Normal form approach to unconditional well-posedness of nonlinear dispersive PDEs on the real line

In this paper, we revisit the infinite iteration scheme of normal form reductions, introduced by the first and second authors (with Z. Guo), in constructing solutions to nonlinear dispersive PDEs. Our main goal is to present a simplified approach to this method. More precisely, we study normal form reductions in an abstract form and reduce multilinear estimates of arbitrarily high degrees to successive applications of basic trilinear estimates. As an application, we prove unconditional well-posedness of canonical nonlinear dispersive equations on the real line. In particular, we implement this simplified approach to an infinite iteration of normal form reductions in the context of the cubic nonlinear Schr\"odinger equation (NLS) and the modified KdV equation (mKdV) on the real line and prove unconditional well-posedness in $H^s(\mathbb R)$ with (i) $s\geq \frac 16$ for the cubic NLS and (ii) $s > \frac 14$ for the mKdV. Our normal form approach also allows us to construct weak solutions to the cubic NLS in $H^s(\mathbb R)$, $0 \leq s < \frac 16$, and distributional solutions to the mKdV in $H^\frac{1}{4}(\mathbb R)$ (with some uniqueness statements).Comment: 60 pages. Typos corrected. To appear in Ann. Fac. Sci. Toulouse Mat

Decision making can be improved through observational learning

Observational learning can debias judgment and decision making. One-shot observational learning-based training interventions (akin to “hot seating”) can produce reductions in cognitive biases in the laboratory (i.e., anchoring, representativeness, and social projection), and successfully teach a decision rule that increases advice taking in a weight on advice paradigm (i.e., the averaging principle). These interventions improve judgment, rule learning, and advice taking more than practice. We find observational learning-based interventions can be as effective as information-based interventions. Their effects are additive for advice taking, and for accuracy when advice is algorithmically optimized. As found in the organizational learning literature, explicit knowledge transferred through information appears to reduce the stickiness of tacit knowledge transferred through observational learning. Moreover, observational learning appears to be a unique debiasing training strategy, an addition to the four proposed by Fischhoff (1982). We also report new scales measuring individual differences in anchoring, representativeness heuristics, and social projection.Published versio

Impatience and Time Inconsistency in Discounting Models

Extant theories of intertemporal choice entangle two aspects of time preference: impatience and time inconsistency. Impatient people focus on present consumption without worrying too much about the future; they may spend freely and avoid exercise. An outsider might question their choices, but impatient people do not experience conflict over those choices. By contrast, people who are time-inconsistent intend to save and exercise, but they fail to do so when temptation is proximate. Such individuals are conflicted; their preferences today differ from their preferences tomorrow. I characterize the interaction between impatience and time inconsistency in three leading models of temporal discounting that go beyond the exponential model, which does not predict time inconsistency at any level of impatience. The quasi-hyperbolic model predicts that time inconsistency increases with patience, whereas the hyperbolic model makes the opposite prediction. The constant-sensitivity model predicts that time inconsistency peaks at a moderate level of impatience. The results of an experiment using real monetary consequences with delays of up to one year align most closely with the prediction of the constant-sensitivity model

Early Cost Realization and College Choice

Student loans defer the cost of college until after graduation, allowing many students access to higher lifetime earnings and colleges and universities they otherwise could not afford. Even with student loans, however, the authors find that students psychologically realize the financial costs of a college education long before their loan repayments begin. This early cost realization frames financial decisions between most pairs of colleges as an intertemporal trade-off. Students choose between investments with (1) smaller short-term costs but smaller long-term returns (a lower-cost, lower-return [LC-LR] college) and (2) larger short-term costs but larger long-term returns (a higher-cost, higher-return [HC-HR] college). The authors find that early cost realization increases preferences for LC-LR colleges—preferences that could reduce lifetime earnings—in both simulations and experiments. Preferences for LC-LR colleges are pronounced among financially impatient students and in choice pairs of LC-LR and HC-HR colleges where the equilibrium is set at a low-discount-rate threshold. A return-on-investment strategy, future uncertainty, and debt aversion cannot explain these results. A decision aid synchronizing the psychological realization of costs and benefits reduced preferences for LC-LR colleges, illustrating that the preference is constructed and receptive to interventions

Early Cost Realization and College Choice

Student loans defer the cost of college until after graduation, allowing many students access to higher lifetime earnings and colleges and universities they otherwise could not afford. Even with student loans, however, the authors find that students psychologically realize the financial costs of a college education long before their loan repayments begin. This early cost realization frames financial decisions between most pairs of colleges as an intertemporal trade-off. Students choose between investments with (1) smaller short-term costs but smaller long-term returns (a lower-cost, lower-return [LC-LR] college) and (2) larger short-term costs but larger long-term returns (a higher-cost, higher-return [HC-HR] college). The authors find that early cost realization increases preferences for LC-LR colleges—preferences that could reduce lifetime earnings—in both simulations and experiments. Preferences for LC-LR colleges are pronounced among financially impatient students and in choice pairs of LC-LR and HC-HR colleges where the equilibrium is set at a low-discount-rate threshold. A return-on-investment strategy, future uncertainty, and debt aversion cannot explain these results. A decision aid synchronizing the psychological realization of costs and benefits reduced preferences for LC-LR colleges, illustrating that the preference is constructed and receptive to interventions

Poly(imide-<i>co</i>-siloxane) as a Thermo-Stable Binder for a Thin Layer Cathode of Thermal Batteries

The polymer binder, poly(imide-co-siloxane) (PIS), was synthesized and applied to form a thin cathode layer of composites for a thermal battery that has an unusually high operating temperature of 450 &#176;C. The PIS was prepared through cross-linking of the polyimide with polysiloxane. The morphology of FeS2/PIS composites showed that FeS2 particles was coated with the PIS cross-linked gel. The FeS2/PIS composites enabled to fabricate mechanically stable thin cathode layer that was 10&#8315;20% of the thickness of a conventional pellet-type cathode. The FeS2/PIS composites were stable up to 400 &#176;C and maintained their morphology at this temperature. PIS coating layers decomposed at 450 &#176;C, and a new residue was generated, which was observed by transmission electron microscopy, and the compositional change was analyzed. The FeS2/PIS composites showed enhanced thermal stability over that of FeS2 in thermogravimetric analysis. The thermal battery with the PIS polymer binder showed a 20% discharge capacity increase when compared to a conventional pellet-type cathode