A compactness theorem for scalar-flat metrics on manifolds with boundary

Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this set is compact for dimensions greater than or equal to 7 under the generic condition that the trace-free 2nd fundamental form of the boundary is nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential Equation

"We live from mother nature":neoliberal globalization, commodification, the 'war on drugs', and biodiversity in Colombia since the 1990s

This article explores how macroeconomic and environmental policies instituted since the 1990s have altered meanings, imaginaries, and the human relationship to nature in Colombia. The Colombian nation-state is pluri-ethnic, multilingual, and megabiodiverse. In this context, indigenous peoples, Afro-Colombians, and some peasant communities survive hybridization of their cultures. They have developed their own ways of seeing, understanding, and empowering the world over centuries of European rule. However, threats to relatively discrete cultural meanings have increased since major changes in the 1990s, when Colombia experienced the emergence of new and modern interpretations of nature, such as “biodiversity,” and a deepening of globalized neoliberal economic and political management. These policies involve a modern logic of being in the world, the establishment of particular regulatory functions for economies, societies, and the environment, and their spread has been facilitated by webs of political and economic power. We trace their local effects with reference to three indigenous groups

Soil carbon and nitrogen stocks in traditional agricultural and agroforestry systems in the semiarid region of Brazil.

Abstract: In the semiarid region of Brazil, inadequate management of cropping systems and low plant biomass production can contribute to reduce soil carbon (C) and nitrogen (N) stocks; therefore, management systems that preserve C and N must be adopted. This study aimed to evaluate the changes in soil C and N stocks that were promoted by agroforestry (agrosilvopastoral and silvopastoral) and traditional agricultural systems (slash-and-burn clearing and cultivation for two and three years) and to compare these systems with the natural Caatinga vegetation after 13 years of cultivation. The experiment was carried out on a typical Ortic Chromic Luvisol in the municipality of Sobral, Ceará, Brazil. Soil samples were collected (layers 0-6, 6-12, 12-20, 20-40 and 40-60 cm) with four replications. The plain, convex and concave landforms in each study situation were analyzed, and the total organic C, total N and densities of the soil samples were assessed. The silvopastoral system promoted the greatest long-term reductions in C and N stocks, while the grosilvopastoral system promoted the smallest losses and therefore represents a sustainable alternative for soil C and N sequestration in these semiarid conditions. The traditional agricultural system produced reductions of 58.87 and 9.57 Mg ha-1 in the organic C and total N stocks, respectively, which suggests that this system is inadequate for these semiarid conditions. The organic C stocks were largest in the concave landform in the agrosilvopastoral system and in the plain landform in the silvopastoral system, while the total N values were highest in the concave landform in the native, agrosilvopastoral and silvopastoral systems. [Estoques de carbono e nitrogênio do solo em sistemas agrícolas tradicional e agroflorestais no semiárido brasileiro]. Na região semiárida, o manejo inadequado dos sistemas de cultivo, aliado à baixa produção de fitomassa, pode contribuir para reduzir os estoques de carbono (C) e nitrogênio (N) do solo; portanto, a adoção de sistemas de manejo para a preservação desses elementos é necessária. Objetivou-se avaliar as alterações promovidas nos estoques de C e N do solo por sistemas agrícolas agroflorestais (agrossilvipastoril e silvipastoril) e tradicional (com derrubada da vegetação, queima e cultivo por dois-três anos), confrontando-os à vegetação natural de Caatinga, após 13 anos, em experimento instalado em um Luvissolo Crômico órtico típico, no município de Sobral, Ceará. Amostras de solo foram coletadas nas profundidades de 0-6, 6-12, 12-20, 20-40 e 40-60 cm, em quatro repetições, considerando os relevos plano, convexo e côncavo em cada situação de estudo, sendo determinados o C orgânico total, o N total e as densidades do solo. Entre os sistemas agroflorestais estudados, o silvipastoril, em longo prazo, promoveu as maiores reduções nos estoques de C e N, enquanto o agrossilvipastoril as menores perdas, representando alternativa sustentável para o sequestro de C e N do solo nessas condições semiáridas. O sistema de cultivo tradicional apresentou reduções de 58,87 e 9,57 Mg ha-1 dos estoques de C orgânico e N total, respectivamente, indicando sua não adequação para as condições semiáridas brasileiras. Os relevos côncavo, no sistema agrossilvipastoril, e plano, no silvipastoril, apresentaram os maiores estoques de C orgânico, enquanto para o N total, a forma côncava apresentou os maiores valores na vegetação nativa, agrossilvipastoril e silvipastoril

Wild felid species richness affected by a corridor in the Lacandona forest, Mexico

