937 resultados para Advanced mathematical thinking
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A neural model of peripheral auditory processing is described and used to separate features of coarticulated vowels and consonants. After preprocessing of speech via a filterbank, the model splits into two parallel channels, a sustained channel and a transient channel. The sustained channel is sensitive to relatively stable parts of the speech waveform, notably synchronous properties of the vocalic portion of the stimulus it extends the dynamic range of eighth nerve filters using coincidence deteectors that combine operations of raising to a power, rectification, delay, multiplication, time averaging, and preemphasis. The transient channel is sensitive to critical features at the onsets and offsets of speech segments. It is built up from fast excitatory neurons that are modulated by slow inhibitory interneurons. These units are combined over high frequency and low frequency ranges using operations of rectification, normalization, multiplicative gating, and opponent processing. Detectors sensitive to frication and to onset or offset of stop consonants and vowels are described. Model properties are characterized by mathematical analysis and computer simulations. Neural analogs of model cells in the cochlear nucleus and inferior colliculus are noted, as are psychophysical data about perception of CV syllables that may be explained by the sustained transient channel hypothesis. The proposed sustained and transient processing seems to be an auditory analog of the sustained and transient processing that is known to occur in vision.
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In this PhD study, mathematical modelling and optimisation of granola production has been carried out. Granola is an aggregated food product used in breakfast cereals and cereal bars. It is a baked crispy food product typically incorporating oats, other cereals and nuts bound together with a binder, such as honey, water and oil, to form a structured unit aggregate. In this work, the design and operation of two parallel processes to produce aggregate granola products were incorporated: i) a high shear mixing granulation stage (in a designated granulator) followed by drying/toasting in an oven. ii) a continuous fluidised bed followed by drying/toasting in an oven. In addition, the particle breakage of granola during pneumatic conveying produced by both a high shear granulator (HSG) and fluidised bed granulator (FBG) process were examined. Products were pneumatically conveyed in a purpose built conveying rig designed to mimic product conveying and packaging. Three different conveying rig configurations were employed; a straight pipe, a rig consisting two 45° bends and one with 90° bend. It was observed that the least amount of breakage occurred in the straight pipe while the most breakage occurred at 90° bend pipe. Moreover, lower levels of breakage were observed in two 45° bend pipe than the 90° bend vi pipe configuration. In general, increasing the impact angle increases the degree of breakage. Additionally for the granules produced in the HSG, those produced at 300 rpm have the lowest breakage rates while the granules produced at 150 rpm have the highest breakage rates. This effect clearly the importance of shear history (during granule production) on breakage rates during subsequent processing. In terms of the FBG there was no single operating parameter that was deemed to have a significant effect on breakage during subsequent conveying. A population balance model was developed to analyse the particle breakage occurring during pneumatic conveying. The population balance equations that govern this breakage process are solved using discretization. The Markov chain method was used for the solution of PBEs for this process. This study found that increasing the air velocity (by increasing the air pressure to the rig), results in increased breakage among granola aggregates. Furthermore, the analysis carried out in this work provides that a greater degree of breakage of granola aggregates occur in line with an increase in bend angle.
