Tabulation of cubic function fields via polynomial binary cubic forms

We present a method for tabulating all cubic function fields over $\mathbb{F}_q(t)$ whose discriminant $D$ has either odd degree or even degree and the leading coefficient of $-3D$ is a non-square in $\mathbb{F}_{q}^*$, up to a given bound $B$ on the degree of $D$. Our method is based on a generalization of Belabas' method for tabulating cubic number fields. The main theoretical ingredient is a generalization of a theorem of Davenport and Heilbronn to cubic function fields, along with a reduction theory for binary cubic forms that provides an efficient way to compute equivalence classes of binary cubic forms. The algorithm requires $O(B^4 q^B)$ field operations as $B \rightarrow \infty$. The algorithm, examples and numerical data for $q=5,7,11,13$ are included.Comment: 30 pages, minor typos corrected, extra table entries added, revamped complexity analysis of the algorithm. To appear in Mathematics of Computatio

Removable Weak Keys for Discrete Logarithm Based Cryptography

We describe a novel type of weak cryptographic private key that can exist in any discrete logarithm based public-key cryptosystem set in a group of prime order $p$ where $p-1$ has small divisors. Unlike the weak private keys based on \textit{numerical size} (such as smaller private keys, or private keys lying in an interval) that will \textit{always} exist in any DLP cryptosystems, our type of weak private keys occurs purely due to parameter choice of $p$, and hence, can be removed with appropriate value of $p$. Using the theory of implicit group representations, we present algorithms that can determine whether a key is weak, and if so, recover the private key from the corresponding public key. We analyze several elliptic curves proposed in the literature and in various standards, giving counts of the number of keys that can be broken with relatively small amounts of computation. Our results show that many of these curves, including some from standards, have a considerable number of such weak private keys. We also use our methods to show that none of the 14 outstanding Certicom Challenge problem instances are weak in our sense, up to a certain weakness bound

The Deglaciation of Maine, USA

The glacial geology of Maine records the northward recession of the Late Wisconsinan Laurentide Ice Sheet, followed by development of a residual ice cap in the Maine-Québec border region due to marine transgression of the St. Lawrence Lowland in Canada. The pattern of deglaciation across southern Maine has been reconstructed from numerous end moraines, deltas and submarine fans deposited during marine transgression of the coastal lowland. Inland from the marine limit, a less-detailed sequence of deglaciation is recorded by striation patterns, meltwater channels, scattered moraines and waterlain deposits that constrain the trend of the ice margin. There is no evidence that the northern Maine ice cap extended as far south-west as the Boundary Mountains and New Hampshire border. Newly-obtained radiocarbon ages from marine and terrestrial ice-proximal environments have improved the chronology of glacial recession in Maine. Many of these ages were obtained by coring late-glacial sediments beneath ponds and lakes. Data from this study show that the state was deglaciated between about 14.5 and 11.0 ka BP (14C years). The coastal moraine belt in southern Maine was deposited by oscillatory ice-margin retreat during the cold pre-Bølling time. Rapid ice recession to northern Maine then occurred between 13 and 11 ka BP, during the warmer Bølling/Allerød chronozones. Radiocarbon-dated pond sediments in western and northern Maine show lithologic evidence of Younger Dryas climatic cooling and persistence of the northern ice cap into Younger Dryas time. A large discrepancy still exists between radiocarbon ages of deglaciation in coastal south-western Maine and the timing of ice retreat indicated by New England varve records in areas to the west. Part of this problem may stem from the uncertainty of reservoir corrections applied to the radiocarbon ages of marine organics

Functionalized Congeners of P2Y 1 Receptor Antagonists: 2-Alkynyl ( N )-Methanocarba 2′-Deoxyadenosine 3′,5′-Bisphosphate Analogues and Conjugation to a Polyamidoamine (PAMAM) Dendrimer Carrier

