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Hypokalaemic diuretics, stimulant laxatives, intravenous amphotericin B, glucocorticoids, tetracosactides; neuroleptics such as pimozide, haloperidol, lithium and imipramine and other antidepressants. The undesirable effects section now states that cases of QT interval prolongation and very rare cases of torsades de pointes have been reported. See SPC. Betaferon injection The summary of product characteristics for Betaferon interferon beta1b ; have been amended Schering Health Care ; . The special precautions for storage section now states: "The user may store unreconstituted Betaferon outside the refrigerator for up to three months, but not above 25C and not exceeding the expiry date." See SPC.
This section summarizes the most important facts about the Extended Calculus of Constructions, ECC , which is the formal basis for the following investigations. ECC [Luo90, Luo94] is an extension of the Calculus of Constructions, CC [CH88], with dependent -types which are useful for representing specifications and mathematical theories see Section 1.1.4 for a motivation ; . The results derived in the following sections for ECC could also be obtained for the subsystem CC . Conversely, passing from CC to ECC does not lead to a significant increase in complexity. We will restrict attention to CC alone whenever more appropriate for the purpose of comparison with other logical theories, as for example in Chapter 3. For readability, we have chosen in this text a term representation which establishes identity of variables via names. There are well-known shortcomings of this representation, such as free variable capture for example, the term x . y.x ; y should not -reduce to y.y ; . In order to avoid naming problems, we will always rename variables appropriately. A conceptually cleaner nameless representation of the calculus with de Bruijn-indices is given in Appendix A.1. The material in this Section 2.1 is not new, apart from some minor definitions and propositions needed for later reference. It has mostly been taken from [Luo90], as well as from other sources cited throughout the text, which should also be consulted for proofs of propositions, for example, lexipro.
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Spectroscopy is the name of the science that studies the way in which light interacts with matter.When light energy strikes an object, it can be transmitted, absorbed or reflected. By shining light on an object and measuring the amount reflected and transmitted, we can tell how much was absorbed, which is the amount that interacted with the object.The light that interacts with the object can tell us things about the object, such as what it is made of, if it is uniform, how much of the different components are present and other information about the substance being analyzed.This method has an advantage over other techniques because it is inexpensive, involves no toxic chemicals and a very small sample can be analyzed. Ordinary white light is a mixture of a variety of different light wavelengths. If you shine white light on a solution, certain wavelengths are more readily absorbed and other wavelengths are transmitted through the solution.A spectrophotometer is a useful scientific tool that can isolate a particular wavelength of light and send it through a sample.This instrument can be used to measure and record absorbance and transmittance.Transmittance is the fraction of the original light that passes through the sample; if 90% of the light is absorbed, then 10% is transmitted. So, if all the light passes through a sample without any absorption, then absorbance is zero, and percent transmittance is 100%. If all the light is absorbed, then percent transmittance is zero, and absorption is infinite. Using a spectrophotometer, we can find out about materials in circumstances where we would not otherwise be able to obtain information. Examples include cases where we don't want to destroy or change the object valuable paintings or jewels ; , the material is not accessible medicine inside a sealed vial ; , too far away distant stars ; , too dangerous inside blast furnaces ; or there is a minute amount of material DNA grown by researchers ; . In order to demonstrate what is going on inside a spectrophotometer and explain what it is really measuring, students are challenged to figure out how to relate the concentration of aspirin in a number of solutions to the amount of light absorbed by a sample in the spectrophotometer. First, standard aspirin solutions are produced by serial dilution.Then the light absorbance of the standard solutions is measured and the data plotted on a graph. Once these steps are complete, the light absorbance of the unknowns can be measured and can be compared to the data derived from the standard solutions. Always wear protective eyewear. Dispose of chemicals properly and legally, because antibiotics.