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This thesis is focused on the design and development of an integrated magnetic (IM) structure for use in high-power high-current power converters employed in renewable energy applications. These applications require low-cost, high efficiency and high-power density magnetic components and the use of IM structures can help achieve this goal. A novel CCTT-core split-winding integrated magnetic (CCTT IM) is presented in this thesis. This IM is optimized for use in high-power dc-dc converters. The CCTT IM design is an evolution of the traditional EE-core integrated magnetic (EE IM). The CCTT IM structure uses a split-winding configuration allowing for the reduction of external leakage inductance, which is a problem for many traditional IM designs, such as the EE IM. Magnetic poles are incorporated to help shape and contain the leakage flux within the core window. These magnetic poles have the added benefit of minimizing the winding power loss due to the airgap fringing flux as they shape the fringing flux away from the split-windings. A CCTT IM reluctance model is developed which uses fringing equations to accurately predict the most probable regions of fringing flux around the pole and winding sections of the device. This helps in the development of a more accurate model as it predicts the dc and ac inductance of the component. A CCTT IM design algorithm is developed which relies heavily on the reluctance model of the CCTT IM. The design algorithm is implemented using the mathematical software tool Mathematica. This algorithm is modular in structure and allows for the quick and easy design and prototyping of the CCTT IM. The algorithm allows for the investigation of the CCTT IM boxed volume with the variation of input current ripple, for different power ranges, magnetic materials and frequencies. A high-power 72 kW CCTT IM prototype is designed and developed for use in an automotive fuelcell-based drivetrain. The CCTT IM design algorithm is initially used to design the component while 3D and 2D finite element analysis (FEA) software is used to optimize the design. Low-cost and low-power loss ferrite 3C92 is used for its construction, and when combined with a low number of turns results in a very efficient design. A paper analysis is undertaken which compares the performance of the high-power CCTT IM design with that of two discrete inductors used in a two-phase (2L) interleaved converter. The 2L option consists of two discrete inductors constructed from high dc-bias material. Both topologies are designed for the same worst-case phase current ripple conditions and this ensures a like-for-like comparison. The comparison indicates that the total magnetic component boxed volume of both converters is similar while the CCTT IM has significantly lower power loss. Experimental results for the 72 kW, (155 V dc, 465 A dc input, 420 V dc output) prototype validate the CCTT IM concept where the component is shown to be 99.7 % efficient. The high-power experimental testing was conducted at General Motors advanced technology center in Torrence, Los Angeles. Calorific testing was used to determine the power loss in the CCTT IM component. Experimental 3.8 kW results and a 3.8 kW prototype compare and contrast the ferrite CCTT IM and high dc-bias 2L concepts over the typical operating range of a fuelcell under like-for-like conditions. The CCTT IM is shown to perform better than the 2L option over the entire power range. An 8 kW ferrite CCTT IM prototype is developed for use in photovoltaic (PV) applications. The CCTT IM is used in a boost pre-regulator as part of the PV power stage. The CCTT IM is compared with an industry standard 2L converter consisting of two discrete ferrite toroidal inductors. The magnetic components are compared for the same worst-case phase current ripple and the experimental testing is conducted over the operation of a PV panel. The prototype CCTT IM allows for a 50 % reduction in total boxed volume and mass in comparison to the baseline 2L option, while showing increased efficiency.
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The recognition and protection of constitutional rights is a fundamental precept. In Ireland, the right to marry is provided for in the equality provisions of Article 40 of the Irish Constitution (1937). However, lesbians and gay men are denied the right to marry in Ireland. The ‘last word’ on this issue came into being in the High Court in 2006, when Katherine Zappone and Ann Louise Gilligan sought, but failed, to have their Canadian marriage recognised in Ireland. My thesis centres on this constitutional court ruling. So as to contextualise the pursuit of marriage equality in Ireland, I provide details of the Irish trajectory vis-à-vis relationship and family recognition for same-sex couples. In Chapter One, I discuss the methodological orientation of my research, which derives from a critical perspective. Chapter Two denotes my theorisation of the principle of equality and the concept of difference. In Chapter Three, I discuss the history of the institution of marriage in the West with its legislative underpinning. Marriage also has a constitutional underpinning in Ireland, which derives from Article 41 of our Constitution. In Chapter Four, I discuss ways in which marriage and family were conceptualised in Ireland, by looking at historical controversies surrounding the legalisation of contraception and divorce. Chapter Five denotes a Critical Discourse Analysis of the High Court ruling in Zappone and Gilligan. In Chapter Six, I critique text from three genres of discourse, i.e. ‘Letters to the Editor’ regarding same-sex marriage in Ireland, communication from legislators vis-à-vis the 2004 legislative impediment to same-sex marriage in Ireland, and parliamentary debates surrounding the 2010 enactment of civil partnership legislation in Ireland. I conclude my research by reflecting on my methodological and theoretical considerations with a view to answering my research questions. Author’s Update: Following the outcome of the 2015 constitutional referendum vis-à-vis Article 41, marriage equality has been realised in Ireland.
