Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

Symbolic Solving of Partial Differential Equation Systems and Compatibility Conditions

An algorithm is produced for the symbolic solving of systems of partial differential equations by means of multivariate Laplace–Carson transform. A system of K equations with M as the greatest order of partial derivatives and right-hand parts of a special type is considered. Initial conditions are input. As a result of a Laplace–Carson transform of the system according to initial condition we obtain an algebraic system of equations. A method to obtain compatibility conditions is discussed.

On Optimal Quadratic Lagrange Interpolation: Extremal Node Systems with Minimal Lebesgue Constant via Symbolic Computation

ACM Computing Classification System (1998): G.1.1, G.1.2.

Weitzenböck Derivations and Classical Invariant Theory II: The Symbolic Method

2000 Mathematics Subject Classification: 13N15, 13A50, 13F20.

Intentional forgetting in dysphoria:investigating the inhibitory effects of thought substitution using independent cues

Background Individuals with clinical and subclinical depression (dysphoria) exhibit problems intentionally forgetting unwanted memories on the think/no-think (TNT) paradigm (Anderson & Green, 2001). However, providing substitute words to think about instead of the to-be-forgotten targets can improve forgetting in depressed patients. Objectives To determine if thought substitution can enhance forgetting in dysphoric participants and to examine the potential mechanisms (blocking or inhibition) that might underpin successful forgetting. Methods Thirty-six dysphoric and 36 non-dysphoric participants learned neutral word-pairs and then practiced responding with the targets to some cues (think trials) and suppressing responses to others (no think trials). Half the participants were provided with substitute words to recall instead of the original targets (aided suppression) and half were simply told to avoid thinking about the targets (unaided suppression). Finally, participants completed two recall tests for the targets; one cued with the original probes and one with independent probes. Results Regardless of suppression condition (aided or unaided), dysphoric participants exhibited impaired forgetting, relative to their non-dysphoric counterparts, but only when cued with the original probes. Furthermore, higher depression scores were associated with poorer forgetting. In the aided condition, successful forgetting was observed on both the original and independent probe tasks, which supports the inhibitory account of thought substitution. Limitations Non-clinical status of the dysphoric participants was not confirmed using a validated measure. Conclusions Findings do not support the utility of thought substitution as a method of improving the forgetting in depressed participants, but do support the inhibition account of thought substitution.

Examining the impact of thought substitution on intentional forgetting in induced and naturally occurring dysphoria

Two experiments were conducted to determine if natural and induced dysphoria is associated with impaired forgetting and, whether a thought-substitution strategy would ameliorate any observed deficits. Study 1: 36 dysphoric & 36 non-dysphoric participants learnt a series of emotional word pairs. Participants were subsequently presented with some of the cues and were asked to recall the targets or prevent the targets from coming to mind. Half of the participants were provided with substitute words to recall instead of the original targets (aided suppression). At final memory testing, participants were asked to recall the targets to all cues. Dysphoric participants exhibited impaired forgetting, even when using a thought substitution strategy. Non-dysphoric participants, however, were able to use substitutes to suppress words. Study 2: 50 healthy participants initially completed the aided condition of the forgetting task. Participants were then given a positive or negative mood-induction, followed by another version of the forgetting task. Although all participants showed a forgetting effect prior to the mood-induction, only the positive group was successful at forgetting after the mood induction. Taken together, these findings do not support the utility of thought-substitution as an aid to forgetting in individuals in a naturally or induced dysphoric mood.

Luminescence of delafossite-type CuAlO2 fibers with Eu substitution for Al cations

CuAlO2 has been examined as a potential luminescent material by substituting Eu for Al cations in the delafossite structure. CuAlO2:Eu3+ nanofibers have been prepared via electrospinning for the ease of mitigating synthesis requirements and for future optoelectronics and emerging applications. Single-phase CuAlO2 fibers could be obtained at a temperature of 1100 °C in air. The Eu was successfully doped in the delafossite structure and two strong emission bands at ~405 and 610 nm were observed in the photoluminescence spectra. These bands are due to the intrinsic near-band-edge transition of CuAlO2 and the f-f transition of the Eu3+ activator, respectively. Further electrical characterization indicated that these fibers exhibit semiconducting behavior and the introduction of Eu could act as band-edge modifiers, thus changing the thermal activation energies. In light of this study, CuAlO2:Eu3+ fibers with both strong photoluminescence and p-type conductivity could be produced by tailoring the rare earth doping concentrations.

