Algebraic properties of generalized Rijndael-like ciphers

We provide conditions under which the set of Rijndael functions considered as permutations of the state space and based on operations of the finite field \GF (p^k) ($p\geq 2$ a prime number) is not closed under functional composition. These conditions justify using a sequential multiple encryption to strengthen the AES (Rijndael block cipher with specific block sizes) in case AES became practically insecure. In Sparr and Wernsdorf (2008), R. Sparr and R. Wernsdorf provided conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field \GF (2^k) is equal to the alternating group on the state space. In this paper we provide conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field \GF (p^k) ($p\geq 2$) is equal to the symmetric group or the alternating group on the state space.Comment: 22 pages; Prelim0

Elliptic Reciprocity

The paper introduces the notions of an elliptic pair, an elliptic cycle and an elliptic list over a square free positive integer d. These concepts are related to the notions of amicable pairs of primes and aliquot cycles that were introduced by Silverman and Stange. Settling a matter left open by Silverman and Stange it is shown that for d=3 there are elliptic cycles of length 6. For d not equal to 3 the question of the existence of proper elliptic lists of length n over d is reduced to the the theory of prime producing quadratic polynomials. For d=163 a proper elliptic list of length 40 is exhibited. It is shown that for each d there is an upper bound on the length of a proper elliptic list over d. The final section of the paper contains heuristic arguments supporting conjectured asymptotics for the number of elliptic pairs below integer X. Finally, for d congruent to 3 modulo 8 the existence of infinitely many anomalous prime numbers is derived from Bunyakowski's Conjecture for quadratic polynomials.Comment: 17 pages, including one figure and two table

Engineering Disulfide Cross‐Links in RNA Using Thiol‐Disulfide Interchange Chemistry

Protocols for postsynthetic modification of 2‐amino‐containing oligoribonucleotides with either an alkyl‐phenyl disulfide or an alkyl thiol group are described. These groups react under mild conditions to form disulfide cross‐links by thiol‐disulfide interchange. These reactants do not form a disulfide bond when incorporated on opposite faces of a short continuous RNA helix, but do form disulfide bonds rapidly when they are placed in proximity. In addition, by incorporating these groups at various positions on large RNAs by semisynthesis, the dynamics of thermal motions can be detected. Such motions are believed to be linked to biological function, and the protocols presented in this unit are among the few simple ways to assess such dynamics.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143724/1/cpnc0501.pd

Arp 65 interaction debris: massive HI displacement and star formation

Context: Pre-merger interactions between galaxies can induce significant changes in the morphologies and kinematics of the stellar and ISM components. Large amounts of gas and stars are often found to be disturbed or displaced as tidal debris. This debris then evolves, sometimes forming stars and occasionally tidal dwarf galaxies. Here we present results from our HI study of Arp 65, an interacting pair hosting extended HI tidal debris. Aims: In an effort to understand the evolution of tidal debris produced by interacting pairs of galaxies, including in situ star and tidal dwarf galaxy formation, we are mapping HI in a sample of interacting galaxy pairs. The Arp 65 pair is one of them. Methods: Our resolved HI 21 cm line survey is being carried out using the Giant Metrewave Radio Telescope (GMRT). We used our HI survey data as well as available SDSS optical, Spitzer infra-red and GALEX UV data to study the evolution of the tidal debris and the correlation of HI with the star-forming regions within it. Results: In Arp 65 we see a high impact pre-merger interaction involving a pair of massive galaxies (NGC 90 and NGC 93) that have a stellar mass ratio of ~ 1:3. The interaction, which probably occurred ~ 1.0 -- 2.5 $\times$ 10$^8$ yr ago, appears to have displaced a large fraction of the HI in NGC 90 (including the highest column density HI) beyond its optical disk. We also find extended ongoing star formation in the outer disk of NGC 90. In the major star-forming regions, we find the HI column densities to be ~ 4.7 $\times$ 10$^{20}$ cm$^{-2}$ or lower. But no signature of star formation was found in the highest column density HI debris, SE of NGC 90. This indicates conditions within the highest column density HI debris remain hostile to star formation and it reaffirms that high HI column densities may be a necessary but not sufficient criterion for star formation.Comment: Accepted in A&

Coexpression of rat P2X2 and P2X6 subunits in Xenopus oocytes.