Los efectos de la presencia de un corredor en la selva Lacandona, en México, en la riqueza de especies de félidos silvestres Los félidos silvestres se encuentran entre las especies más vulnerables ante la pérdida de hábitat causada por la fragmentación de los ecosistemas. Se analizó el efecto de la presencia de un corredor estructural, definido como una franja de vegetación que conecta dos fragmentos de hábitat, en la riqueza y ocupación de félidos en tres sitios de Marqués de Comillas, en Chiapas: uno comprende dos fragmentos de bosque aislados, otro presenta un corredor estructural y el último se encuentra dentro de la reserva de la biosfera Montes Azules. Se encontraron cuatro especies en el interior de la Reserva, cinco en el corredor estructural y únicamente dos (L. pardalis y H. yagouaroundi) en los fragmentos de bosque aislados. La presencia del corredor no afectó de forma significativa a la ocupación, pero debido a la baja tasa de detección, se necesita seguir investigando para descartar diferencias. Nuestros resultados resaltan la necesidad de manejar la conectividad del hábitat en los bosques remanentes para lograr la conservación de la comunidad de félidos en Marqués de Comillas, en Chiapas, México.Los efectos de la presencia de un corredor en la selva Lacandona, en México, en la riqueza de especies de félidos silvestres Los félidos silvestres se encuentran entre las especies más vulnerables ante la pérdida de hábitat causada por la fragmentación de los ecosistemas. Se analizó el efecto de la presencia de un corredor estructural, definido como una franja de vegetación que conecta dos fragmentos de hábitat, en la riqueza y ocupación de félidos en tres sitios de Marqués de Comillas, en Chiapas: uno comprende dos fragmentos de bosque aislados, otro presenta un corredor estructural y el último se encuentra dentro de la reserva de la biosfera Montes Azules. Se encontraron cuatro especies en el interior de la Reserva, cinco en el corredor estructural y únicamente dos (L. pardalis y H. yagouaroundi) en los fragmentos de bosque aislados. La presencia del corredor no afectó de forma significativa a la ocupación, pero debido a la baja tasa de detección, se necesita seguir investigando para descartar diferencias. Nuestros resultados resaltan la necesidad de manejar la conectividad del hábitat en los bosques remanentes para lograr la conservación de la comunidad de félidos en Marqués de Comillas, en Chiapas, México.Wild felids are one of the most vulnerable species due to habitat loss caused by fragmentation of ecosystems. We analyzed the effect of a structural corridor, defined as a strip of vegetation connecting two habitat patches, on the richness and habitat occupancy of felids on three sites in Marqués de Comillas, Chiapas, one with two isolated forest patches, the second with a structural corridor, and the third inside the Montes Azules Biosphere Reserve. We found only two species (L. pardalis and H. yagouaroundi) in the isolated forest patches, five species in the structural corridor, and four species inside the Reserve. The corridor did not significantly affect occupancy, but due to the low detection rates, further investigation is needed to rule out differences. Our results highlight the need to manage habitat connectivity in the remaining forests in order to preserve the felid community of Marqués de Comillas, Chiapas, México

Sharp constants in weighted trace inequalities on Riemannian manifolds

We establish some sharp weighted trace inequalities W^{1,2}(\rho^{1-2\sigma}, M)\hookrightarrow L^{\frac{2n}{n-2\sigma}}(\pa M) on $n+1$ dimensional compact smooth manifolds with smooth boundaries, where $\rho$ is a defining function of $M$ and $\sigma\in (0,1)$. This is stimulated by some recent work on fractional (conformal) Laplacians and related problems in conformal geometry, and also motivated by a conjecture of Aubin.Comment: 34 page

