. We give necessary and sufficient conditions for the existence, and present a complete parametrization of all stabilizing controllers. This parametrization allows us to transform the constrained control problem into a standard problem which can be solved using usualH 2 orH ∞ optimization methods. The approach is illustrated by a simple numerical example showing the various steps of the proposed algorithm.

Notes: Abstract A continuous stationary signal possessing non-Gaussian higher order statistics cannot be correctly modelled by any discrete process based on passing independently and identically distributed noise through a linear filter. In particular, it is shown that at third order there exists no discrete skewed linear model with a discrete bispectrum that is the same as that obtained from the Nyquist samples of any continuous stationary process. The nature of the problem is elucidated and an alternative method for modelling the third order statistics of continuous stationary processes is proposed.