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1.
Appl Opt ; 59(26): 7853-7864, 2020 Sep 10.
Article in English | MEDLINE | ID: mdl-32976457

ABSTRACT

We propose designs of pupil-domain optical diffusers for a snapshot spectral imaging system using binary-phase encoding. The suggested designs enable the creation of point-spread functions with defined optical response, having profiles that are dependent on incident wavefront wavelength. This efficient combination of dispersive and diffusive optical responses enables us to perform snapshot spectral imaging using compressed sensing algorithms while keeping a high optical throughput alongside a simple fabrication process. Experimental results are reported.

2.
Appl Opt ; 59(4): 1058-1070, 2020 Feb 01.
Article in English | MEDLINE | ID: mdl-32225242

ABSTRACT

We propose a snapshot spectral imaging method for the visible spectral range using two digital cameras placed side-by-side: a regular red-green-blue (RGB) camera and a monochromatic camera equipped with a dispersive diffractive diffuser placed at the pupil of the imaging lens. While spectral imaging was shown to be feasible using a single monochromatic camera with a pupil diffuser [Appl. Opt.55, 432 (2016)APOPAI0003-693510.1364/AO.55.000432], adding an RGB camera provides more spatial and spectral information for stable reconstruction of the spectral cube of a scene. Results of optical experiments confirm that the combined data from the two cameras relax the complexity of the underdetermined reconstruction problem and improve the reconstructed image quality obtained using compressed sensing-based algorithms.

3.
Strahlenther Onkol ; 195(6): 517-525, 2019 Jun.
Article in English | MEDLINE | ID: mdl-30443682

ABSTRACT

BACKGROUND AND PURPOSE: To evaluate the effect of changes in bladder volume during high-dose intensity-modulated-radiotherapy (IMRT) of prostate cancer on acute genitourinary (GU) toxicity and prospectively evaluate a simple biofeedback technique for reproducible bladder filling with the aim of reducing acute GU toxicity. METHODS: One hundred ninety-three patients were trained via a biofeedback mechanism to maintain a partially filled bladder with a reproducible volume of 200-300 cc at planning CT and subsequently at each fraction of radiotherapy. We prospectively analyzed whether and to what extent the patients' ability to maintain a certain bladder filling influenced the degree of acute GU toxicity and whether cut-off values could be differentiated. RESULTS: We demonstrated that the ability to reach a reproducible bladder volume above a threshold volume of 180 cc and maintain that volume via biofeedback throughout treatment predicts for a decrease in acute GU toxicity during curative high-dose IMRT of the prostate. Patients who were not able to reach a partial bladder filling to that cut-off value and were not able to maintain a partially filled bladder throughout treatment had a significantly higher risk of developing ≥grade 2 GU acute toxicity. CONCLUSION: Our results support the hypothesis that a biofeedback training for the patient is an easy-to-apply, useful, and cost-effective tool for reducing acute GU toxicity in high-dose IMRT of the prostate. Patients who are not able to reach and maintain a certain bladder volume during planning and treatment-two independent risk factors-might need special consideration.


Subject(s)
Prostatic Neoplasms/radiotherapy , Radiotherapy, Intensity-Modulated/adverse effects , Urinary Bladder/radiation effects , Urogenital System/radiation effects , Aged , Aged, 80 and over , Biofeedback, Psychology , Humans , Male , Middle Aged , Neoplasm Grading , Neoplasm Staging , Organ Size/radiation effects , Prospective Studies , Prostatic Neoplasms/diagnostic imaging , Prostatic Neoplasms/pathology , Radiation Injuries/diagnostic imaging , Radiation Injuries/prevention & control , Radiotherapy Dosage , Radiotherapy Planning, Computer-Assisted , Tomography, X-Ray Computed , Urinary Bladder/diagnostic imaging , Urinary Bladder/pathology , Urogenital System/diagnostic imaging , Urogenital System/pathology
4.
Nature ; 560(7716): 41-48, 2018 08.
Article in English | MEDLINE | ID: mdl-30068955

ABSTRACT

Our knowledge of the fundamental particles of nature and their interactions is summarized by the standard model of particle physics. Advancing our understanding in this field has required experiments that operate at ever higher energies and intensities, which produce extremely large and information-rich data samples. The use of machine-learning techniques is revolutionizing how we interpret these data samples, greatly increasing the discovery potential of present and future experiments. Here we summarize the challenges and opportunities that come with the use of machine learning at the frontiers of particle physics.