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The work in this thesis concerns the advanced development of polymeric membranes of two types; pervaporation and lateral-flow. The former produced from a solution casting method and the latter from a phase separation. All membranes were produced from casting lacquers. Early research centred on the development of viable membranes. This led to a supported polymer blend pervaporation membrane. Selective layer: plasticized 4:1 mass ratio sodium-alginate: poly(vinyl-alcohol) polymer blend. Using this membrane, pervaporation separation of ethanol/water mixtures was carefully monitored as a function of film thickness and time. Contrary to literature expectations, these films showed increased selectivity and decreased flux as film thickness was reduced. It is argued that morphology and structure of the polymer blend changes with thickness and that these changes define membrane efficiency. Mixed matrix membrane development was done using spherical, discreet, size-monodisperse mesoporous silica particles of 1.8 - 2μm diameter, with pore diameters of ~1.8 nm were incorporated into a poly(vinyl alcohol) [PVA] matrix. Inclusion of silica benefitted pervaporation performance for the dehydration of ethanol, improving flux and selectivity throughout in all but the highest silica content samples. Early lateral-flow membrane research produced a membrane from a basic lacquer composition required for phase inversion; polymer, solvent and non-solvent. Results showed that bringing lacquers to cloud point benefits both the pore structure and skin layers of the membranes. Advancement of this work showed that incorporation of ethanol as a mesosolvent into the lacquer effectively enhances membrane pore structure resulting in an improvement in lateral flow rates of the final membranes. This project details the formation mechanics of pervaporation and lateral-flow membranes and how these can be controlled. The principle methods of control can be applied to the formation of any other flat sheet polymer membranes, opening many avenues of future membrane research and industrial application.
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In the last decade, we have witnessed the emergence of large, warehouse-scale data centres which have enabled new internet-based software applications such as cloud computing, search engines, social media, e-government etc. Such data centres consist of large collections of servers interconnected using short-reach (reach up to a few hundred meters) optical interconnect. Today, transceivers for these applications achieve up to 100Gb/s by multiplexing 10x 10Gb/s or 4x 25Gb/s channels. In the near future however, data centre operators have expressed a need for optical links which can support 400Gb/s up to 1Tb/s. The crucial challenge is to achieve this in the same footprint (same transceiver module) and with similar power consumption as today’s technology. Straightforward scaling of the currently used space or wavelength division multiplexing may be difficult to achieve: indeed a 1Tb/s transceiver would require integration of 40 VCSELs (vertical cavity surface emitting laser diode, widely used for short‐reach optical interconnect), 40 photodiodes and the electronics operating at 25Gb/s in the same module as today’s 100Gb/s transceiver. Pushing the bit rate on such links beyond today’s commercially available 100Gb/s/fibre will require new generations of VCSELs and their driver and receiver electronics. This work looks into a number of state‐of-the-art technologies and investigates their performance restraints and recommends different set of designs, specifically targeting multilevel modulation formats. Several methods to extend the bandwidth using deep submicron (65nm and 28nm) CMOS technology are explored in this work, while also maintaining a focus upon reducing power consumption and chip area. The techniques used were pre-emphasis in rising and falling edges of the signal and bandwidth extensions by inductive peaking and different local feedback techniques. These techniques have been applied to a transmitter and receiver developed for advanced modulation formats such as PAM-4 (4 level pulse amplitude modulation). Such modulation format can increase the throughput per individual channel, which helps to overcome the challenges mentioned above to realize 400Gb/s to 1Tb/s transceivers.