Protocol analysis modulo combination of theories: A case study in Maude-NPA

There is a growing interest in formal methods and tools to analyze cryptographic protocols modulo algebraic properties of their underlying cryptographic functions. It is well-known that an intruder who uses algebraic equivalences of such functions can mount attacks that would be impossible if the cryptographic functions did not satisfy such equivalences. In practice, however, protocols use a collection of well-known functions, whose algebraic properties can naturally be grouped together as a union of theories E 1... ¿ n. Reasoning symbolically modulo the algebraic properties E 1... ¿ n requires performing (E 1... ¿ n)-unification. However, even if a unification algorithm for each individual E i is available, this requires combining the existing algorithms by methods that are highly non-deterministic and have high computational cost. In this work we present an alternative method to obtain unification algorithms for combined theories based on variant narrowing. Although variant narrowing is less efficient at the level of a single theory E i, it does not use any costly combination method. Furthermore, it does not require that each E i has a dedicated unification algorithm in a tool implementation. We illustrate the use of this method in the Maude-NPA tool by means of a well-known protocol requiring the combination of three distinct equational theories. © 2011 Springer-Verlag.R. Sasse and J. Meseguer have been partially supported by NSF Grants CNS0716638, CNS-0831064 and CNS-0904749. S. Escobar has been partially supported by the EU (FEDER) and the Spanish MEC/MICINN under grant TIN 2007-68093- C02-02. C. Meadows has been partially supported by NSF Grant CNS-0904749National Science Foundation, EEUUSasse, R.; Escobar Román, S.; Meadows, C.; Meseguer, J. (2011). Protocol analysis modulo combination of theories: A case study in Maude-NPA. En Security and Trust Management. Springer Verlag (Germany). 6710:163-178. doi:10.1007/978-3-642-22444-7_11S1631786710Abadi, M., Cortier, V.: Deciding knowledge in security protocols under equational theories. Theoretical Computer Science 367(1-2), 2–32 (2006)Armando, A., Basin, D.A., Boichut, Y., Chevalier, Y., Compagna, L., Cuéllar, J., Drielsma, P.H., Héam, P.-C., Kouchnarenko, O., Mantovani, J., Mödersheim, S., von Oheimb, D., Rusinowitch, M., Santiago, J., Turuani, M., Viganò, L., Vigneron, L.: The avispa tool for the automated validation of internet security protocols and applications. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 281–285. Springer, Heidelberg (2005)Baader, F., Schulz, K.U.: Unification in the union of disjoint equational theories: Combining decision procedures. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 50–65. Springer, Heidelberg (1992)Basin, D.A., Mödersheim, S., Viganò, L.: An on-the-fly model-checker for security protocol analysis. In: Snekkenes, E., Gollmann, D. (eds.) ESORICS 2003. LNCS, vol. 2808, pp. 253–270. Springer, Heidelberg (2003)Baudet, M., Cortier, V., Delaune, S.: YAPA: A generic tool for computing intruder knowledge. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 148–163. Springer, Heidelberg (2009)Blanchet, B.: An efficient cryptographic protocol verifier based on prolog rules. In: CSFW, pp. 82–96. IEEE Computer Society, Los Alamitos (2001)Bursuc, S., Comon-Lundh, H.: Protocol security and algebraic properties: Decision results for a bounded number of sessions. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 133–147. Springer, Heidelberg (2009)Chevalier, Y., Küsters, R., Rusinowitch, M., Turuani, M.: An NP decision procedure for protocol insecurity with XOR. In: LICS, pp. 261–270. IEEE Computer Society, Los Alamitos (2003)Chevalier, Y., Rusinowitch, M.: Hierarchical combination of intruder theories. Inf. Comput. 206(2-4), 352–377 (2008)Chevalier, Y., Rusinowitch, M.: Symbolic protocol analysis in the union of disjoint intruder theories: Combining decision procedures. Theor. Comput. Sci. 411(10), 1261–1282 (2010)Ciobâcă, Ş., Delaune, S., Kremer, S.: Computing knowledge in security protocols under convergent equational theories. