Finite Frames and Graph Theoretic Uncertainty Principles

The subject of analytical uncertainty principles is an important field within harmonic analysis, quantum physics, and electrical engineering. We explore uncertainty principles in the context of the graph Fourier transform, and we prove additive results analogous to the multiplicative version of the classical uncertainty principle. We establish additive uncertainty principles for finite Parseval frames. Lastly, we examine the feasibility region of simultaneous values of the norms of a graph differential operator acting on a function $f\in l^2(G)$ and its graph Fourier transform

Ecological drift and competitive interactions predict unique patterns in temporal fluctuations of population size

Recent studies have highlighted the importance of higher-order competitive interactions in stabilizing population dynamics in multi-species communities. But how does the structure of competitive hierarchies affect population dynamics and extinction processes? We tackled this important question by using spatially explicit simulations of ecological drift (10 species in a homogeneous landscape of 64 patches) in which birth rates were influenced by interspecific competition. Specifically, we examined how transitive (linear pecking orders) and intransitive (pecking orders with loops) competitive hierarchies affected extinction rates and population dynamics in simulated communities through time. In comparison to a pure neutral model, an ecological drift model including transitive competition increased extinction rates, caused synchronous density-dependent population fluctuations, and generated a white-noise distribution of population sizes. In contrast, the drift model with intransitive competitive interactions decreased extinctions rates, caused asynchronous (compensatory) density-dependent population fluctuations, and generated a brown noise distribution of population sizes. We also explored the effect on community stability of more complex patterns of competitive interactions in which pairwise competitive relationships were assigned probabilistically. These probabilistic competition models also generated density-dependent trajectories and a brown noise distribution of population sizes. However, extinction rates and the degree of population synchrony were comparable to those observed in purely neutral communities. Collectively, our results confirm that intransitive competition has a strong and stabilizing effect on local populations in species-poor communities. This effect wanes with increasing species richness. Empirical assemblages characterized by brown spectral noise, density-dependent regulation, and asynchronous (compensatory) population fluctuations may indicate a signature of intransitive competitive interactions

TRX: A Formally Verified Parser Interpreter

Parsing is an important problem in computer science and yet surprisingly little attention has been devoted to its formal verification. In this paper, we present TRX: a parser interpreter formally developed in the proof assistant Coq, capable of producing formally correct parsers. We are using parsing expression grammars (PEGs), a formalism essentially representing recursive descent parsing, which we consider an attractive alternative to context-free grammars (CFGs). From this formalization we can extract a parser for an arbitrary PEG grammar with the warranty of total correctness, i.e., the resulting parser is terminating and correct with respect to its grammar and the semantics of PEGs; both properties formally proven in Coq.Comment: 26 pages, LMC

Trichloroethylene Exposure during Cardiac Valvuloseptal Morphogenesis Alters Cushion Formation and Cardiac Hemodynamics in the Avian Embryo

It is controversial whether trichloroethylene (TCE) is a cardiac teratogen. We exposed chick embryos to 0, 0.4, 8, or 400 ppb TCE/egg during the period of cardiac valvuloseptal morphogenesis (2–3.3 days’ incubation). Embryo survival, valvuloseptal cellularity, and cardiac hemodynamics were evaluated at times thereafter. TCE at 8 and 400 ppb/egg reduced embryo survival to day 6.25 incubation by 40–50%. At day 4.25, increased proliferation and hypercellularity were observed within the atrioventricular and outflow tract primordia after 8 and 400 ppb TCE. Doppler ultrasound revealed that the dorsal aortic and atrioventricular blood flows were reduced by 23% and 30%, respectively, after exposure to 8 ppb TCE. Equimolar trichloroacetic acid (TCA) was more potent than TCE with respect to increasing mortality and causing valvuloseptal hypercellularity. These results independently confirm that TCE disrupts cardiac development of the chick embryo and identifies valvuloseptal development as a period of sensitivity. The hypercellular valvuloseptal profile is consistent with valvuloseptal heart defects associated with TCE exposure. This is the first report that TCA is a cardioteratogen for the chick and the first report that TCE exposure depresses cardiac function. Valvuloseptal hypercellularity may narrow the cardiac orifices, which reduces blood flow through the heart, thereby compromising cardiac output and contributing to increased mortality. The altered valvuloseptal formation and reduced hemodynamics seen here are consistent with such an outcome. Notably, these effects were observed at a TCE exposure (8 ppb) that is only slightly higher than the U.S. Environmental Protection Agency maximum containment level for drinking water (5 ppb)

