The Complexity of Infinite Computations In Models of Set Theory

We prove the following surprising result: there exist a 1-counter B\"uchi automaton and a 2-tape B\"uchi automaton such that the \omega-language of the first and the infinitary rational relation of the second in one model of ZFC are \pi_2^0-sets, while in a different model of ZFC both are analytic but non Borel sets. This shows that the topological complexity of an \omega-language accepted by a 1-counter B\"uchi automaton or of an infinitary rational relation accepted by a 2-tape B\"uchi automaton is not determined by the axiomatic system ZFC. We show that a similar result holds for the class of languages of infinite pictures which are recognized by B\"uchi tiling systems. We infer from the proof of the above results an improvement of the lower bound of some decision problems recently studied by the author

On the level density of spin chains of Haldane--Shastry type

We provide a rigorous proof of the fact that the level density of all su(m) spin chains of Haldane-Shastry type associated with the A_{N-1} root system approaches a Gaussian distribution as the number of spins N tends to infinity. Our approach is based on the study of the large N limit of the characteristic function of the level density, using the description of the spectrum in terms of motifs and the asymptotic behavior of the dispersion relation.Comment: 6 pages, revte

A plan for the characterization, calibration, and evaluation of LAPR-2

A new airborne Linear Array Pushbroom Radiometer (LAPR-II) was built. LAPR-II will use linear arrays of silicon detectors to acquire four channels of digital image data for spectral bands within the visible and near infrared portions of the spectrum (0.4 - 1.0 micrometers). The data will be quantized to 10 bits, and spectral filters for each channel will be changeable in flight. The instrument will initially be flown aboard a NASA/Wallops' aircraft, and off nadir pointing of LAPR-II will be possible. Together, the instrument and its platform will provide a flexible readily available source of digital image data for scientific experiments. If LAPR-II is to serve as a precise scientific instrument, the instrument's characteristics must be quantitatively described and the data must be calibrated with respect to absolute radiometric units. The LAPR-II is described and the work required to characterize the instrument's spectral response, radiometric response, and spatial resolution and to calibrate the response from the many detectors per array is outlined

Rates of erosion and landscape change along the Blue Ridge escarpment, southern Appalachian Mountains, estimated from in situ cosmogenic 10Be

The Blue Ridge escarpment, located within the southern Appalachian Mountains of Virginia and North Carolina, forms a distinct, steep boundary between the lower-elevation Piedmont and higher-elevation Blue Ridge physiographic provinces. To understand better the rate at which this landform and the adjacent landscape are changing, we measured cosmogenic 10Be in quartz separated from sediment samples (n = 50) collected in thirty-two streams and from three exposed bedrock outcrops along four transects normal to the escarpment, allowing us to calculate erosion rates integrated over 104–105 years. These basin-averaged erosion rates (5.4–49 m My-1) are consistent with those measured elsewhere in the southern Appalachians and show a positive relationship between erosion rate and average basin slope. Erosion rates show no relationship with basin size or relative position of the Brevard fault zone, a fundamental structural element of the region. The cosmogenic isotopic data, when considered along with the distribution of average basin slopes in each physiographic province, suggest that the escarpment is eroding on average more rapidly than the Blue Ridge uplands, which are eroding more rapidly than the Piedmont lowlands. This difference in erosion rates by geomorphic setting suggests that the elevation difference between the uplands and lowlands adjacent to the escarpment is being reduced but at extremely slow rates

Approaching the Coverability Problem Continuously

The coverability problem for Petri nets plays a central role in the verification of concurrent shared-memory programs. However, its high EXPSPACE-complete complexity poses a challenge when encountered in real-world instances. In this paper, we develop a new approach to this problem which is primarily based on applying forward coverability in continuous Petri nets as a pruning criterion inside a backward coverability framework. A cornerstone of our approach is the efficient encoding of a recently developed polynomial-time algorithm for reachability in continuous Petri nets into SMT. We demonstrate the effectiveness of our approach on standard benchmarks from the literature, which shows that our approach decides significantly more instances than any existing tool and is in addition often much faster, in particular on large instances.Comment: 18 pages, 4 figure

Forward Analysis and Model Checking for Trace Bounded WSTS

We investigate a subclass of well-structured transition systems (WSTS), the bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete deterministic ones, which we claim provide an adequate basis for the study of forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth. Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered previously for the termination of forward analysis, boundedness is decidable. Boundedness turns out to be a valuable restriction for WSTS verification, as we show that it further allows to decide all $\omega$-regular properties on the set of infinite traces of the system

A New Algebraization of the Lame Equation

We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form. This yields, in a natural way, an explicit formula for both the Lame polynomials and the classical non-meromorphic Lame functions in terms of Chebyshev polynomials and of a certain family of weakly orthogonal polynomialsComment: Latex2e with AMS-LaTeX and cite packages; 32 page