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The following should not be co-administered with erythromycin: amisulpride, simvastatin, ergotamine, dihydroergotamine, tolterodine, cisapride, pimozide, terfenadine and mizolastine. Erythromycin may increase serum concentrations of CYP metabolised drugs including: atorvastatin, bromocryptine, carbamazepine, cilostazole, ciclosporin, clozapine, midazolam, phenytoin, quinidine, tacrolimus, rifabutin, theophylline * , valproate, alfentanil, zopiclone, warfarin and digoxin. Increased erythromycin levels may occur with other CYP3A inhibitors, such as `azole' antifungals, some calcium channel blockers diltiazem, verapamil ; , anti-HIV protease inhibitors e.g. amprenavir, ritonavir, saquinavir and orinase.
The action potentials became broader in the presence of cbm and ucl 2027 at concentrations of 3 m and 10 m table 2 ; figure 4b ; , though the effects were statistically significant only at 3 m.
Appendix 7ARV Drugs in Use in Burkina Faso . 53 and tolbutamide, for example, xanax.
See Chapter 6: Shock and Chapter 13: Medical Emergencies. The Throat Emergencies algorithm in Appendix A provides an overview of triage and management for problems involving the throat.
Omeprazole, Cont. ; 4 Theophyllines, 1208 4 Tolazamide, 1119 4 Tolbutamide, 1119 3 Triazolam, 199 5 Vitamin B12, 1308 4 Warfarin, 118 Omniflox, see Temafloxacin Omnipen, see Ampicillin Omnipen-N, see Ampicillin Oncovin, see Vincristine Ondansetron, 2 Rifabutin, 919 2 Rifampin, 919 2 Rifamycins, 919 2 Rifapentine, 919 Opium, 2 Barbiturate Anesthetics, 165 4 Cimetidine, 870 4 Histamine H2 Antagonists, 870 2 Methohexital, 165 2 Thiamylal, 165 2 Thiopental, 165 Orap, see Pimzide Orasone, see Prednisone Orazinc, see Zinc Sulfate Oretic, see Hydrochlorothiazide Oreton Methyl, see Methyltestosterone Organidin, see Iodinated Glycerol Original Doan's, see Magnesium Salicylate Orinase, see Tolbutamide ORLAAM, see Levomethadyl Orphenadrine, 5 Acetaminophen, 1 2 Acetophenazine, 941 4 Amantadine, 60 4 Atenolol, 216 5 Bendroflumethiazide, 1225 5 Benzthiazide, 1225 4 Beta Blockers, 216 5 Chlorothiazide, 1225 2 Chlorpromazine, 941 5 Chlorthalidone, 1225 5 Cimetidine, 303 4 Digoxin, 468 2 Ethopropazine, 941 2 Fluphenazine, 941 2 Haloperidol, 609 5 Hydrochlorothiazide, 1225 5 Hydroflumethiazide, 1225 5 Indapamide, 1225 5 Levodopa, 736 2 Mesoridazine, 941 2 Methdilazine, 941 2 Methotrimeprazine, 941 5 Methyclothiazide, 1225 5 Metolazone, 1225 5 Nitrofurantoin, 888 2 Perphenazine, 941 2 Phenothiazines, 941 5 Polythiazide, 1225 2 Prochlorperazine, 941 2 Promazine, 941 2 Promethazine, 941 2 Propiomazine, 941 5 Quinethazone, 1225 5 Thiazide Diuretics, 1225 2 Thiethylperazine, 941 2 Thioridazine, 941 5 Trichlormethiazide, 1225 2 Trifluoperazine, 941 2 Triflupromazine, 941 2 Trimeprazine, 941 and olanzapine.