5.
Chem Sci ; 7(4): 2728-2735, 2016 Apr 21.
Article in English | MEDLINE | ID: mdl-28660048

ABSTRACT

Proton relays are known to increase reaction rates for H2 evolution and lower overpotentials in electrocatalytic reactions. In this report we describe two electrocatalysts, [Fe4N(CO)11(PPh3)]- (1-) which has no proton relay, and hydroxyl-containing [Fe4N(CO)11(Ph2P(CH2)2OH)]- (2-). Solid state structures indicate that these phosphine-substituted clusters are direct analogs of [Fe4N(CO)12]- where one CO ligand has been replaced by a phosphine. We show that the proton relay changes the selectivity of reactions: CO2 is reduced selectively to formate by 1- in the absence of a relay, and protons are reduced to H2 under a CO2 atmosphere by 2-. These results implicate a hydride intermediate in the mechanism of the reactions and demonstrate the importance of controlling proton delivery to control product selectivity. Thermochemical measurements performed using infrared spectroelectrochemistry provided pKa and hydricity values for [HFe4N(CO)11(PPh3)]-, which are 23.7, and 45.5 kcal mol-1, respectively. The pKa of the hydroxyl group in 2- was determined to fall between 29 and 41, and this suggests that the proximity of the proton relay to the active catalytic site plays a significant role in the product selectivity observed, since the acidity alone does not account for the observed results. More generally, this work emphasizes the importance of substrate delivery kinetics in determining the selectivity of CO2 reduction reactions that proceed through metal-hydride intermediates.

6.
Toxicol Rep ; 2: 617-623, 2015.
Article in English | MEDLINE | ID: mdl-28962397

ABSTRACT

Nannochloropsis oculata is a marine-water microalgae that is considered to be a good source of omega-3 fatty acids, specifically eicosapentaenoic acid (EPA), utilized in the production of an omega-3 oil for use as a dietary supplement. This study investigates the safety of N. oculata in male and female Sprague-Dawley rats administered a 0 or 10 mL/kg bw/rat N. oculata (10E8 viable cells/mL) suspension by oral gavage once daily for 14 consecutive days. No mortalities occurred and no signs of toxicity were observed during the study. No treatment-related effects were seen for body weight, food consumption, urinalysis, clinical chemistry, hematology, gross pathology, organ weights, or histopathology. Although statistically significant effects were noted for some endpoints, none were considered to be of toxicological significance. The N. oculata suspension was concluded to have no toxicity in rats, confirming that the algal strain used in the production of omega-3 oil is not pathogenic when administered orally to rats.

7.
Food Funct ; 6(1): 186-92, 2015 Jan.
Article in English | MEDLINE | ID: mdl-25360534

ABSTRACT

Long-chain omega-3 polyunsaturated fatty acids (LC n-3 PUFA) exert health benefits which are dependent upon their incorporation into blood, cells and tissues. Plasma and tissue deposition of LC n-3 PUFA from oils extracted from the micro-algae Nannochloropsis oculata and from krill were compared in rats. The algal oil provides eicosapentaenoic acid (EPA) partly conjugated (15%) to phospholipids and glycolipids but no docosahexaenoic acid (DHA), whereas krill oil provides both EPA and DHA conjugated in part (40%) to phospholipids. Rats fed a standard diet received either krill oil or polar-lipid rich algal oil by gavage daily for 7 days (5 ml oil per kg body weight each day). Fatty acid concentrations were analyzed in plasma, brain and liver, and two adipose depots since these represent transport, functional and storage pools of fatty acids, respectively. When measuring total LC n-3 PUFA (sum of EPA, docosapentaenoic acid (DPA) and DHA), there was no statistically significant difference between the algal oil and krill oil for plasma, brain, liver and gonadal adipose tissue. Concentrations of LC n-3 PUFA were higher in the retroperitoneal adipose tissue from the algal oil group. Tissue uptake of LC n-3 PUFA from an algal oil containing 15% polar lipids (glycolipids and phospholipids) was found to be equivalent to krill oil containing 40% phospholipids. This may be due to glycolipids forming smaller micelles during ingestive hydrolysis than phospholipids. Ingestion of fatty acids with glycolipids may improve bioavailability, but this needs to be further explored.