Reducing relative termination to dependency pair problems

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-21401-6_11Relative termination, a generalized notion of termination, has been used in a number of different contexts like proving the confluence of rewrite systems or analyzing the termination of narrowing. In this paper, we introduce a new technique to prove relative termination by reducing it to dependency pair problems. To the best of our knowledge, this is the first significant contribution to Problem #106 of the RTA List of Open Problems. The practical significance of our method is illustrated by means of an experimental evaluation.Germán Vidal is partially supported by the EU (FEDER) and the Spanish Ministerio de Economía y Competitividad under grant TIN2013-44742-C4-R and by the Generalitat Valenciana under grant PROMETEOII201/013. Akihisa Yamadais supported by the Austrian Science Fund (FWF): Y757Iborra, J.; Nishida, N.; Vidal Oriola, GF.; Yamada, A. (2015). Reducing relative termination to dependency pair problems. En Automated Deduction - CADE-25. Springer. 163-178. https://doi.org/10.1007/978-3-319-21401-6_11S163178Alarcón, B., Lucas, S., Meseguer, J.: A dependency pair framework for A $$\vee$$ C-termination. In: Ölveczky, P.C. (ed.) WRLA 2010. LNCS, vol. 6381, pp. 35–51. Springer, Heidelberg (2010)Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theor. Comput. Sci. 236(1–2), 133–178 (2000)Arts, T., Giesl, J.: A collection of examples for termination of term rewriting using dependency pairs. Technical report AIB-2001-09, RWTH Aachen (2001)Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)Dershowitz, N.: Termination of rewriting. J. Symb. Comput. 3(1&2), 69–115 (1987)Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. J. Autom. Reasoning 40(2–3), 195–220 (2008)Geser, A.: Relative termination. Dissertation, Fakultät für Mathematik und Informatik, Universität Passau, Germany (1990)Giesl, J., Kapur, D.: Dependency pairs for equational rewriting. In: Middeldorp, A. (ed.) RTA 2001. LNCS, vol. 2051, pp. 93–107. Springer, Heidelberg (2001)Giesl, J., Schneider-Kamp, P., Thiemann, R.: AProVE 1.2: automatic termination proofs in the dependency pair framework. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 281–286. Springer, Heidelberg (2006)Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing and improving dependency pairs. J. Autom. Reasoning 37(3), 155–203 (2006)Hirokawa, N., Middeldorp, A.: Polynomial interpretations with negative coefficients. In: Buchberger, B., Campbell, J. (eds.) AISC 2004. LNCS (LNAI), vol. 3249, pp. 185–198. Springer, Heidelberg (2004)Hirokawa, N., Middeldorp, A.: Dependency pairs revisited. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 249–268. Springer, Heidelberg (2004)Hirokawa, N., Middeldorp, A.: Decreasing diagrams and relative termination. J. Autom. Reasoning 47(4), 481–501 (2011)Hullot, J.M.: Canonical forms and unification. CADE-5. LNCS, vol. 87, pp. 318–334. Springer, Heidelberg (1980)Iborra, J., Nishida, N., Vidal, G.: Goal-directed and relative dependency pairs for proving the termination of narrowing. In: De Schreye, D. (ed.) LOPSTR 2009. LNCS, vol. 6037, pp. 52–66. Springer, Heidelberg (2010)Kamin, S., Lévy, J.J.: Two generalizations of the recursive path ordering (1980, unpublished note)Klop, J.W.: Term rewriting systems: a tutorial. Bull. Eur. Assoc. Theor. Comput. Sci. 32, 143–183 (1987)Koprowski, A., Zantema, H.: Proving liveness with fairness using rewriting. In: Gramlich, B. (ed.) FroCos 2005. LNCS (LNAI), vol. 3717, pp. 232–247. Springer, Heidelberg (2005)Koprowski, A.: TPA: termination proved automatically. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 257–266. Springer, Heidelberg (2006)Korp, M., Sternagel, C., Zankl, H., Middeldorp, A.: Tyrolean termination tool 2. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 295–304. Springer, Heidelberg (2009)Lankford, D.: Canonical algebraic simplification in computational logic. Technical report ATP-25, University of Texas (1975)Liu, J., Dershowitz, N., Jouannaud, J.-P.: Confluence by critical pair analysis. In: Dowek, G. (ed.) RTA-TLCA 2014. LNCS, vol. 8560, pp. 287–302. Springer, Heidelberg (2014)Nishida, N., Sakai, M., Sakabe, T.: Narrowing-based simulation of term rewriting systems with extra variables. ENTCS 86(3), 52–69 (2003)Nishida, N., Vidal, G.: Termination of narrowing via termination of rewriting. Appl. Algebra Eng. Commun. Comput. 21(3), 177–225 (2010)Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer-Verlag, London (2002)Thiemann, R., Allais, G., Nagele, J.: On the formalization of termination techniques based on multiset orderings. In: RTA 2012. LIPIcs, vol. 15, pp. 339–354. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)Vidal, G.: Termination of narrowing in left-linear constructor systems. In: Garrigue, J., Hermenegildo, M.V. (eds.) FLOPS 2008. LNCS, vol. 4989, pp. 113–129. Springer, Heidelberg (2008)Yamada, A., Kusakari, K., Sakabe, T.: Nagoya termination tool. In: Dowek, G. (ed.) RTA-TLCA 2014. LNCS, vol. 8560, pp. 466–475. Springer, Heidelberg (2014)Yamada, A., Kusakari, K., Sakabe, T.: A unified ordering for termination proving. Sci. Comput. Program. (2014). doi: 10.1016/j.scico.2014.07.009Zantema, H.: Termination of term rewriting by semantic labelling. Fundamenta Informaticae 24(1/2), 89–105 (1995)Zantema, H.: Termination. In: Bezem, M., Klop, J.W., de Vrijer, R. (eds.) Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55, pp. 181–259. Cambridge University Press, Cambridge (2003