CLASS: non-nucleoside analog also called non-nucleoside reverse transcriptase inhibitor, NNRTI or non-nuke ; STANDARD DOSE: Two 200 mg tablets or four 100 mg tablets three times a day every 8 hours ; . Only the 100 mg tablets can be dissolved in liquid, however avoid grapefruit juice; no food restrictions may be taken with or without food ; . Take missed dose as soon as possible, but do not double up on your next dose. AWP: $316.35 month for 200 mg MANUFACTURER CONTACT: Pharmacia and Upjohn Company, a Pfizer company, pfi zer , 1 212 ; 5731000 AIDSINFO: 1 800 ; HIV0440 4480440 ; , aidsinfo.nih.gov POTENTIAL SIDE EFFECTS AND TOXICITY: Most common side effects include headache, nausea, vomiting, diarrhea, fatigue, elevated liver enzymes, itchy skin or rash. A serious side effect of the NNRTI class is rash, which can be life-threatening. Most rashes occur within the first 13 weeks after starting Rescriptor. If you experience blistering, mouth lesions, conjunctivitis redness or inflammation of eye, which if untreated may result in permanent vision loss ; , swelling, muscle or joint aches, fever or general malaise general ill feeling ; , you may need to stop the medications so seek medical attention immediately. Body fat accumulation or redistribution may occur. POTENTIAL DRUG INTERACTIONS: You cannot take Rescriptor with Versed midazolam ; , Halcion triazolam ; and Xanax alprazolam ; , pimozide a psychiatric medication ; , ergot alkaloids, used for migraine headaches Wigraine, Methergine, and Cafergot ; in any form, or the herb St. John's wort hypericum perforatum ; . Do not use Zocor simvastatin ; or Mevacor lovastatin ; cholesterol lipid ; lowering meds; suggested alternatives are Lipitor atorvastatin ; , Lescol fluvastatin ; , Crestor rosuvastatin ; , and Pravachol pravastatin, the one with less incidence of problems and interactions according to study data ; . Liver enzymes should be checked regularly if you are on these cholesterol meds, as they can increase risk for liver toxicity with Rescriptor. Certain amphetamines and antiarrhythmic drugs should not be used with Rescriptor, therefore inform your healthcare provider if you have a history of heart or blood pressure problems. Potential toxicity when given with Biaxin clarithromycin ; , dapsone, Mycobutin rifabutin ; , Procardia or Adalat nifedipine ; , Norvasc amlodipine ; , Plendil felodipine ; , Coumadin warfarin ; , Propulsid cisapride ; , and quinidine. Tegretol carbamazepine, an anti-seizure medication used to treat peripheral neuropathy ; , phenobarbital, Dilantin phenytoin ; , Mycobutin rifabutin ; and rifampin used to treat tuberculosis ; are drugs that decrease Rescriptor levels. Rescriptor increases levels of Crixivan, Lexiva, Invirase, Kaletra, Norvir, Reyataz, Viracept, immunosuppressants, birth control pills ethinyl estradiol ; , and methadone, so caution is advised if using together. Cialis, Levitra, and Viagra levels are increased by Rescriptor; doses should not exceed 10 mg Cialis per 72 hours, 2.5 mg Levitra per 24 hours, or 25 mg Viagra per 48 hours. Rescriptor is not recommended with either rifampin or rifabutin, used for tuberculosis or MAC infections. Also, increased levels of Desyrel trazodone ; can occur with Rescriptor, which may lead to nausea, dizziness, low blood pressure, or loss of consciousness. A lower dose of Desyrel is recommended. Increased levels of the inhaled and nasal sprays that contain fluticasone, a steroid for asthma or alleries found in Advair, Flonase, and Flovent ; can occur with Rescriptor and therefore should be used with caution. TIPS: Research demonstrates smaller doses of Rescriptor increase blood levels of some protease inhibitors, making it unique among the NNRTIs. Antacids like Tagamet, Zantac, Prilosec, and Tums ; and gastric achlorhydria low stomach acid ; decreases absorption of Rescriptor, so take at least one hour apart from these drugs and take with acidic beverages such as orange or cranberry juice.