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This portfolio of exploration explores the role of transformative thinking and practice in a property entrepreneur’s response to the financial crisis which swept over Ireland from 2008. The complexity of this challenge and the mental capacity to meet its demands is at the core of the exploration. This inquiry emerged from the challenges the financial crisis presented to my values, beliefs, assumptions, and theories, i.e. the interpretive lens through which I make meaning of my experiences. Given the issue identified, this inquiry is grounded in aspects of theories of constructive developmental psychology, applied developmental science, and philosophy. Integrating and linking these elements to business practice is the applied element of the Portfolio. As the 2008 crisis unfolded I realised I was at the limits of my way of knowing. I came to understand that the underlying structure of a way of knowing is the ‘subject-object relationship’ i.e. what a way of knowing can reflect upon, look at, have perspective on, in other words, make object, as against what is it embedded in, attached to, identified within, or subject to. My goal became enhancing my awareness of how I made meaning and how new insights, which would transform a way of knowing, are created. The focus was on enhancing my practice. This Portfolio is structured into three essays. Essay One reported on my self-reflection and external evaluation out of which emerged my developmental goals. In Essay Two I undertake a reading for change programme in which different meaning making systems were confronted in order to challenge me as a meaning maker. Essay Three reported on my experiment which concerned the question whether it was possible for me as a property entrepreneur, and for others alike, to retain bank finance in the face of the overwhelming objective of the bank to deleverage their balance sheet of property loans. The output of my research can be grouped into General Developmental and Specific Business Implications. Firstly I address those who are interested in a transformational-based response to the challenges of operating in the property sector in Ireland during a crisis. I outline the apparatus of thought that I used to create insight, and thus transform how I thought, these are Awareness, Subject-object separation, Exploring other’s perspectives from the position of incompleteness, Dialectical thinking and Collingwood’s Questioning activity. Secondly I set out my learnings from the crisis and their impact on entrepreneurial behaviour and the business of property development. I identify ten key insights that have emerged from leading a property company through the crisis. Many of these are grounded in common sense, however, in my experience these were, to borrow Shakespeare’s words, “More honor'd in the breach than the observance” in pre Crisis Ireland. Finally I set out a four-step approach for forging a strategy. This requires my peer practitioners to identify (i) what they are subject to, (ii) Assess the Opportunity or challenge in a Systemic Context, (iii) Explore Multiple Perspectives on the opportunity or Challenge with an Orientation to change how you know and (iv) Using the Questioning Activity to create Knowledge. Based on my experience I conclude that transformative thinking and practice is a key enabler for a property entrepreneur, in responding to a major collapse of traditional (bank debt) funding.
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In breast cancer, chemotherapy regimens that include infusional 5-fluorouracil (5-FU) lead to high response rates, but require central venous access and pumps. To avoid these inconveniences, we substituted infusional 5-FU with capecitabine. The main objective of this study was to determine the maximum tolerated dose (MTD) of capecitabine when given in combination with fixed doses of epirubicin and cyclophosphamide (100 and 600 mg/m(2) day 1 every (q) 3 weeks) as primary treatment for large operable or locally advanced/inflammatory breast cancer without distant metastasis. Capecitabine was escalated from 750 mg/m(2) twice a day (bid) to 1250 mg/m(2) bid from day 1 to day 14 in four dose levels. Dose escalation was permitted if 0/3 or 1/6 patients experienced dose-limiting toxicity (DLT). A total of 23 patients were included and 117 courses were administered. At dose level 4, 2 of 2 patients presented DLTs defining the MTD. A high rate of capecitabine treatment modification was required with capecitabine 1050 mg/m(2) bid (dose level 3). 19 patients achieved an objective response (83%). In conclusion, we believe that capecitabine 900 mg/m(2) bid (dose level 2) is the recommended dose in combination with epirubicin 100 mg/m(2) and cyclophosphamide 600 mg/m(2). The acceptable toxicity profile and encouraging activity of this regimen warrant further evaluation.