Transcripts for P2X(2) and P2X(6) subunits are present in rat CNS and frequently colocalize in the same brainstem nuclei. When rat P2X(2) (rP2X(2)) and rat P2X(6) (rP2X(6)) receptors were expressed individually in Xenopus oocytes and studied under voltage-clamp conditions, only homomeric rP2X(2) receptors were fully functional and gave rise to large inward currents (2-3 microA) to extracellular ATP. Coexpression of rP2X(2) and rP2X(6) subunits in Xenopus oocytes resulted in a heteromeric rP2X(2/6) receptor, which showed a significantly different phenotype from the wild-type rP2X(2) receptor. Differences included reduction in agonist potencies and, in some cases (e.g., Ap(4)A), significant loss of agonist activity. ATP-evoked inward currents were biphasic at the heteromeric rP2X(2/6) receptor, particularly when Zn(2+) ions were present or extracellular pH was lowered. The pH range was narrower for H(+) enhancement of ATP responses at the heteromeric rP2X(2/6) receptor. Also, H(+) ions inhibited ATP responses at low pH levels (<pH 6.3). The pH-dependent blocking activity of suramin was changed at this heteromeric receptor, although the potentiating effect of Zn(2+) on ATP responses was unchanged. Thus, the rP2X(2/6) receptor is a functionally modified P2X(2)-like receptor with a distinct pattern of pH modulation of ATP activation and suramin blockade. Although homomeric P2X(6) receptors function poorly, the P2X(6) subunit can contribute to functional heteromeric P2X channels and may influence the phenotype of native P2X receptors in those cells in which it is expressed

A novel role for the CBF3 kinetochore–scaffold complex in regulating septin dynamics and cytokinesis

In budding yeast, the kinetochore scaffold complex centromere binding factor 3 (CBF3) is required to form kinetochores on centromere DNA and to allow proper chromosome segregation. We have previously shown that SKP1 and SGT1 balance the assembly and turnover of CBF3 complexes, a cycle that we suggest is independent of its role in chromosome segregation (Rodrigo-Brenni, M.C., S. Thomas, D.C. Bouck, and K.B. Kaplan. 2004. Mol. Biol. Cell. 15:3366–3378). We provide evidence that this cycle contributes to a second, kinetochore-independent function of CBF3. In this study, we show that inhibiting the assembly of CBF3 causes disorganized septins and defects in cell polarity that give rise to cytokinesis failures. Specifically, we show that septin ring separation and disassembly is delayed in anaphase, suggesting that CBF3 regulates septin dynamics. Only mutations that affect the CBF3 cycle, and not mutants in outer kinetochore subunits, cause defects in septins. These results demonstrate a novel role for CBF3 in regulating cytokinesis, a role that is reminiscent of passenger proteins. Consistent with this possibility, we find that CBF3 interacts with Bir1p, the homologue of the passenger protein Survivin. Mutants in Bir1p similarly affect septin organization, leading us to propose that CBF3 and Bir1p act as passenger proteins to coordinate chromosome segregation with cytokinesis

Spitzer Phase Curves of KELT-1b and the Signatures of Nightside Clouds in Thermal Phase Observations

We observed two full orbital phase curves of the transiting brown dwarf KELT-1b, at 3.6um and 4.5um, using the Spitzer Space Telescope. Combined with previous eclipse data from Beatty et al. (2014), we strongly detect KELT-1b's phase variation as a single sinusoid in both bands, with amplitudes of $964\pm36$ ppm at 3.6um and $979\pm54$ ppm at 4.5um, and confirm the secondary eclipse depths measured by Beatty et al. (2014). We also measure noticeable Eastward hotspot offsets of $28.4\pm3.5$ degrees at 3.6um and $18.6\pm5.2$ degrees at 4.5um. Both the day-night temperature contrasts and the hotspot offsets we measure are in line with the trends seen in hot Jupiters (e.g., Crossfield 2015), though we disagree with the recent suggestion of an offset trend by Zhang et al. (2018). Using an ensemble analysis of Spitzer phase curves, we argue that nightside clouds are playing a noticeable role in modulating the thermal emission from these objects, based on: 1) the lack of a clear trend in phase offsets with equilibrium temperature, 2) the sharp day-night transitions required to have non-negative intensity maps, which also resolves the inversion issues raised by Keating & Cowan (2017), 3) the fact that all the nightsides of these objects appear to be at roughly the same temperature of 1000K, while the dayside temperatures increase linearly with equilibrium temperature, and 4) the trajectories of these objects on a Spitzer color-magnitude diagram, which suggest colors only explainable via nightside clouds.Comment: AJ in press. Updated to reflect the accepted versio