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DRUGS TO AVOID WHILE ON KETEK partial listing ; : Cholesterol drugs- Lipitor, Mevacor, Zocor and Crestor NOTE: Pravastatin Pravochol ; and fluvastatin Lescol ; are OK, as are ezetimibe Zetia ; , colesevelam Welchol ; and cholestyramine Questran ; . Anti-arrhythmic heart drugs- Class 1A quinidine, procainamide, etc. ; , Class III dofetilide, etc. ; Cisapride Propulcid ; , pimozide Orap ; Antifungals- itraconazole Sporanox ; , ketoconazole Nizoral ; , voriconazole Vfend ; . Ergot alkaloids for Migraine DRUGS WHICH MAY REQUIRE DOSAGE ADJUSTMENTS partial listing ; : Levels of these drugs go up: Sedatives and anesthetics-Midazolam Versed ; , triazolam Halcion ; Heart drugs-sotalol Betapace ; , metoprolol Lopressor, Toprol ; , digoxin Lanoxin ; HIV drugs- rionavir Norvir ; , sirolimus Rapamune anti-rejection drug tacrolimus Prograf ; , cyclosporine phenytoin Dilantin ; , phenobarbital These drugs lower Ketek levels: rifampin, phenytoin Dilantin ; , tegretol, phenobarbital QTc INTERVAL o o o Measure the precordial lead that has the best T wave usually V-2 or V-5 ; Measure from the start of the Q wave to the end of the T wave QT interval is inversely related to the heart rate slow pulse results in a longer QT ; QTc is the QT corrected for heart rate QTc QT RR interval Normals: Females 450 ms, Males 470 ms Want K + 4.0, Mg + 2.0; avoid hypocalcemia Check EKG at baseline, then, if there is still concern, repeat the EKG at least 5 half-lives after medication is begun.
DRUG INTERACTIONS Serious Drug Interactions Concomitant administration of SPORANOX oral solution with quinidine, cisapride and pimozide may result in serious cardiovascular events. Concomitant administration of SPORANOX oral solution with ergot alkaloids, such as dihydroergotamine, ergometrine and ergotamine may result in serious and or lifethreatening ischemia. Concomitant administration of SPORANOX oral solution with HMG-CoA reductase inhibitors, such as lovastatin and simvastatin, may increase the risk of skeletal muscle toxicity including rhabdomyolysis. Concomitant administration of SPORANOX oral solution with benzodiazepines, such as midazolam and triazolam, could potentiate and prolong hypnotic and sedative effects. Concomitant administration of SPORANOX with fentanyl could increase or prolong fentanyl plasma concentrations and may cause potentially fatal respiratory depression. Concomitant administration of eletriptan with SPORANOX can elevate plasma eletriptan concentrations which could result in serious adverse events. See CONTRAINDICATIONS, WARNINGS AND PRECAUTIONS, and Drug-Drug Interactions. ; Overview Itraconazole and its major metabolite, hydroxy-itraconazole, are inhibitors of CYP3A4. Therefore, the following drug interactions may occur see Table 1.2 below and the drug class subheadings that follow ; : 1. SPORANOX may decrease the elimination of drugs metabolized by CYP3A4, resulting in increased plasma concentrations of these drugs when they are administered with SPORANOX. These elevated plasma concentrations may increase or prolong both therapeutic and adverse effects of these drugs. Whenever possible, plasma concentrations of these drugs should be monitored, and dosage adjustments made after concomitant SPORANOX therapy is initiated. When appropriate, clinical monitoring for signs or symptoms of increased or prolonged pharmacologic effects is advised. Upon discontinuation, depending on the dose and duration of treatment, itraconazole plasma concentrations decline gradually especially in patients with hepatic cirrhosis or in those receiving CYP3A4 inhibitors ; . This is particularly important when initiating therapy with drugs whose metabolism is affected by itraconazole. Inducers of CYP3A4 may decrease the plasma concentrations of itraconazole. SPORANOX may not be effective in patients concomitantly taking SPORANOX and one and ondansetron.