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PURPOSE: The association of continuous infusion 5-fluorouracil, epirubicin (50 mg/m2 q 3 weeks) and a platinum compound (cisplatin or carboplatin) was found to be very active in patients with either locally advanced/inflammatory (LA/I) [1, 2] or large operable (LO) breast cancer (BC) [3]. The same rate of activity in terms of response rate (RR) and response duration was observed in LA/I BC patients when cisplatin was replaced by cyclophosphamide [4]. The dose of epirubicin was either 50 mg/m2 [ 1, 2, 3] or 60 mg/m2/cycle [4]. The main objective of this study was to determine the maximum tolerated dose (MTD) of epirubicin when given in combination with fixed doses of cyclophosphamide and infusional 5-fluorouracil (CEF-infu) as neoadjuvant therapy in patients with LO or LA/I BC for a maximum of 6 cycles. PATIENTS AND METHODS: Eligible patients had LO or LA/I BC, a performance status 0-1, adequate organ function and were <65 years old. Cyclophosphamide was administered at the dose of 400 mg/m2 day 1 and 8, q 4 weeks and infusional 5-fluorouracil 200 mg/m2/day was given day 1-28, q 4 weeks. Epirubicin was escalated from 30 to 45 and to 60 mg/m2 day 1 and 8; dose escalation was permitted if 0/3 or 1/6 patients experienced dose limiting toxicity (DLT) during the first 2 cycles of therapy. DLT for epirubicin was defined as febrile neutropenia, grade 4 neutropenia lasting for >7 days, grade 4 thrombocytopenia, or any non-haematological toxicity of CTC grade > or =3, excluding alopecia and plantar-palmar erythrodysesthesia (this toxicity was attributable to infusional 5-fluorouracil and was not considered a DLT of epirubicin). RESULTS: A total of 21 patients, median age 44 years (range 29-63) have been treated. 107 courses have been delivered, with a median number of 5 cycles per patient (range 4-6). DLTs on cycles I and 2 on level 1, 2, 3: grade 3 (G3) mucositis occurred in 1/10 patients treated at the third dose level. An interim analysis showed that G3 PPE occurred in 5/16 pts treated with the 28-day infusional 5-FU schedule at the 3 dose levels. The protocol was subsequently amended to limit the duration of infusional 5-fluorouracil infusion from 4 to 3 weeks. No G3 PPE was detected in 5 patients treated with this new schedule. CONCLUSIONS: This study establishes that epirubicin 60mg/m2 day 1 and 8, cyclophosphamide 400mg/m2 day 1 and 8 and infusional 5-fluorouracil 200 mg/m2/day day 1-21. q 4 weeks is the recommended dose level. Given the encouraging activity of this regimen (15/21 clinical responses) we have replaced infusional 5-fluorouracil by oral capecitabine in a recently activated study.
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SCOPUS: cp.j
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INTRODUCTION: The characterization of urinary calculi using noninvasive methods has the potential to affect clinical management. CT remains the gold standard for diagnosis of urinary calculi, but has not reliably differentiated varying stone compositions. Dual-energy CT (DECT) has emerged as a technology to improve CT characterization of anatomic structures. This study aims to assess the ability of DECT to accurately discriminate between different types of urinary calculi in an in vitro model using novel postimage acquisition data processing techniques. METHODS: Fifty urinary calculi were assessed, of which 44 had >or=60% composition of one component. DECT was performed utilizing 64-slice multidetector CT. The attenuation profiles of the lower-energy (DECT-Low) and higher-energy (DECT-High) datasets were used to investigate whether differences could be seen between different stone compositions. RESULTS: Postimage acquisition processing allowed for identification of the main different chemical compositions of urinary calculi: brushite, calcium oxalate-calcium phosphate, struvite, cystine, and uric acid. Statistical analysis demonstrated that this processing identified all stone compositions without obvious graphical overlap. CONCLUSION: Dual-energy multidetector CT with postprocessing techniques allows for accurate discrimination among the main different subtypes of urinary calculi in an in vitro model. The ability to better detect stone composition may have implications in determining the optimum clinical treatment modality for urinary calculi from noninvasive, preprocedure radiological assessment.