Timing of Resource Availability Drives Divergent Social Systems and Home Range Dynamics in Ecologically Similar Tree Squirrels

Intraspecific variation in home range size has important implications for the distribution of animals across landscapes and the spatial structuring of population, community, and ecosystem processes. Among species of similar trophic guild and body mass, differences in home range size can reflect extrinsic variables that exert divergent selective forces upon spacing behavior and social organization. We tested predictions about how resource availability and timing influence social system, home range size, and territoriality in two tree squirrel species of similar size and ecological niches but that differ in foraging strategy and social organization. We estimated home range size and intraspecific home range core overlap in the Mt. Graham red squirrel (Tamiasciurus fremonti grahamensis; Arizona USA; MGRS) and the Eurasian red squirrel (Sciurus vulgaris; Alps, Italy; ERS) as functions of species, sex, season, and individual's body mass. However, body mass did not explain differences found between the two species. We found MGRS home ranges being three times smaller with higher core area exclusivity compared to ERS in all seasons. In fact, territorial MGRS evolved in a system of brief resource pulses and are larder hoarders, whereas ERS experience prolonged resource availability and are non-territorial. Only male MGRSs increased their home range during the breeding season, reflecting interspecific differences in social organization and mating behavior. Male ERS home ranges always overlap with several females to enhance mating success although male and female MGRS maintain nearly exclusive territories throughout the year. Only during spring and summer do males temporarily leave their food-based territory to increase mating opportunities with neighboring estrus females. Home range comparisons between ecologically similar species emphasize the importance of divergent extrinsic factors in shaping variability in body size–home range size scaling relationships. Timing in resource availability influenced the social structure and space use in tree squirrels of similar body size, highlighting how the coevolution of arboreal squirrels with conifer tree species has shaped their natural history

Comparative Study of Anterior Eye Segment Measurements with Spectral Swept-Source and Time-Domain Optical Coherence Tomography in Eyes with Corneal Dystrophies

Purpose. To compare anterior eye segment measurements and morphology obtained with two optical coherence tomography systems (TD OCT, SS OCT) in eyes with corneal dystrophies (CDs). Methods. Fifty healthy volunteers (50 eyes) and 54 patients (96 eyes) diagnosed with CD (epithelial basement membrane dystrophy, EBMD = 12 eyes; Thiel-Behnke CD = 6 eyes; lattice CD TGFBI type = 15 eyes; granular CD type 1 = 7 eyes, granular CD type 2 = 2 eyes; macular CD = 23 eyes; and Fuchs endothelial CD = 31 eyes) were recruited for the study. Automated and manual central corneal thickness (aCCT, mCCT), anterior chamber depth (ACD), and nasal and temporal trabecular iris angle (nTIA, tTIA) were measured and compared with Bland-Altman plots. Results. Good agreement between the TD and SS OCT measurements was demonstrated for mCCT and aCCT in normal individuals and for mCCT in the CDs group. The ACD, nTIA, and tTIA measurements differed significantly in both groups. TBCD, LCD, and FECD caused increased CCT. MCD caused significant corneal thinning. FECD affected all analyzed parameters. Conclusions. Better agreement between SS OCT and TD OCT measurements was demonstrated in normal individuals compared to the CDs group. OCT provides comprehensive corneal deposits analysis and demonstrates the association of CD with CCT, ACD, and TIA measurements