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Dosages of all agents. Nelfinavir was administered at 55 mg kg every 12 hours and ritonavir at 400 mg m2 every 12 hours, except for the child younger than 2 years, who was given 450 mg m2 . Saquinavir was initially administered at 350 mg m2 every 12 hours when given in conjunction with ritonavir until February 2000, 10 when it was increased to 50 mg kg every 12 hours. VIROLOGIC RESPONSES AFTER INITIATION OF HAART The median RNA level before HAART was 4.9 log10 range, 3.3-6.5 log10 ; Table 2 ; . After initiation of HAART, all children experienced a decrease in plasma HIV-1 RNA concentration, with the plasma RNA nadir being below 50 copies mL 1.7 log10 ; in 32 children 89% ; . The median RNA level at the last follow-up during 4- or 5-drug HAART was 1.7 log10 range, 1.7-5.8 log10 ; , with 28 children 78% ; having RNA levels suppressed to below 50 copies mL. Virologic rebound, defined as an increase in RNA levels to greater than 50 copies mL on at least 2 time points 4 weeks apart or 1 value greater than 1000 copies mL, occurred in 13 children during 4- or 5-drug therapy. Failure to achieve RNA suppression or viral rebound was associated with documented nonadherence, either chronic or episodic, in 10 of the 13 children. In 5 of the 13 children, viral suppression was again achieved after adjusting their regimens. New resistance mutations did not develop at the time of the viral rebound RNA increases to 3.1 and 3.4 log10 ; in 2 children, and viral levels decreased to below 50 copies mL and zofran.
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Thods, their effectiveness, routes of administration, side effects and cost. The teenager is also assessed as to her lifestyle , her place in the family and her ability to take charge of her life and health. Confidentiality is respected when required by the adolescent and most of the time samples of birth control pills provided by the pharmaceutical companies are given in order to increase chances of compliance. DMPA injection is provided by both institutions and given free. The nurses are available for further information and advice on the phone during the clinics' working hours and will see adolescents who present without an appointment for concerns about birth control. Both clinics also provide first trimester abortion services to adolescents who are patients of the clinics or referrals from other adolescent services, private physicians and school based nurses. Table 1: Profile o f patients given DMPA 151 . Mean age at first injection . Parity GPA ; 16.7 years.
Miscellaneous section 9 of 10 authors and editors introduction clinical differentials workup treatment medication follow-up miscellaneous references medical legal pitfalls involuntary hospitalization for depression: in the clearest case of the bipolar depressed phase, the patient is suicidal and homicidal in a few situations this can result in homicide followed by suicide and trileptal.
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| To increased serum levels and risk of seizures. Fluvoxamine can cause large increases in clozapine serum levels, and the combination of the two drugs should be avoided. Some other SSRIs and nefazodone may also cause clinically significant increases in clozapine serum levels and should be used carefully in clozapine-treated patients. Clozapine serum levels should be monitored after adding one of the antidepressants discussed earlier to the medication regimen of patients treated with clozapine. Because bupropion itself is associated with a risk of seizures, a pharmacodynamic interaction with clozapine exists. Therefore, the combination of clozapine and bupropion should be avoided. There are many sources of information about drug-drug interactions. A useful, frequently updated web site maintained by D. Flockhart at Indiana University is available at : medicine.iupui flockhart. Another useful drug interaction computer program maintained by J. Oesterheld and D. Osser is available at : mhc Cytochromes. Implementation. Use of antidepressants in schizophrenia generally has been studied by using the doses and titration schedules that are usually used when the agents are administered by themselves. There is no reason to think that dosing should be modified on the basis of coexisting schizophrenia. As noted earlier, however, the potential for drug-drug interactions suggests that close monitoring of side effects is warranted. Monitoring of the blood levels of the antipsychotic at baseline and after several weeks of antidepressant treatment may be helpful, particularly for clozapine, where there is evidence that high blood levels are