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 355–370. Springer, Heidelberg (2009)Comon-Lundh, H., Delaune, S.: The finite variant property: How to get rid of some algebraic properties. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 294–307. Springer, Heidelberg (2005)Cortier, V., Delaitre, J., Delaune, S.: Safely composing security protocols. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 352–363. Springer, Heidelberg (2007)Cremers, C.J.F.: The scyther tool: Verification, falsification, and analysis of security protocols. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 414–418. Springer, Heidelberg (2008)Escobar, S., Meadows, C., Meseguer, J.: A rewriting-based inference system for the NRL protocol analyzer and its meta-logical properties. Theoretical Computer Science 367(1-2), 162–202 (2006)Escobar, S., Meadows, C., Meseguer, J.: Maude-NPA: Cryptographic protocol analysis modulo equational properties. In: Aldini, A., Barthe, G., Gorrieri, R. (eds.) FOSAD 2007/2008/2009 Tutorial Lectures. LNCS, vol. 5705, pp. 1–50. Springer, Heidelberg (2009)Escobar, S., Meseguer, J., Sasse, R.: Effectively checking or disproving the finite variant property. Technical Report UIUCDCS-R-2008-2960, Department of Computer Science - University of Illinois at Urbana-Champaign (April 2008)Escobar, S., Meseguer, J., Sasse, R.: Effectively checking the finite variant property. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 79–93. Springer, Heidelberg (2008)Escobar, S., Meseguer, J., Sasse, R.: Variant narrowing and equational unification. Electr. Notes Theor. Comput. Sci. 238(3), 103–119 (2009)Escobar, S., Sasse, R., Meseguer, J.: Folding variant narrowing and optimal variant termination. In: Ölveczky, P.C. (ed.) WRLA 2010. LNCS, vol. 6381, pp. 52–68. Springer, Heidelberg (2010)Fabrega, F.J.T., Herzog, J., Guttman, J.: Strand Spaces: What Makes a Security Protocol Correct? Journal of Computer Security 7, 191–230 (1999)Guo, Q., Narendran, P.: Unification and matching modulo nilpotence. In: CADE-13. LNCS, vol. 1104, pp. 261–274. Springer, Heidelberg (1996)Harkins, D., Carrel, D.: The Internet Key Exchange (IKE), IETF RFC 2409, (November 1998)Jouannaud, J.-P., Kirchner, C., Kirchner, H.: Incremental construction of unification algorithms in equational theories. In: Díaz, J. (ed.) ICALP 1983. LNCS, vol. 154, pp. 361–373. Springer, Heidelberg (1983)Küsters, R., Truderung, T.: Reducing protocol analysis with xor to the xor-free case in the Horn theory based approach. In: ACM Conference on Computer and Communications Security, pp. 129–138 (2008)Küsters, R., Truderung, T.: Using ProVerif to analyze protocols with Diffie-Hellman exponentiation. In: CSF, pp. 157–171. IEEE Computer Society, Los Alamitos (2009)Lafourcade, P., Terrade, V., Vigier, S.: Comparison of cryptographic verification tools dealing with algebraic properties. In: Degano, P., Guttman, J.D. (eds.) FAST 2009. LNCS, vol. 5983, pp. 173–185. Springer, Heidelberg (2010)Lowe, G.: Breaking and fixing the Needham-Schroeder public-key protocol using FDR. In: Margaria, T., Steffen, B. (eds.) TACAS 1996. LNCS, vol. 1055, pp. 147–166. Springer, Heidelberg (1996)Meadows, C.: The NRL protocol analyzer: An overview. J. Log. Program. 26(2), 113–131 (1996)Meseguer, J.: Conditional rewriting logic as a united model of concurrency. Theor. Comput. Sci. 96(1), 73–155 (1992)Meseguer, J.: Membership algebra as a logical framework for equational specification. In: Parisi-Presicce, F. (ed.) WADT 1997. LNCS, vol. 1376, pp. 18–61. Springer, Heidelberg (1998)Meseguer, J., Thati, P.: Symbolic reachability analysis using narrowing and its application to verification of cryptographic protocols. Higher-Order and Symbolic Computation 20(1–2), 123–160 (2007)Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, Heidelberg (2002)Santiago, S., Talcott, C.L., Escobar, S., Meadows, C., Meseguer, J.: A graphical user interface for Maude-NPA. Electr. Notes Theor. Comput. Sci. 258(1), 3–20 (2009)Schmidt-Schauß, M.: Unification in a combination of arbitrary disjoint equational theories. J. Symb. Comput. 8(1/2), 51–99 (1989)Terese (ed.): Term Rewriting Systems. Cambridge University Press, Cambridge (2003)Turuani, M.: The CL-atse protocol analyser. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 277–286. Springer, Heidelberg (2006

