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

A Cost-Benefit Interpretation of the Substantially Similar Hurdle in the Congressional Review Act: Can OSHA Ever Utter the E-Word (Ergonomics) Again?

The Congressional Review Act permits Congress to veto proposed regulations via a joint resolution, and prohibits an agency from reissuing a rule “in substantially the same form” as the vetoed rule. Some scholars—and officials within the agencies themselves—have understood the “substantially the same” standard to bar an agency from regulating in the same substantive area covered by a vetoed rule. Courts have not yet provided an authoritative interpretation of the standard. This Article examines a spectrum of possible understandings of the standard, and relates them to the legislative history (of both the Congressional Review Act itself and the congressional veto of the Occupational Safety and Health Administration’s ergonomics rule), the statutory text, case law, and “good government” rationales. It concludes that the outlook is not as bleak as the agency officials and earlier scholarship predict: an agency may reissue a regulation in the same substantive area as a vetoed rule as long as the new rule has significantly greater benefits and/or significantly lower costs than the original rule. The Article then notes the practical implications for future rulemaking in the field of ergonomics, and closes with recommendations to amend the Congressional Review Act so as to better effect its underlying purpose

Quasi-exactly Solvable Lie Superalgebras of Differential Operators

In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional superalgebras whose odd subspace is nontrivial, we find those admitting a finite-dimensional invariant module of smooth vector-valued functions, and classify all the resulting finite-dimensional modules. The latter Lie superalgebras and their modules are the building blocks in the construction of QES quantum mechanical models for spin 1/2 particles in one dimension.Comment: LaTeX2e using the amstex and amssymb packages, 24 page

Safety verification of asynchronous pushdown systems with shaped stacks

In this paper, we study the program-point reachability problem of concurrent pushdown systems that communicate via unbounded and unordered message buffers. Our goal is to relax the common restriction that messages can only be retrieved by a pushdown process when its stack is empty. We use the notion of partially commutative context-free grammars to describe a new class of asynchronously communicating pushdown systems with a mild shape constraint on the stacks for which the program-point coverability problem remains decidable. Stacks that fit the shape constraint may reach arbitrary heights; further a process may execute any communication action (be it process creation, message send or retrieval) whether or not its stack is empty. This class extends previous computational models studied in the context of asynchronous programs, and enables the safety verification of a large class of message passing programs

Whole lifespan microscopic observation of budding yeast aging through a microfluidic dissection platform

Important insights into aging have been generated with the genetically tractable and short-lived budding yeast. However, it is still impossible today to continuously track cells by high-resolution microscopic imaging (e.g., fluorescent imaging) throughout their entire lifespan. Instead, the field still needs to rely on a 50-y-old laborious and time-consuming method to assess the lifespan of yeast cells and to isolate differentially aged cells for microscopic snapshots via manual dissection of daughter cells from the larger mother cell. Here, we are unique in achieving continuous and high-resolution microscopic imaging of the entire replicative lifespan of single yeast cells. Our microfluidic dissection platform features an optically prealigned single focal plane and an integrated array of soft elastomer-based micropads, used together to allow for trapping of mother cells, removal of daughter cells, monitoring gradual changes in aging, and unprecedented microscopic imaging of the whole aging process. Using the platform, we found remarkable age-associated changes in phenotypes (e.g., that cells can show strikingly differential cell and vacuole morphologies at the moment of their deaths), indicating substantial heterogeneity in cell aging and death. We envision the microfluidic dissection platform to become a major tool in aging research.

Beryllium-10 and Aluminum-26 in Individual Cosmic Spherules from Antarctica

We present data for the cosmogenic nuclides Be-10 and A-26 in a suite of 24 extraterrestrial spherules, collected from Antarctic moraines and deep sea sediments. All of the 10 large spherules collected in glacial till at Lewis Cliff are extraterrestrial. As in earlier work, the great majority of particles show prominent solar cosmic-ray (SCR) production of Al-26, indicating bombardment ages on the order of 106 years or even longer. These long ages are in direct contradiction to model ages for small particles in the inner Solar System and may require reconsideration of models of small particle lifetimes. A small fraction of the particles so far measured (6/42) possess cosmogenic radionuclide patterns consistent with predictions for meteoroid spall droplets. We believe that most of the spherules were bombarded in space primarily as bodies not much larger than their present size. The content of in situ produced Be-10 and Al-26 in quartz pebbles in the same moraine suggests that these spherules may have on average a significant terrestrial age

Homeomorphic Embedding for Online Termination of Symbolic Methods

Well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of techniques for program analysis, specialisation, transformation, and verification. In this paper we survey and discuss this use of homeomorphic embedding and clarify the advantages of such an approach over one using well-founded orders. We also discuss various extensions of the homeomorphic embedding relation. We conclude with a study of homeomorphic embedding in the context of metaprogramming, presenting some new (positive and negative) results and open problems

Phase Transition in a Random Fragmentation Problem with Applications to Computer Science

We study a fragmentation problem where an initial object of size x is broken into m random pieces provided x>x_0 where x_0 is an atomic cut-off. Subsequently the fragmentation process continues for each of those daughter pieces whose sizes are bigger than x_0. The process stops when all the fragments have sizes smaller than x_0. We show that the fluctuation of the total number of splitting events, characterized by the variance, generically undergoes a nontrivial phase transition as one tunes the branching number m through a critical value m=m_c. For m<m_c, the fluctuations are Gaussian where as for m>m_c they are anomalously large and non-Gaussian. We apply this general result to analyze two different search algorithms in computer science.Comment: 5 pages RevTeX, 3 figures (.eps

On the families of orthogonal polynomials associated to the Razavy potential

We show that there are two different families of (weakly) orthogonal polynomials associated to the quasi-exactly solvable Razavy potential V(x)=(\z \cosh 2x-M)^2 (\z>0, $M\in\mathbf N$). One of these families encompasses the four sets of orthogonal polynomials recently found by Khare and Mandal, while the other one is new. These results are extended to the related periodic potential U(x)=-(\z \cos 2x -M)^2, for which we also construct two different families of weakly orthogonal polynomials. We prove that either of these two families yields the ground state (when $M$ is odd) and the lowest lying gaps in the energy spectrum of the latter periodic potential up to and including the $(M-1)^{\rm th}$ gap and having the same parity as $M-1$. Moreover, we show that the algebraic eigenfunctions obtained in this way are the well-known finite solutions of the Whittaker--Hill (or Hill's three-term) periodic differential equation. Thus, the foregoing results provide a Lie-algebraic justification of the fact that the Whittaker--Hill equation (unlike, for instance, Mathieu's equation) admits finite solutions.Comment: Typeset in LaTeX2e using amsmath, amssymb, epic, epsfig, float (24 pages, 1 figure