associated with increased risk of seizures and low levels may be ineffective. The same considerations apply when an antidepressant is being discontinued. c ; Antipsychotics. Most reports on the combination of antipsychotics describe the effects of combinations with clozapine. The only randomized, controlled trial used sulpiride, a dopamine receptor antagonist similar to firstgeneration antipsychotics that is available in Europe but not in North America. Shiloh et al. 1131 ; added placebo or sulpiride, titrated up to a dose of 600 mg day, to clozapine for 10 weeks in the treatment of 28 partially responsive patients who were taking stable doses of clozapine and who had BPRS scores 42. The sulpiride group had significantly greater decreases in BPRS 15% ; , Scale for the Assessment of Negative Symptoms 10% ; , and Scale for the Assessment of Positive Symptoms 12% ; scores. Case series show improvements in residual positive symptoms with the addition of a number of other antipsychotics to clozapine. These agents include loxapine 233 ; , pimoxide 234 ; , and risperidone 232 ; . Although the quality of the evidence for augmentation of clozapine with another antipsychotic is modest, this strategy seems reasonable in treating patients whose response to clozapine is fair at best. Before taking this step, however, the clinician should be sure that the clozapine.
100 American Journal of Police other states. Federal policymakers then looked at Kentucky's marijuana cultivation as a national issue and not as a state or local issue. As a result of the federal recognition of Kentucky's importance as a marijuana producer, federal support for eradication was enhanced. Federal funds continued and increased, as did the addition of logistical support from the Drug Enforcement Administration DEA ; for the program. In 1983, the eradication program netted 177, 850 plants in 520 plots, which resulted in 163 arrests. By 1984 federal support for the eradication program had increased to $150, 000. In 1984, 300, 798 plants were eradicated in 623 different plots, located in 97 of Kentucky's 120 counties. In 1984 there were 243 arrests attendant to the eradication program. In 1985, federal funding had reached $170, 000. The 1985 program resulted in the destruction of 305, 907 plants, in 1, 315 plots, resulting in 168 arrests. The 1985 eradication effort also highlighted two additional enforcement strategies in the eradication effort. For the first time, the Kentucky State Police seized property a farm in rural Henry County ; in an eradication case, and initiated forfeiture procedures. Second, "Operation Delta Nine" took effect. This was a coordinated effort to conduct simultaneous eradication raids across the country. The operation was designed to produce two results: first, to create a great deal of publicity about marijuana cultivation; and, second to test a system of federal-state coordination in marijuana eradication programs. In Kentucky, Operation Delta Nine resulted in the destruction of 26, 668 plants in 68 separate plots, ranking Kentucky sixth in the nation in the one-day exercise and oxytetracycline and pimozide, because lexipro.
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The evidence in the light most favorable to the state shows that the defendant drove erratically, had blood-shot eyes, smelled of alcohol, fumbled with his wallet, staggered, and failed to pass three field sobriety tests. He admitted to drinking beer and to taking prescription medications. The presence of prescription medications was confirmed by blood analysis, and the testimony showed that the and paroxetine.
Explants from nontransgenic greenhouse plants Fig. 4C ; . The CDKB2; 1 protein was detectable 1 d after the treatment and showed a similar accumulation pattern as in the case of wounded leaves. These experiments were performed in parallel with 2, 4-D-treated leaf explants Fig. 4D ; . The GUS activity staining of the leaf explants showed that the CDKB2; 1 promoter is activated after 3 d Fig. 4D ; . Western-blot assay on 2, 4-D-treated nontransgenic leaves confirmed this result; the CDKB2; 1 kinase appeared on the third day, but its level became highly elevated from the fourth day Fig. 4D ; . For the analysis of the effects of wounding and hormone treatments on activation of cell cycle, nuclei were isolated for flow cytometry. Figure 4E shows that there was no change in the DNA content of the wounded or ethephon-treated leaf cells during the examined period similarly to the negative control not wounded leaves cultivated on hormone-free medium ; . However, in the 2, 4-D-treated leaf explants, increased frequency of S- and G2-phase cells indicated that cell.