Subject(s)
Dietary Supplements , Euphausiacea/chemistry , Fatty Acids, Omega-3/metabolism , Microalgae/chemistry , Oils/metabolism , Stramenopiles/chemistry , Adipose Tissue, White/metabolism , Animals , Brain/metabolism , Docosahexaenoic Acids/administration & dosage , Docosahexaenoic Acids/blood , Docosahexaenoic Acids/metabolism , Eicosapentaenoic Acid/administration & dosage , Eicosapentaenoic Acid/blood , Eicosapentaenoic Acid/metabolism , Fatty Acids, Omega-3/administration & dosage , Fatty Acids, Omega-3/blood , Female , Glycolipids/administration & dosage , Glycolipids/metabolism , Liver/metabolism , Male , Organ Specificity , Phospholipids/administration & dosage , Phospholipids/metabolism , Rats, Sprague-Dawley
8.
Int J Toxicol ; 33(6): 459-74, 2014.
Article in English | MEDLINE | ID: mdl-25305242

ABSTRACT

Almega PL is an eicosapentaenoic acid-rich ω-3 oil that is isolated from Nannochloropsis oculata algae and developed as a dietary supplement. The safety of the algal oil was evaluated in 14- and 90-day studies in Sprague-Dawley rats by oral gavage at dose levels of 0, 250, 500, and 2500 mg/kg/d and 0, 200, 400, and 2000 mg/kg/d, respectively. No mortalities occurred and no signs of toxicity were observed during the studies. No treatment-related effects were seen for body weight, food consumption, ophthalmology, neurological effects, urinalysis, clinical pathology, gross pathology, organ weights, or histopathology. Although statistically significant effects were noted for some end points, none were considered to be of toxicological significance. The no observed adverse effect level for Almega PL was 2000 mg/kg/d. Additionally, Almega PL was not mutagenic in Salmonella typhimurium or Escherichia coli, did not induce chromosome aberrations in Chinese hamster ovary cells, and did not induce genotoxic effects in vivo in rat bone marrow erythrocytes.


Subject(s)
Eicosapentaenoic Acid/toxicity , Microalgae , Oils/toxicity , Stramenopiles , Animals , CHO Cells , Chromosome Aberrations , Cricetulus , Erythrocytes/drug effects , Escherichia coli/drug effects , Escherichia coli/genetics , Female , Male , Maximum Tolerated Dose , Mutagenicity Tests , No-Observed-Adverse-Effect Level , Rats, Sprague-Dawley , Salmonella typhimurium/drug effects , Salmonella typhimurium/genetics , Toxicity Tests, Subacute , Toxicity Tests, Subchronic
9.
Phys Chem Chem Phys ; 16(20): 9294-301, 2014 May 28.
Article in English | MEDLINE | ID: mdl-24714721

ABSTRACT

Molecular dynamics simulations employing reactive potentials were used to determine the activation barriers to the dissolution of the amorphous SiO2 surface in the presence of a 2 nm overlayer of water. The potential of mean force calculations of the reactions of water molecules with 15 different starting Q4 sites (Qi is the Si site with i bridging oxygen neighbors) to eventually form the dissolved Q0 site were used to obtain the barriers. Activation barriers for each step in the dissolution process, from the Q4 to Q3 to Q2 to Q1 to Q0 were obtained. Relaxation runs between each reaction step enabled redistribution of the water above the surface in response to the new Qi site configuration. The rate-limiting step observed in the simulations was in both the Q32 reaction (a Q3 site changing to a Q2 site) and the Q21 reaction, each with an average barrier of ∼14.1 kcal mol(-1). However, the barrier for the overall reaction from the Q4 site to a Q0 site, averaged over the maximum barrier for each of the 15 samples, was 15.1 kcal mol(-1). This result is within the lower end of the experimental data, which varies from 14-24 kcal mol(-1), while ab initio calculations using small cluster models obtain values that vary from 18-39 kcal mol(-1). Constraints between the oxygen bridges from the Si site and the connecting silica structure, the presence of pre-reaction strained siloxane bonds, and the location of the reacting Si site within slight concave surface contours all affected the overall activation barriers.