Controversy over generic substitution

Substitution of branded medicine with a generic equivalent is already common. Robin Ferner, Warren Lenney, and John Marriott argue that concerns about UK plans to let pharmacists make the decision are unwarranted.

Inflation, currency substitution and dollarization: The case of Argentina

This dissertation discusses the relationship between inflation, currency substitution and dollarization that has taken place in Argentina for the past several decades.^ First, it is shown that when consumers are able to hold only domestic monetary balances (without capital mobility) an increase in the rate of inflation will produce a balance of payments deficit. We then look at the same issue but with heterogeneous consumers, this heterogeneity being generated by non-proportional lump-sum transfers.^ Second, we discussed some necessary assumptions related to currency substitution models and concluded that there was no a-priori conclusion on whether currencies should be assumed to be "cooperant" or "non-cooperant" in utility. That is to say, whether individuals held different currencies together or one instead of the other.^ Third, we went into discussing the issue of currency substitution as being a constraint on governments' inflationary objectives rather than a choice of those governments to avoid hyperinflations. We showed that imperfect substitutability between currencies does not "reduce the scope for rational (hyper)inflationary processes" as it had been previously argued. It will ultimately depend on the parametrization used and not on the intrinsic characteristics of imperfect substitutability between currencies.^ We further showed that in Argentina, individuals have been able to endogenize the money supply by holding foreign monetary balances. We argued that the decision to hold foreign monetary balances by individuals is always a second best due to the trade-off between holding foreign monetary balances and consumption. For some levels of income, consumption, and foreign inflation, individuals would prefer to hold domestic monetary balances rather than foreign ones.^ We then modeled the distinction between dollarization and currency substitution. We concluded that although dollarization is necessary for currency substitution to take place, the decision to use foreign monetary balances for transactions purposes is largely independent from the dollarization process.^ Finally, we concluded that Argentina should not fully dollarize its economy because dollarization is always a second best to using a domestic currency. Further, we argued that a fixed exchange system would be better than a flexible exchange rate or a "crawling-peg" system because of the characteristics of the political system and the possibilities of "mass praetorianism" to develop, which is intricately linked to "populist" solutions. ^

A quantitative application of symbolic interactionism to advance directive completion by older adults

This study examined contextual and situational influences on older adults' decision to complete advance directives by means of a conceptual framework derived from symbolic interactionist theory and a cross-sectional, correlational research design. It was hypothesized that completion of advance directives among older adults would be associated with visiting or participating in the care of a terminally ill or permanently incompetent individual sustained by technology. Using a 53-item questionnaire, computer assisted telephone interviews (CATI) were conducted with 398 community dwelling adults between September and October 2003. Respondents were contacted using random-select dialing from a listed sample of 99% of household telephone numbers in one South Florida census tract. Over 90% of households in this tract include an individual age 65 or older. ^ The results revealed that contrary to most reports in the literature a substantial proportion of older adults (82%) had completed advance directives and that the link between older adults and document completion was mainly through attorneys and not mandated agents, health care professionals. Further, more than one third of older adults reported that religion/spirituality was not an important part of their life, suggesting that the recommended practice of offering religious/spiritual counseling to all those approaching death be reexamined. The hypothesis was not supported (p > .05) and is explained by the situational emphasis on the variables rather than on structural influences. In logistic regression analysis, only increasing age (p = .001) and higher education (p = < .001) were significant but explained only 10% of the variance in document completion. ^ Based on the findings, increased interdisciplinary collaboration is suggested with regard to the advance directive agenda. Since attorneys play a key role in document completion, other professions should seek their expertise and collaboration. In addition, the inclusion of a religious/spiritual preference section in all living wills should be considered as an essential part of a holistic and individually appropriate document. Implications for social work education, practice, and advocacy are discussed as well as suggestions for further research. ^