The P2Y1 receptor is a prothrombotic G protein-coupled receptor (GPCR) activated by ADP. Preference for the North (N) ring conformation of the ribose moiety of adenine nucleotide 3′,5′-bisphosphate antagonists of the P2Y1 receptor was established by using a ring-constrained methanocarba (a bicyclo[3.1.0]hexane) ring as a ribose substitute. A series of covalently linkable N6-methyl-(N)-methanocarba-2′-deoxyadenosine-3′,5′-bisphosphates containing extended 2-alkynyl chains was designed and binding affinity at the human (h) P2Y1 receptor determined. The chain of these functionalized congeners contained hydrophilic moieties, a reactive substituent, or biotin, linked via an amide. Variation of the chain length and position of an intermediate amide group revealed high affinity of carboxylic congener 8 (Ki 23 nM) and extended amine congener 15 (Ki 132 nM), both having a 2-(1-pentynoyl) group. A biotin conjugate 18 containing an extended ε-aminocaproyl spacer chain exhibited higher affinity than a shorter biotinylated analogue. Alternatively, click coupling of terminal alkynes of homologous 2-dialkynyl nucleotide derivatives to alkyl azido groups produced triazole derivatives that bound to the P2Y1 receptor following deprotection of the bisphosphate groups. The preservation of receptor affinity of the functionalized congeners was consistent with new P2Y1 receptor modeling and ligand docking. Attempted P2Y1 antagonist conjugation to PAMAM dendrimer carriers by amide formation or palladium-catalyzed reaction between an alkyne on the dendrimer and a 2-iodopurine-derivatized nucleotide was unsuccessful. A dialkynyl intermediate containing the chain length favored in receptor binding was conjugated to an azide-derivatized dendrimer, and the conjugate inhibited ADP-promoted human platelet aggregation. This is the first example of attaching a strategically functionalized P2Y receptor antagonist to a PAMAM dendrimer to produce a multivalent conjugate exhibiting a desired biological effect, i.e. antithrombotic action

The Atacama Cosmology Telescope: Cosmological parameters from three seasons of data

We present constraints on cosmological and astrophysical parameters from high-resolution microwave background maps at 148 GHz and 218 GHz made by the Atacama Cosmology Telescope (ACT) in three seasons of observations from 2008 to 2010. A model of primary cosmological and secondary foreground parameters is fit to the map power spectra and lensing deflection power spectrum, including contributions from both the thermal Sunyaev-Zeldovich (tSZ) effect and the kinematic Sunyaev-Zeldovich (kSZ) effect, Poisson and correlated anisotropy from unresolved infrared sources, radio sources, and the correlation between the tSZ effect and infrared sources. The power ell^2 C_ell/2pi of the thermal SZ power spectrum at 148 GHz is measured to be 3.4 +\- 1.4 muK^2 at ell=3000, while the corresponding amplitude of the kinematic SZ power spectrum has a 95% confidence level upper limit of 8.6 muK^2. Combining ACT power spectra with the WMAP 7-year temperature and polarization power spectra, we find excellent consistency with the LCDM model. We constrain the number of effective relativistic degrees of freedom in the early universe to be Neff=2.79 +\- 0.56, in agreement with the canonical value of Neff=3.046 for three massless neutrinos. We constrain the sum of the neutrino masses to be Sigma m_nu < 0.39 eV at 95% confidence when combining ACT and WMAP 7-year data with BAO and Hubble constant measurements. We constrain the amount of primordial helium to be Yp = 0.225 +\- 0.034, and measure no variation in the fine structure constant alpha since recombination, with alpha/alpha0 = 1.004 +/- 0.005. We also find no evidence for any running of the scalar spectral index, dns/dlnk = -0.004 +\- 0.012.Comment: 26 pages, 22 figures. This paper is a companion to Das et al. (2013) and Dunkley et al. (2013). Matches published JCAP versio

High-Frequency (>100 GHz) and High-Speed (<1 ps) Electronic Devices

Contains an introduction, reports on three research projects and a list of publications.Advanced Research Projects Agency Contract MDA972-90-C-0021National Aeronautics and Space Administration Grant NAG2-693National Aeronautics and Space Administration Contract 959705National Science Foundation/MRSEC Grant DMR 94-00334MIT Lincoln Laboratory Advanced Concept Program Contract BX-5464MIT Research Laboratory of Electronics Postdoctoral FellowshipRome Air Force Laboratory Graduate FellowshipU.S. Army Research Office Grant DAAL03-92-G-0251Hertz Foundation FellowshipU.S. Army Research Office/ASSERT Grant DAAH04-94-G-016