10.
Lipids Health Dis ; 12: 102, 2013 Jul 15.
Article in English | MEDLINE | ID: mdl-23855409

ABSTRACT

BACKGROUND: The long-chain n-3 fatty acids eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) have human health benefits. Alternatives to fish as sources of EPA and DHA are needed. Oil from the micro-algae Nannochloropsis oculata contains a significant amount of EPA conjugated to phospholipids and glycolipids and no DHA. Krill oil contains EPA and DHA conjugated to phospholipids. We compare the appearance of fatty acids in blood plasma of healthy humans after consuming a high fat meal followed by either algal oil or krill oil. METHODS: Ten healthy males aged 18-45 years consumed a standard high fat (55 g) breakfast followed by either algal oil (providing 1.5 g EPA and no DHA) or krill oil (providing 1.02 g EPA and 0.54 g DHA). All participants consumed both oils in random order and separated by 7 days. Blood samples were collected before the breakfast and at several time points up to 10 hours after taking the oils. Fatty acid concentrations (µg/ml) in plasma were determined by gas chromatography. RESULTS: Fatty acids derived mainly from the breakfast appeared rapidly in plasma, peaking about 3 hours after consuming the breakfast, and in a pattern that reflected their content in the breakfast. There were time-dependent increases in the concentrations of both EPA and DHA with both algal oil (P < 0.001 for EPA; P = 0.027 for DHA) and krill oil (P < 0.001 for both EPA and DHA). The concentration of EPA was higher with algal oil than with krill oil at several time points. DHA concentration did not differ between oils at any time point. The maximum concentration of EPA was higher with algal oil (P = 0.010) and both the area under the concentration curve (AUC) and the incremental AUC for EPA were greater with algal oil (P = 0.020 and 0.006). There was no difference between oils in the AUC or the incremental AUC for DHA. CONCLUSION: This study in healthy young men given a single dose of oil indicates that the polar-lipid rich oil from the algae Nannochloropis oculata is a good source of EPA in humans.


Subject(s)
Docosahexaenoic Acids/administration & dosage , Eicosapentaenoic Acid/administration & dosage , Lipids , Adolescent , Adult , Animals , Diet, High-Fat , Docosahexaenoic Acids/blood , Docosahexaenoic Acids/metabolism , Eicosapentaenoic Acid/blood , Eicosapentaenoic Acid/metabolism , Euphausiacea/chemistry , Fatty Acids, Omega-3/administration & dosage , Fatty Acids, Omega-3/blood , Humans , Lipids/administration & dosage , Lipids/blood , Male , Microalgae/chemistry , Middle Aged , Young Adult
12.
Strahlenther Onkol ; 186(10): 572-9, 2010 Oct.
Article in English | MEDLINE | ID: mdl-20936458

ABSTRACT

PURPOSE: To evaluate the acute toxicity of simultaneous integrated boost (SIB) technique for dose escalation with helical tomotherapy (HT) in patients with locally advanced cervical cancer. PATIENTS AND METHODS: 20 patients (FIGO IB1 pN1-IIIB) underwent primary chemoradiation. Prior to chemoradiation, a laparoscopic pelvic and para-aortic lymphadenectomy was performed. A boost region was defined using titanium clips during staging for planning target volume (PTV-B). Patients were treated with five weekly fractions of 1.8 Gy to a total dose of 50.4 Gy to the tumor region and the pelvic (para-aortic) lymph node region (PTV-A), and five weekly fractions of 2.12 Gy to a total dose of 59.36 Gy to the PTV-B. Chemotherapy consisted of weekly cisplatin 40 mg/m(2). 19 patients underwent brachytherapy. Dose-volume histograms were evaluated and acute gastrointestinal (GI), genitourinary (GU), and hematologic toxicity were documented (CTCAE v3.0). RESULTS: Pelvic and para-aortic lymph node metastases were confirmed in nine and four patients, respectively. Five patients refused laparoscopic staging. The mean volume of PTV-A and PTV-B was 1,570 ± 404 cm(3) and 341 ± 125 cm(3), respectively. The mean dose to the bladder, rectum, and small bowel was 47.85 Gy, 45.76 Gy, and 29.71 Gy, respectively. No grade 4/5 toxicity was observed. Grade 2/3 hematologic toxicity occurred in 50% of patients and 5% experienced grade 3 diarrhea. There was no grade 3 GU toxicity. 19 patients underwent curettage 6-9 weeks after chemoradiation without any evidence of tumor. CONCLUSION: The concept of SIB for dose escalation in patients with locally advanced cervical cancer is feasible with a low rate of acute toxicity. Whether dose escalation can translate into improved outcome will be assessed after a longer follow-up.


