A class of well-posed parabolic final value problems

This paper focuses on parabolic final value problems, and well-posedness is proved for a large class of these. The clarification is obtained from Hilbert spaces that characterise data that give existence, uniqueness and stability of the solutions. The data space is the graph normed domain of an unbounded operator that maps final states to the corresponding initial states. It induces a new compatibility condition, depending crucially on the fact that analytic semigroups always are invertible in the class of closed operators. Lax--Milgram operators in vector distribution spaces constitute the main framework. The final value heat conduction problem on a smooth open set is also proved to be well posed, and non-zero Dirichlet data are shown to require an extended compatibility condition obtained by adding an improper Bochner integral.Comment: 16 pages. To appear in "Applied and numerical harmonic analysis"; a reference update. Conference contribution, based on arXiv:1707.02136, with some further development

UV radiation below an Arctic vortex with severe ozone depletion

The erythemally weighted (UV) irradiance below the severely depleted Arctic vortices in spring 1996 and 1997 were substantially elevated. On average the UV increased 36 and 33% relative to the 1979-1981 mean assuming clear skies from day 80-100 in 1996 and 1997, respectively. On clear sky days large regions of the Arctic experienced maximum UV increases exceeding 70 and 50% on single days in 1996 and 1997, respectively. A minor fraction of these increases are not anthropogenic and have a dynamical origin as seen by comparison to 1982, when hardly any ozone depletion is expected

A Transformational Approach to Resource Analysis with Typed-Norms

In order to automatically infer the resource consumption of programs, analyzers track how data sizes change along a program s execution. Typically, analyzers measure the sizes of data by applying norms which are mappings from data to natural numbers that represent the sizes of the corresponding data. When norms are defined by taking type information into account, they are named typed-norms. The main contribution of this paper is a transformational approach to resource analysis with typed-norms. The analysis is based on a transformation of the program into an intermediate abstract program in which each variable is abstracted with respect to all considered norms which are valid for its type. We also sketch a simple analysis that can be used to automatically infer the required, useful, typed-norms from programs.This work was funded partially by the EU project FP7-ICT-610582 ENVISAGE: Engineering Virtualized Services (http://www.envisage-project.eu) and by the Spanish projects TIN2008-05624 and TIN2012-38137. Raúl Gutiérrez is also partially supported by a Juan de la Cierva Fellowship from the Spanish MINECO, ref. JCI-2012-13528.Albert Albiol, EM.; Genaim, S.; Gutiérrez Gil, R. (2014). A Transformational Approach to Resource Analysis with Typed-Norms. Lecture Notes in Computer Science. 8901:38-53. https://doi.org/10.1007/978-3-319-14125-1_3S38538901Albert, E., Arenas, P., Genaim, S., Gómez-Zamalloa, M., Puebla, G.: Cost Analysis of Concurrent OO Programs. In: Yang, H. (ed.) APLAS 2011. LNCS, vol. 7078, pp. 238–254. Springer, Heidelberg (2011)Albert, E., Arenas, P., Genaim, S., Puebla, G., Zanardini, D.: Cost Analysis of Java Bytecode. In: De Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 157–172. Springer, Heidelberg (2007)Albert, E., Arenas, P., Genaim, S., Puebla, G., Zanardini, D.: Removing Useless Variables in Cost Analysis of Java Bytecode. In: Proc. of SAC 2008, pp. 368–375. ACM (2008)Alonso, D., Arenas, P., Genaim, S.: Handling Non-linear Operations in the Value Analysis of COSTA. In: Proc. of BYTECODE 2011. ENTCS, vol. 279, pp. 3–17. Elsevier (2011)Bossi, A., Cocco, N., Fabris, M.: Proving Termination of Logic Programs by Exploiting Term Properties. In: Proc. of TAPSOFT 1991. LNCS, vol. 494, pp. 153–180. Springer (1991)Bruynooghe, M., Codish, M., Gallagher, J., Genaim, S., Vanhoof, W.: Termination Analysis of Logic Programs through Combination of Type-Based norms. TOPLAS 29(2), Art. 10 (2007)Claessen, K., Hughes, J.: QuickCheck: A Lightweight Tool for Random Testing of Haskell Programs. In: Proc. of ICFP 2000, pp. 268–279. ACM (2000)Fähndrich, M.: Static Verification for Code Contracts. In: Cousot, R., Martel, M. (eds.) SAS 2010. LNCS, vol. 6337, pp. 2–5. Springer, Heidelberg (2010)Genaim, S., Codish, M., Gallagher, J.P., Lagoon, V.: Combining Norms to Prove Termination. In: Cortesi, A. (ed.) VMCAI 2002. LNCS, vol. 2294, pp. 123–138. Springer, Heidelberg (2002)Johnsen, E.B., Hähnle, R., Schäfer, J., Schlatte, R., Steffen, M.: ABS: A Core Language for Abstract Behavioral Specification. In: Aichernig, B.K., de Boer, F.S., Bonsangue, M.M. (eds.) Formal Methods for Components and Objects. LNCS, vol. 6957, pp. 142–164. Springer, Heidelberg (2011)King, A., Shen, K., Benoy, F.: Lower-bound Time-complexity Analysis of Logic Programs. In: Proc. of ILPS 1997, pp. 261–275. MIT Press (1997)Serrano, A., Lopez-Garcia, P., Bueno, F., Hermenegildo, M.: Sized Type Analysis for Logic Programs. In: Tech. Comms. of ICLP 2013. Cambridge U. Press (2013) (to appear)Spoto, F., Mesnard, F., Payet, É.: A Termination Analyser for Java Bytecode based on Path-Length. TOPLAS 32(3), Art. 8 (2010)Vallée-Rai, R., Hendren, L., Sundaresan, V., Lam, P., Gagnon, E., Co, P.: Soot - a Java Optimization Framework. In: Proc. of CASCON 1999. pp. 125–135. IBM (1999)Vasconcelos, P.: Space Cost Analysis using Sized Types. Ph.D. thesis, School of CS, University of St. Andrews (2008)Vasconcelos, P.B., Hammond, K.: Inferring Cost Equations for Recursive, Polymorphic and Higher-Order Functional Programs. In: Trinder, P., Michaelson, G.J., Peña, R. (eds.) IFL 2003. LNCS, vol. 3145, pp. 86–101. Springer, Heidelberg (2004)Wegbreit, B.: Mechanical Program Analysis. Commun. ACM 18(9), 528–539 (1975