A Finite Representation of the Narrowing Space

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-14125-1_4Narrowing basically extends rewriting by allowing free variables in terms and by replacing matching with unification. As a consequence, the search space of narrowing becomes usually infinite, as in logic programming. In this paper, we introduce the use of some operators that allow one to always produce a finite data structure that still represents all the narrowing derivations. Furthermore, we extract from this data structure a novel, compact equational representation of the (possibly infinite) answers computed by narrowing for a given initial term. Both the finite data structure and the equational representation of the computed answers might be useful in a number of areas, like program comprehension, static analysis, program transformation, etc.Nishida, N.; Vidal, G. (2013). A Finite Representation of the Narrowing Space. En Logic-Based Program Synthesis and Transformation. Springer. 54-71. doi:10.1007/978-3-319-14125-1_4S5471Albert, E., Vidal, G.: The Narrowing-Driven Approach to Functional Logic Program Specialization. New Generation Computing 20(1), 3–26 (2002)Alpuente, M., Falaschi, M., Vidal, G.: Partial Evaluation of Functional Logic Programs. ACM Transactions on Programming Languages and Systems 20(4), 768–844 (1998)Alpuente, M., Falaschi, M., Vidal, G.: Compositional Analysis for Equational Horn Programs. In: Rodríguez-Artalejo, M., Levi, G. (eds.) ALP 1994. LNCS, vol. 850, pp. 77–94. Springer, Heidelberg (1994)Antoy, S., Ariola, Z.: Narrowing the Narrowing Space. In: Hartel, P.H., Kuchen, H. (eds.) PLILP 1997. LNCS, vol. 1292, pp. 1–15. Springer, Heidelberg (1997)Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science 236(1–2), 133–178 (2000)Arts, T., Zantema, H.: Termination of Logic Programs Using Semantic Unification. In: Proietti, M. (ed.) LOPSTR 1995. LNCS, vol. 1048, pp. 219–233. Springer, Heidelberg (1996)Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press (1998)Bae, K., Escobar, S., Meseguer, J.: Abstract Logical Model Checking of Infinite-State Systems Using Narrowing. In: Proceedings of the 24th International Conference on Rewriting Techniques and Applications. LIPIcs, vol. 21, pp. 81–96. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)De Schreye, D., Glück, R., Jørgensen, J., Leuschel, M., Martens, B., Sørensen, M.: Conjunctive partial deduction: foundations, control, algorihtms, and experiments. Journal of Logic Programming 41(2&3), 231–277 (1999)Escobar, S., Meadows, C., Meseguer, J.: A rewriting-based inference system for the NRL Protocol Analyzer and its meta-logical properties. Theoretical Computer Science 367(1–2), 162–202 (2006)Escobar, S., Meseguer, J.: Symbolic Model Checking of Infinite-State Systems Using Narrowing. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 153–168. Springer, Heidelberg (2007)Fribourg, L.: SLOG: A Logic Programming Language Interpreter Based on Clausal Superposition and Rewriting. In: Proceedings of the Symposium on Logic Programming, pp. 172–185. IEEE Press (1985)Gnaedig, I., Kirchner, H.: Proving weak properties of rewriting. Theoretical Computer Science 412(34), 4405–4438 (2011)Hanus, M.: The integration of functions into logic programming: From theory to practice. Journal of Logic Programming 19&20, 583–628 (1994)Hanus, M. (ed.): Curry: An integrated functional logic language (vers. 0.8.3) (2012). http://www.curry-language.orgHermenegildo, M., Rossi, F.: On the Correctness and Efficiency of Independent And-Parallelism in Logic Programs. In: Lusk, E., Overbeck, R. (eds.) Proceedings of the 1989 North American Conf. on Logic Programming, pp. 369–389. The MIT Press, Cambridge (1989)Hölldobler, S. (ed.): Foundations of Equational Logic Programming. LNCS, vol. 353. Springer, Heidelberg (1989)Meseguer, J., Thati, P.: Symbolic Reachability Analysis Using Narrowing and its Application to Verification of Cryptographic Protocols. Electronic Notes in Theoretical Computer Science 117, 153–182 (2005)Middeldorp, A., Okui, S.: A Deterministic Lazy Narrowing Calculus. Journal of Symbolic Computation 25(6), 733–757 (1998)Nishida, N., Sakai, M., Sakabe, T.: Generation of Inverse Computation Programs of Constructor Term Rewriting Systems. IEICE Transactions on Information and Systems J88–D–I(8), 1171–1183 (2005) (in Japanese)Nishida, N., Sakai, M., Sakabe, T.: Partial Inversion of Constructor Term Rewriting Systems. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 264–278. Springer, Heidelberg (2005)Nishida, N., Vidal, G.: Program inversion for tail recursive functions. In: Schmidt-Schauß, M. (ed.) Proceedings of the 22nd International Conference on Rewriting Techniques and Applications. LIPIcs, vol. 10, pp. 283–298. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)Nishida, N., Vidal, G.: Computing More Specific Versions of Conditional Rewriting Systems. In: Albert, E. (ed.) LOPSTR 2012. LNCS, vol. 7844, pp. 137–154. Springer, Heidelberg (2013)Nutt, W., Réty, P., Smolka, G.: Basic Narrowing Revisited. Journal of Symbolic Computation 7(3/4), 295–317 (1989)Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, London, UK (2002)Palamidessi, C.: Algebraic Properties of Idempotent Substitutions. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 386–399. Springer, Heidelberg (1990)Ramos, J.G., Silva, J., Vidal, G.: Fast Narrowing-Driven Partial Evaluation for Inductively Sequential Systems. In: Danvy, O., Pierce, B.C. (eds.) Proceedings of the 10th ACM SIGPLAN International Conference on Functional Programming, pp. 228–239. ACM Press (2005)Slagle, J.R.: Automated theorem-proving for theories with simplifiers, commutativity and associativity. Journal of the ACM 21(4), 622–642 (1974