Subject(s)
Uterine Cervical Neoplasms/radiotherapy , Adult , Aged , Dose Fractionation, Radiation , Female , Humans , Intestine, Small/diagnostic imaging , Laparoscopy , Middle Aged , Neoplasm Metastasis/pathology , Neoplasm Staging , Radiation Injuries/etiology , Radiation Injuries/pathology , Radiotherapy/adverse effects , Radiotherapy Dosage , Radiotherapy Planning, Computer-Assisted/methods , Rectum/diagnostic imaging , Tomography, X-Ray Computed/methods , Urinary Bladder/diagnostic imaging , Uterine Cervical Neoplasms/diagnostic imaging , Uterine Cervical Neoplasms/pathology , Uterine Cervical Neoplasms/surgery
13.
Radiat Oncol ; 5: 63, 2010 Jul 02.
Article in English | MEDLINE | ID: mdl-20598136

ABSTRACT

BACKGROUND: Chemoradiation for cervical cancer patients is associated with considerable gastrointestinal toxicity. Intensity-modulated radiotherapy (IMRT) has demonstrated superiority in terms of target coverage and normal tissue sparing in comparison to conventional 3D planning in gynaecological malignancies. Whether IMRT in prone (PP) or supine position (SP) might be beneficial for cervical cancer patients remains partially unanswered. METHODS: 10 patients on FIGO stage IB-III cervical cancer, 6 patients for definitive and 4 patients for adjuvant external beam pelvic RT, were planned in PP and SP using a 7-field IMRT technique. IMRT plans for PP and SP (mean dose, Dmean 50.4 Gy) were optimized in terms of PTV coverage (1st priority) and small bowel sparing (2nd priority). A comparison of DVH parameters for PTV, small bowel, bladder, and rectum was performed. RESULTS: The comparison showed a similar PTV coverage of 95% of the prescribed dose and for target conformity in IMRT plans (PP, SP). PTV, rectum and bladder volumes were comparable for PP and SP. Significantly larger volumes of small bowel were found in PP (436 cc, + 35%, p = 0.01). PP decreased the volume of small bowel at 20-50.4 Gy (p < 0.05) and increased the rectum volumes covered by doses from 10-40 Gy (p < 0.01), the V50.4 was < 5% in both treatment positions. Bladder sparing was significant better at 50.4 Gy (p = 0.03) for PP. CONCLUSION: In this dosimetric study, we demonstrated that pelvic IMRT in prone position for patients with cervical cancer seems to be beneficial in reducing small bowel volume at doses >or=20 Gy while providing similar target coverage and target conformity. The use of frequent image guidance with KV (kilovolt) or MV (megavolt) computer tomography can reduce set-up deviations, and treatment in prone position can be done with a higher set-up accuracy. Clinical outcome studies are needed to affirm lower toxicity.


Subject(s)
Radiotherapy, Intensity-Modulated/methods , Uterine Cervical Neoplasms/radiotherapy , Female , Humans , Neoplasm Staging , Prone Position , Radiometry , Radiotherapy Dosage , Supine Position , Uterine Cervical Neoplasms/pathology
14.
J Comb Chem ; 11(4): 704-19, 2009.
Article in English | MEDLINE | ID: mdl-19459687

ABSTRACT

A 23-member library of pyrrolobenzodiazepine derivatives with vasopressin agonist activity was purified on a 100-mg per injection scale using normal-phase (NP) automated mass-directed HPLC. Analytical NP APCI-LC/MS on an experimental monolith silica CN column utilizing gradients of methanol in ethoxynonafluorobutane (hexane-like solvent) was used to provide data on chromatographic purity and ionization of the solutes. The analytical data collected were used to program a preparative LC/MS instrument for "smart" fraction collection based on the protonated molecular ion of the component of interest. Preparative HPLC was carried out on a preparative cyano column with gradients of polar organic solvents in heptane containing n-propylamine as a basic additive. Flow rates twice as high as conventional ones were used for purification of library compounds. Small aliquots of the preparative flow were mixed with makeup solvent and introduced into an APCI source of a quadrupole mass spectrometer, which triggered collection of solutes. Two methods with fixed instrument parameters were used for purification. The system utilized commercially available instrumentation and software, which provided excellent recovery and purity of the library components and appeared to be useful as a fast and efficient alternative to traditional purification technologies based on reversed-phase LC/MS.