Implementing Goal Setting Activities with LD Adolescents

This research was published by the KU Center for Research on Learning, formerly known as the University of Kansas Institute for Research in Learning Disabilities.In this study, LD adolescents were taught to set realistic goals, to expend effort to achieve the goals, and to accept responsibility for achieving or failing to achieve their goals. The intervention produced a significant increase in the number of students exhibiting realistic goal setting strategies. During training, LD students produced a significantly greater number of effort attributions than ability, task difficulty, or luck attributions. The treatment group also increased internal attributions

A Preliminary Account of the Danish Pearyland Expedition, 1948-9

Brief account of the organization, financing, supply transport by ship, then by Catalina planes from the base at Young Sund (74 16 N).; the preliminary scouting expedition in the summer of 1947; roster of personnel and brief summaries of the "work carried out and the results obtained on sledge journeys and on walking and motor boat trips during the first wintering of 1948-9" at Jorgen Bronlunds Fjord, 82 11 N, 31 30 W: geology summarized by J. Troelsen, botany, by K. Holmen, zoology, by P. Johnsen, meteorology and glaciology, by B. Fristrup, archeology by E. Knuth (leader)

Binary pattern tile set synthesis is NP-hard

In the field of algorithmic self-assembly, a long-standing unproven conjecture has been that of the NP-hardness of binary pattern tile set synthesis (2-PATS). The $k$-PATS problem is that of designing a tile assembly system with the smallest number of tile types which will self-assemble an input pattern of $k$ colors. Of both theoretical and practical significance, $k$-PATS has been studied in a series of papers which have shown $k$-PATS to be NP-hard for $k = 60$, $k = 29$, and then $k = 11$. In this paper, we close the fundamental conjecture that 2-PATS is NP-hard, concluding this line of study. While most of our proof relies on standard mathematical proof techniques, one crucial lemma makes use of a computer-assisted proof, which is a relatively novel but increasingly utilized paradigm for deriving proofs for complex mathematical problems. This tool is especially powerful for attacking combinatorial problems, as exemplified by the proof of the four color theorem by Appel and Haken (simplified later by Robertson, Sanders, Seymour, and Thomas) or the recent important advance on the Erd\H{o}s discrepancy problem by Konev and Lisitsa using computer programs. We utilize a massively parallel algorithm and thus turn an otherwise intractable portion of our proof into a program which requires approximately a year of computation time, bringing the use of computer-assisted proofs to a new scale. We fully detail the algorithm employed by our code, and make the code freely available online

An Application of Attribution Theory to Developing Self-Esteem in Learning Disabled Adolescents

This research was published by the KU Center for Research on Learning, formerly known as the University of Kansas Institute for Research in Learning Disabilities.The study found that LD adolescents did not differ significantly from non-LD adolescents in their esponses to general self esteem and attribution questionnaires. Effort attribution training brought no significant increase in effort attributions for the experimental group of LD students. LD students reported the effort was a factor that explained success or failure in achievement tasks, but also reported that factors other than effort explained their personal success or failure on a specific spelling task

Multiplication and Composition in Weighted Modulation Spaces

We study the existence of the product of two weighted modulation spaces. For this purpose we discuss two different strategies. The more simple one allows transparent proofs in various situations. However, our second method allows a closer look onto associated norm inequalities under restrictions in the Fourier image. This will give us the opportunity to treat the boundedness of composition operators.Comment: 49 page