Seven male research volunteers mean age 7 SD ; 24 years ; completed the 35-day experiment. An additional group of four male volunteers started but did not complete the study: one had a custody court date, one did not like the food options, one reported stomach discomfort during marijuana withdrawal and placebo THC maintenance ; , and one had an abnormal EKG during marijuana withdrawal and placebo THC maintenance ; . Prior to study participation, volunteers provided a detailed drug and medical history, received complete medical and psychiatric evaluations shortly before study onset, and gave written informed consent for all aspects of the study. Those who completed the study reported smoking 9.6 7 6.2 ; marijuana cigarettes per day, 6.2 7 1.3 ; days per week. Six participants also reported drinking alcohol weekly 2.3 7 1.5 days week, 2.7 7 1.5 drinks occasion ; . Six smoked tobacco cigarettes, and continued to do so during the experiment. Other drug use was infrequent. One participant reported weekly intranasal cocaine use, but was able to maintain abstinence for the duration of the study, confirmed by frequent urine toxicologies. Participants who did not diet were within accepted weight ranges for their heights 71.5 7 7.7 kg ; , and had no self-reported eating abnormalities. Participants were instructed that the study investigated how medications influence the effects of marijuana. They were told that they may receive an antidepressant, an anticonvulsant, a medication to increase appetite, or a placebo. They were also told that the strength of the medication and marijuana cigarettes might change at any time throughout the study. Prior to discharge, participants were fully informed about the experimental and drug.
We could deal with this problem by keeping track of all pure equilibria of each restricted game, and determine caseby-case whether two equilibria can be combined by checking whether agents could profitably deviate from one restricted game to the other ; . But as we combine the restricted games to form larger restricted games and eventually the unrestricted game on the entire action graph G, the number of equilibria we would have to store could grow exponentially. Perhaps we don't need to keep track of all partial solutions. Imagine we had a function ch that summarized them, i.e. it mapped each partial solution to a characteristic from a finite set C which is smaller than the set of partial solutions. For this characteristic function to be useful, it need to be equilibrium-preserving, defined as follows. Definition 8. For X S, a function ch ; that maps partial solutions to their characteristics is equilibriumpreserving if for all pairs of partial solutions s|X , s |X , if s|X ; ch s |X ; then s|X can be extended ; s |X can be extended ; . Intuitively, an equilibrium-preserving characteristic function ch ; induces a partition of the set of partial solutions into equivalence classes. All partial solutions with the same characteristic behave the same way, so we only need to consider the set of all distinct characteristics. For X S, we define AX C to the set of characteristics of partial solutions on X. Formally, AX . Given such a function ch, a dynamic-programming algorithm for determining the existence of pure equilibria of is: 1. Partition S into X such that the size of each Xi is bounded by a constant. 2. For each Xi X , compute AXi , the set of characteristics of partial solutions on Xi . While |X | 2: Take X, Y X . Remove them from X . b ; Compute AXY from AX and AY . c ; Add X Y to Now X has only one member, S. 5. Return TRUE iff AS is not empty. Since a partial solution on S is definition a pure equilibrium of , there exists a pure equilibrium of if and only if AS is not empty. For this algorithm to run in polynomial time, the function ch ; must satisfy the following properties: Property 1: At all times during the algorithm, for all X X , the size of AX is polynomial. This is necessary since all restricted strategy profiles could potentially be partial solutions, and so AX could potentially be the set of all possible characteristics for X. Property 2: For each Xi of bounded size, AXi can be computed in polynomial time. Property 3: AXY can be computed from AX and AY in polynomial time. The NP-Completeness results from the previous section imply that we will not find a ch ; that satisfies the above for.
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