Revisiting Synthesis for One-Counter Automata

We study the (parameter) synthesis problem for one-counter automata with parameters. One-counter automata are obtained by extending classical finite-state automata with a counter whose value can range over non-negative integers and be tested for zero. The updates and tests applicable to the counter can further be made parametric by introducing a set of integer-valued variables called parameters. The synthesis problem for such automata asks whether there exists a valuation of the parameters such that all infinite runs of the automaton satisfy some omega-regular property. Lechner showed that (the complement of) the problem can be encoded in a restricted one-alternation fragment of Presburger arithmetic with divisibility. In this work (i) we argue that said fragment, called AERPADPLUS, is unfortunately undecidable. Nevertheless, by a careful re-encoding of the problem into a decidable restriction of AERPADPLUS, (ii) we prove that the synthesis problem is decidable in general and in N2EXP for several fixed omega-regular properties. Finally, (iii) we give a polynomial-space algorithm for the special case of the problem where parameters can only be used in tests, and not updates, of the counter

Revisiting the contribution of transpiration to global terrestrial evapotranspiration

Even though knowing the contributions of transpiration (T), soil and open water evaporation (E), and interception (I) to terrestrial evapotranspiration (ET=T+E+I) is crucial for understanding the hydrological cycle and its connection to ecological processes, the fraction of T is unattainable by traditional measurement techniques over large scales. Previously reported global mean T/(E+T+I) from multiple independent sources, including satellite-based estimations, reanalysis, land surface models, and isotopic measurements, varies substantially from 24% to 90%. Here we develop a new ET partitioning algorithm, which combines global evapotranspiration estimates and relationships between leaf area index (LAI) and T/(E+T) for different vegetation types, to upscale a wide range of published site-scale measurements. We show that transpiration accounts for about 57.2% (with standard deviation6.8%) of global terrestrial ET. Our approach bridges the scale gap between site measurements and global model simulations,and can be simply implemented into current global climate models to improve biological CO2 flux simulations

Fruit and Fish: Alison Goodwin’s Reimaging of the Modernist Motif

Alison Goodwin’s painting Cantaloupe (2008) at first appears, perhaps naively, to depict a still life of fruit and flowers on a table: pomegranate, cantaloupe, sunflowers, and a drink. Beneath two rusty red and murky green lines, a diamond pattern demarcates the floor from the wall above. Next to the mottled green-and-red wall is a view through an open window. Three narrow houses lean precariously to the left; the windows are indicated, almost carelessly, by blocks of watery black paint. Two stylized trees with foliage shaped into bulbous spheres punctuate the row of buildings. Goodwin’s particular style, with its emphasis on a skewed perspective, flattened forms, and broadly applied colors, cannot—and should not—be read as unsophisticated or unknowing. Rather, Goodwin’s paintings reinterpret the work of some of the most important nineteenth- and early twentieth-century painters. She deliberately evokes the style and subjects of European modernists such as Henri Matisse, Paul Gauguin, and Vincent van Gogh. Each of her paintings recalls the implied formal tension between depicted three-dimensional space and the literal flatness of painted planes of color and stylized forms that her predecessors welcomed. Matisse, Cézanne, and others in the late nineteenth century rejected academic norms of picture making (painting realistically through modeling, shade, and one-point perspective). By revisiting these artists’ aesthetic, Goodwin complicates this historical progression and inserts her own mark onto the modernist (and particularly male-dominated) canon. [excerpt