Space-for-Time Substitution Works in Everglades Ecological Forecasting Models

Space-for-time substitution is often used in predictive models because long-term time-series data are not available. Critics of this method suggest factors other than the target driver may affect ecosystem response and could vary spatially, producing misleading results. Monitoring data from the Florida Everglades were used to test whether spatial data can be substituted for temporal data in forecasting models. Spatial models that predicted bluefin killifish (Lucania goodei) population response to a drying event performed comparably and sometimes better than temporal models. Models worked best when results were not extrapolated beyond the range of variation encompassed by the original dataset. These results were compared to other studies to determine whether ecosystem features influence whether space-for-time substitution is feasible. Taken in the context of other studies, these results suggest space-for-time substitution may work best in ecosystems with low beta-diversity, high connectivity between sites, and small lag in organismal response to the driver variable.

Space-for-Time Substitution Works in Everglades Ecological Forecasting Models

Space-for-time substitution is often used in predictive models because long-term time-series data are not available. Critics of this method suggest factors other than the target driver may affect ecosystem response and could vary spatially, producing misleading results. Monitoring data from the Florida Everglades were used to test whether spatial data can be substituted for temporal data in forecasting models. Spatial models that predicted bluefin killifish (Lucania goodei) population response to a drying event performed comparably and sometimes better than temporal models. Models worked best when results were not extrapolated beyond the range of variation encompassed by the original dataset. These results were compared to other studies to determine whether ecosystem features influence whether space-for-time substitution is feasible. Taken in the context of other studies, these results suggest space-fortime substitution may work best in ecosystems with low beta-diversity, high connectivity between sites, and small lag in organismal response to the driver variable.

A software tool that generates symbolic model verifier (SMV) input language from a predicate transition net

The purpose of this research was to apply model checking by using a symbolic model checker on Predicate Transition Nets (PrT Nets). A PrT Net is a formal model of information flow which allows system properties to be modeled and analyzed. The aim of this thesis was to use the modeling and analysis power of PrT nets to provide a mechanism for the system model to be verified. Symbolic Model Verifier (SMV) was the model checker chosen in this thesis, and in order to verify the PrT net model of a system, it was translated to SMV input language. A software tool was implemented which translates the PrT Net into SMV language, hence enabling the process of model checking. The system includes two parts: the PrT net editor where the representation of a system can be edited, and the translator which converts the PrT net into an SMV program.

Inflation, currency substitution, and dollarization : the case of Argentina

This dissertation discusses the relationship between inflation, currency substitution and dollarization that has taken place in Argentina for the past several decades. First, it is shown that when consumers are able to hold only domestic monetary balances (without capital mobility) an increase in the rate of inflation will produce a balance of payments deficit. We then look at the same issue but with heterogeneous consumers, this heterogeneity being generated by non-proportional lump-sum transfers. Second, we discussed some necessary assumptions related to currency substitution models and concluded that there was no a-priori conclusion on whether currencies should be assumed to be "cooperant" or "non-cooperant" in utility. That is to say, whether individuals held different currencies together or one instead of the other. Third, we went into discussing the issue of currency substitution as being a constraint on governments inflationary objectives rather than a choice of those governments to avoid hyperinflations. We showed that imperfect substitutability between currencies does not "reduce the scope for rational (hyper)inflationary processes" as it had been previously argued. It will ultimately depend on the parametrization used and not on the intrinsic characteristics of imperfect substitutability between currencies. We further showed that in Argentina, individuals have been able to endogenize the money supply by holding foreign monetary balances. We argued that the decision to hold foreign monetary balances by individuals is always a second best due to the trade-off between holding foreign monetary balances and consumption. For some levels of income, consumption, and foreign inflation, individuals would prefer to hold domestic monetary balances rather than foreign ones. We then modeled the distinction between dollarization and currency substitution. We concluded that although dollarization is necessary for currency substitution to take place, the decision to use foreign monetary balances for transactions purposes is largely independent from the dollarization process. Finally, we concluded that Argentina should not fully dollarize its economy because dollarization is always a second best to using a domestic currency. Further, we argued that a fixed exchange system would be better than a flexible exchange rate or a "crawling-peg" system because of the characteristics of the political system and the possibilities of "mass praetorianism" to develop, which is intricately linked to "populist" solutions.

La substitution du Dasein chez Levinas

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.