Implicitly representing arrangements of lines or segments

Anarrangement ofn lines (or line segments) in the plane is the partition of the plane defined by these objects. Such an arrangement consists ofO(n ²) regions, calledfaces. In this paper we study the problem of calculating and storing arrangementsimplicitly, using subquadratic space and preprocessing, so that, given any query pointp, we can calculate efficiently the face containingp. First, we consider the case of lines and show that with (n) space¹ and (n ^3/2) preprocessing time, we can answer face queries in (n)+O(K) time, whereK is the output size. (The query time is achieved with high probability.) In the process, we solve three interesting subproblems: (1) given a set ofn points, find a straight-edge spanning tree of these points such that any line intersects only a few edges of the tree, (2) given a simple polygonal path , form a data structure from which we can find the convex hull of any subpath of quickly, and (3) given a set of points, organize them so that the convex hull of their subset lying above a query line can be found quickly. Second, using random sampling, we give a tradeoff between increasing space and decreasing query time. Third, we extend our structure to report faces in an arrangement of line segments in (n ^1/3)+O(K) time, given(n ^4/3) space and (n ^5/3) preprocessing time. Lastly, we note that our techniques allow us to computem faces in an arrangement ofn lines in time (m ^2/3 n ^2/3+n), which is nearly optimal.The first author is pleased to acknowledge the support of Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and National Science Foundation Grant CCR-8714565. Work on this paper by the fifth author has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant NSF-DCR-83-20085, by grants from the Digital Equipment Corporation, and the IBM Corporation, and by a research grant from the NCRD—the Israeli National Council for Research and Development. The sixth author was supported in part by a National Science Foundation Graduate Fellowship. This work was begun while the non-DEC authors were visiting at the DEC Systems Research Center.     

Windmill polynomials over fields of characteristic two

Chambers andSmeets [3] have designed a windmill arrangement of linear feedback shift registers (LFSRs) to generate pn-sequences overGF(2) with high speed. When the windmill hasv vanes, the associated minimal feedback polynomial (having degreen, relatively prime tov) can be taken to have the shapef ₁(x ^v )+x ⁿ f ₂(x ^–v ), where the polynomialsf ₁ andf ₂ have degree [n/v]. Their numerical evidence, whenv is divisible by 4, suggests that, surprisingly, there areno such windmill polynomials which are irreducible ifn±3 (mod 8), while about twice as many irreducible and primitive windmill polynomials as they expected occur ifn±1 (mod 8). A discussion of this behaviour is presented here with proofs. The brief explanation is that the Galois group of the underlying generic windmill polynomial overGF (4) is equal to the alternating groupA _n .     

A reliable two-dimensional gel electrophoresis procedure for separating neural proteins

A facile two-dimensional gel electrophoresis procedure has been developed for the analysis of neural tissue proteins which eliminates the serious problems associated with protein insolubility at the point of sample application onto polymerized first-dimension isoelectric focusing gels. This was accomplished by combining the methods of two previously published procedures. Our procedure provides an alternative method to the complex gel systems often employed for less soluble proteins, and yields very reproducible, high resolution separations. This procedure, which is in routine use in our laboratories for the analysis of total proteins extracted from retina and brain, produces protein patterns that are easily compared using both visual and computer-assisted image analysis techniques. Presented here are the results of a set of experiments designed to identify proteins unique to retina. This procedure should be useful to investigators studying protein changes resulting from genetic mutation, development, drug treatment or disease, in neural tissue as well as in virtually all other tissues.     

The mechanism of photoinduced acylation of amines by N-acyl-5,7-dinitroindoline as determined by time-resolved infrared spectroscopy

[reaction: see text] The photochemistry of N-acyl-5,7-dinitroindoline (1) was studied in acetonitrile using nanosecond time-resolved infrared (TRIR) spectroscopy. Upon photolysis, two nearly but not completely overlapping sets of transient IR bands are observed that are assigned to two non-interconvertible conformers of mixed acetic nitronic anhydride 7. While syn-7 reverts rapidly to 1, anti-7 is long-lived and is able to acylate amines. Results of density functional theory calculations support conclusions based on experimental TRIR data.     

Analyse de couches minces de verres chalcogenures par diffusion elastique de protons et mesure de gammas prompts

Résumé Une méthode d'étude de la composition stoéchiométrique de couches minces (10 à 500 μg/cm²) de verres chalcogénures est développée. L'étude des réactions nucléaire; induites par bombardement de protons de basse énergie (<4 MeV) sur les éléments constitutifs Ge, As, Te et S, conduit à choisir la diffusion élastique et la détection de gammas prompts pour le dosage simulatené. La précision et la sensibilité de la méthode sont discutées à partir des résultats obtenus. L'utilisation de la résonance fine sur le soufre (p, p'γ) est appliquée à l'étude de l'homogénéité des cibles.     

High-tech breakthrough DNA scanner for reading sequence and detecting gene mutation

The 17″×14″ X-ray film, gels, and blots are widely used in DNA research. However, DNA laser scanners are costly and unaffordable for the majority of surveyed biotech scientists who need it. The high-tech breakthrough analytical personal scanner (PS) presented in this report is an inexpensive 1 lb hand-held scanner priced at 2–4% of the bulky and costly 30–95 lb conventional laser scanners. This PS scanner is affordable from an operation budget and biotechnologists, who originate most science breakthroughs, can acquire it to enhance their speed, accuracy, and productivity. Compared to conventional laser scanners that are currently available only through hard-to-get capital-equipment budgets, the new PS scanner offers improved spatial resolution of 20 μm, higher speed (scan up to 17″×14″ molecular X-ray film in 48 s), 1–32,768 gray levels (16-bits), student routines, versatility, and, most important affordability. Its programs image the film, read DNA sequences automatically, and detect gene mutation. In parallel to the wide laboratory use of PC computers instead of mainframes, this PS scanner might become an integral part of a PC-PS powerful and cost-effective system where the PS performs the digital imaging and the PC acts on the data.     

An Eclipsed C(sp3)-CH3 Bond in a Crystalline Hydrated Tricyclic Orthoamide: Evidence for C?H…︁O hydrogen bonds

Accurate, low-temperature (81 K) X-ray analyses have been made for two crystalline modifications of the tricyclic orthoamide 1b : a cubic trihydrate in space group Pa3 (Z = 8), where the molecule has crystallographic threefold rotation symmetry, and an anhydrous monoclinic form in space group P2₁/c (Z = 8) where two symmetry-independent molecules have different configurations, one ail-trans. (as in the cubic trihydrate), the other cis, cis, trans. In the cubic trihydrate, each orthoamide molecule is attached to a triad of H₂o molecules by OH…?N H-bonds. A remarkable feature of this structure is the nearly eclipsed conformation about the central C-CH₃ bond. In the anhydrous crystal, both types of molecule have the normal staggered orientation of their Me groups. The reversal of the Me orientation in the trihydrate is attributed to C? H…?O H-bonding, which must be much stronger and more directionally specific than has been previously assumed.