Subject(s)
Benzodiazepines/isolation & purification , Pyrroles/isolation & purification , Small Molecule Libraries/isolation & purification , Vasopressins/agonists , Benzodiazepines/chemistry , Chromatography, High Pressure Liquid/methods , Pyrroles/chemistry , Small Molecule Libraries/chemistry
15.
J Med Chem ; 51(21): 6980-7004, 2008 Nov 13.
Article in English | MEDLINE | ID: mdl-18834188

ABSTRACT

Novel compounds combining a 5-HT 1A moiety (3-aminochroman scaffold) and a 5-HT transporter (indole analogues) linked through a common basic nitrogen via an alkyl chain attached at the 1- or 3-position of the indole were evaluated for dual affinity at both the 5-HT reuptake site and the 5-HT 1A receptor. Compounds of most interest were found to have a 5-carbamoyl-8-fluoro-3-amino-3,4-dihydro-2 H-1-benzopyran linked to a 3-alkylindole (straight chain), more specifically substituted with a 5-fluoro (( R)-(-)- 35c), 5-cyano ((-)- 52a), or 5,7-difluoro ((-)- 52g). Several factors contributed to 5-HT 1A affinity, serotonin rat transporter affinity, and functional antagonism in vitro. Although most of our analogues showed good to excellent affinities at both targets, specific features such as cyclobutyl substitution on the basic nitrogen and stereochemistry at the 3-position of the chroman moiety seemed necessary for antagonism at the 5-HT 1A receptor. Branched linkers seemed to impart antagonism even as racemates; however, the potency of these analogues in the functional assay was not desirable enough to further pursue these compounds.


Subject(s)
Antidepressive Agents/chemical synthesis , Antidepressive Agents/pharmacology , Benzopyrans/chemical synthesis , Benzopyrans/pharmacology , Selective Serotonin Reuptake Inhibitors/chemical synthesis , Serotonin 5-HT1 Receptor Antagonists , Serotonin Plasma Membrane Transport Proteins/metabolism , Animals , Antidepressive Agents/chemistry , Benzopyrans/chemistry , Cell Line , Cricetinae , Cross-Linking Reagents/chemistry , Humans , Molecular Structure , Rats , Receptor, Serotonin, 5-HT1A/metabolism , Selective Serotonin Reuptake Inhibitors/chemistry , Selective Serotonin Reuptake Inhibitors/pharmacology , Structure-Activity Relationship
16.
Chirality ; 19(9): 658-82, 2007 Sep.
Article in English | MEDLINE | ID: mdl-17390370

ABSTRACT

The application of Chiral Technology, or the (extensive) use of techniques or tools for the determination of absolute stereochemistry and the enantiomeric or chiral separation of racemic small molecule potential lead compounds, has been critical to successfully discovering and developing chiral drugs in the pharmaceutical industry. This has been due to the rapid increase over the past 10-15 years in potential drug candidates containing one or more asymmetric centers. Based on the experiences of one pharmaceutical company, a summary of the establishment of a Chiral Technology toolbox, including the implementation of known tools as well as the design, development, and implementation of new Chiral Technology tools, is provided.


Subject(s)
Chemistry, Pharmaceutical/methods , Drug Industry/methods , Stereoisomerism , Chromatography/methods , Circular Dichroism , Drug Design , Electrons , Humans , Magnetic Resonance Spectroscopy/methods , Models, Chemical , Molecular Conformation , Salts/pharmacology , Technology, Pharmaceutical/methods
17.
Chaos ; 1(4): 455-461, 1991 Dec.
Article in English | MEDLINE | ID: mdl-12779941

ABSTRACT

It is shown that a phenomenon analogous to the geometric phase shifts of Berry and Hannay occurs for dissipative oscillatory systems and can be detected in numerical simulations of chemical oscillators. The approach herein to the theory of geometric phases begins with a study of simple first-order differential equations on the circle (circle dynamics). It is shown how more complicated systems exhibit geometric phases through reduction to a circle dynamics. In this way, the various manifestations of the phenomenon are seen from a single unified perspective. The results are illustrated in numerical experiments on several model systems ranging from analytically solvable, but contrived, to realistic models of chemical oscillators.

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