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INTRODUCTION: Anti-cholinergic medications have been associated with increased risks of cognitive impairment, premature mortality and increased risk of hospitalisation. Anti-cholinergic load associated with medication increases as death approaches in those with advanced cancer, yet little is known about associated adverse outcomes in this setting. METHODS: A substudy of 112 participants in a randomised control trial who had cancer and an Australia modified Karnofsky Performance Scale (AKPS) score (AKPS) of 60 or above, explored survival and health service utilisation; with anti-cholinergic load calculated using the Clinician Rated Anti-cholinergic Scale (modified version) longitudinally to death. A standardised starting point for prospectively calculating survival was an AKPS of 60 or above. RESULTS: Baseline entry to the sub-study was a mean 62 +/- 81 days (median 37, range 1-588) days before death (survival), with mean of 4.8 (median 3, SD 4.18, range 1 - 24) study assessments in this time period. Participants spent 22% of time as an inpatient. There was no significant association between anti-cholinergic score and time spent as an inpatient (adjusted for survival time) (p = 0.94); or survival time. DISCUSSION: No association between anti-cholinergic load and survival or time spent as an inpatient was seen. Future studies need to include cognitively impaired populations where the risks of symptomatic deterioration may be more substantial.
A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula
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Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.
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Therapeutic anticancer vaccines are designed to boost patients' immune responses to tumors. One approach is to use a viral vector to deliver antigen to in situ DCs, which then activate tumor-specific T cell and antibody responses. However, vector-specific neutralizing antibodies and suppressive cell populations such as Tregs remain great challenges to the efficacy of this approach. We report here that an alphavirus vector, packaged in virus-like replicon particles (VRP) and capable of efficiently infecting DCs, could be repeatedly administered to patients with metastatic cancer expressing the tumor antigen carcinoembryonic antigen (CEA) and that it overcame high titers of neutralizing antibodies and elevated Treg levels to induce clinically relevant CEA-specific T cell and antibody responses. The CEA-specific antibodies mediated antibody-dependent cellular cytotoxicity against tumor cells from human colorectal cancer metastases. In addition, patients with CEA-specific T cell responses exhibited longer overall survival. These data suggest that VRP-based vectors can overcome the presence of neutralizing antibodies to break tolerance to self antigen and may be clinically useful for immunotherapy in the setting of tumor-induced immunosuppression.
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BACKGROUND: Serotonin is a neurotransmitter that has been linked to a wide variety of behaviors including feeding and body-weight regulation, social hierarchies, aggression and suicidality, obsessive compulsive disorder, alcoholism, anxiety, and affective disorders. Full understanding of serotonergic systems in the central nervous system involves genomics, neurochemistry, electrophysiology, and behavior. Though associations have been found between functions at these different levels, in most cases the causal mechanisms are unknown. The scientific issues are daunting but important for human health because of the use of selective serotonin reuptake inhibitors and other pharmacological agents to treat disorders in the serotonergic signaling system. METHODS: We construct a mathematical model of serotonin synthesis, release, and reuptake in a single serotonergic neuron terminal. The model includes the effects of autoreceptors, the transport of tryptophan into the terminal, and the metabolism of serotonin, as well as the dependence of release on the firing rate. The model is based on real physiology determined experimentally and is compared to experimental data. RESULTS: We compare the variations in serotonin and dopamine synthesis due to meals and find that dopamine synthesis is insensitive to the availability of tyrosine but serotonin synthesis is sensitive to the availability of tryptophan. We conduct in silico experiments on the clearance of extracellular serotonin, normally and in the presence of fluoxetine, and compare to experimental data. We study the effects of various polymorphisms in the genes for the serotonin transporter and for tryptophan hydroxylase on synthesis, release, and reuptake. We find that, because of the homeostatic feedback mechanisms of the autoreceptors, the polymorphisms have smaller effects than one expects. We compute the expected steady concentrations of serotonin transporter knockout mice and compare to experimental data. Finally, we study how the properties of the the serotonin transporter and the autoreceptors give rise to the time courses of extracellular serotonin in various projection regions after a dose of fluoxetine. CONCLUSIONS: Serotonergic systems must respond robustly to important biological signals, while at the same time maintaining homeostasis in the face of normal biological fluctuations in inputs, expression levels, and firing rates. This is accomplished through the cooperative effect of many different homeostatic mechanisms including special properties of the serotonin transporters and the serotonin autoreceptors. Many difficult questions remain in order to fully understand how serotonin biochemistry affects serotonin electrophysiology and vice versa, and how both are changed in the presence of selective serotonin reuptake inhibitors. Mathematical models are useful tools for investigating some of these questions.