On sets of irreducible polynomials closed by composition

Let $\mathcal S$ be a set of monic degree $2$ polynomials over a finite field and let $C$ be the compositional semigroup generated by $\mathcal S$. In this paper we establish a necessary and sufficient condition for $C$ to be consisting entirely of irreducible polynomials. The condition we deduce depends on the finite data encoded in a certain graph uniquely determined by the generating set $\mathcal S$. Using this machinery we are able both to show examples of semigroups of irreducible polynomials generated by two degree $2$ polynomials and to give some non-existence results for some of these sets in infinitely many prime fields satisfying certain arithmetic conditions

Algorithms for zero-dimensional ideals using linear recurrent sequences

Inspired by Faug\`ere and Mou's sparse FGLM algorithm, we show how using linear recurrent multi-dimensional sequences can allow one to perform operations such as the primary decomposition of an ideal, by computing the annihilator of one or several such sequences.Comment: LNCS, Computer Algebra in Scientific Computing CASC 201

An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups

Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in extraspecial groups. Our approach is quite different from the recent algorithms presented in [17] and [2] for the Heisenberg group, the extraspecial p-group of size p3 and exponent p. Exploiting certain nice automorphisms of the extraspecial groups we define specific group actions which are used to reduce the problem to hidden subgroup instances in abelian groups that can be dealt with directly.Comment: 10 page

Self-consistent theory of reversible ligand binding to a spherical cell

In this article, we study the kinetics of reversible ligand binding to receptors on a spherical cell surface using a self-consistent stochastic theory. Binding, dissociation, diffusion and rebinding of ligands are incorporated into the theory in a systematic manner. We derive explicitly the time evolution of the ligand-bound receptor fraction p(t) in various regimes . Contrary to the commonly accepted view, we find that the well-known Berg-Purcell scaling for the association rate is modified as a function of time. Specifically, the effective on-rate changes non-monotonically as a function of time and equals the intrinsic rate at very early as well as late times, while being approximately equal to the Berg-Purcell value at intermediate times. The effective dissociation rate, as it appears in the binding curve or measured in a dissociation experiment, is strongly modified by rebinding events and assumes the Berg-Purcell value except at very late times, where the decay is algebraic and not exponential. In equilibrium, the ligand concentration everywhere in the solution is the same and equals its spatial mean, thus ensuring that there is no depletion in the vicinity of the cell. Implications of our results for binding experiments and numerical simulations of ligand-receptor systems are also discussed.Comment: 23 pages with 4 figure

A solvable model for the diffusion and reaction of neurotransmitters in a synaptic junction

<p>Abstract</p> <p>Background</p> <p>The diffusion and reaction of the transmitter acetylcholine in neuromuscular junctions and the diffusion and binding of Ca²⁺in the dyadic clefts of ventricular myocytes have been extensively modeled by Monte Carlo simulations and by finite-difference and finite-element solutions. However, an analytical solution that can serve as a benchmark for testing these numerical methods has been lacking.</p> <p>Result</p> <p>Here we present an analytical solution to a model for the diffusion and reaction of acetylcholine in a neuromuscular junction and for the diffusion and binding of Ca²⁺in a dyadic cleft. Our model is similar to those previously solved numerically and our results are also qualitatively similar.</p> <p>Conclusion</p> <p>The analytical solution provides a unique benchmark for testing numerical methods and potentially provides a new avenue for modeling biochemical transport.</p

The Study of TeV Variability and Duty Cycle of Mrk 421 from 3 Years of Observations with the Milagro Observatory

TeV flaring activity with time scales as short as tens of minutes and an orphan TeV flare have been observed from the blazar Markarian 421 (Mrk 421). The TeV emission from Mrk 421 is believed to be produced by leptonic synchrotron self-Compton (SSC) emission. In this scenario, correlations between the X-ray and the TeV fluxes are expected, TeV orphan flares are hardly explained and the activity (measured as duty cycle) of the source at TeV energies is expected to be equal or less than that observed in X-rays if only SSC is considered. To estimate the TeV duty cycle of Mrk 421 and to establish limits on its variability at different time scales, we continuously observed Mrk 421 with the Milagro observatory. Mrk 421 was detected by Milagro with a statistical significance of 7.1 standard deviations between 2005 September 21 and 2008 March 15. The observed spectrum is consistent with previous observations by VERITAS. We estimate the duty cycle of Mrk 421 for energies above 1 TeV for different hypothesis of the baseline flux and for different flare selections and we compare our results with the X-ray duty cycle estimated by Resconi et al. 2009. The robustness of the results is discussed.Comment: 27 pages, 6 figures, ApJ accepte

Verifiable Elections That Scale for Free

In order to guarantee a fair and transparent voting process, electronic voting schemes must be verifiable. Most of the time, however, it is important that elections also be anonymous. The notion of a verifiable shuffle describes how to satisfy both properties at the same time: ballots are submitted to a public bulletin board in encrypted form, verifiably shuffled by several mix servers (thus guaranteeing anonymity), and then verifiably decrypted by an appropriate threshold decryption mechanism. To guarantee transparency, the intermediate shuffles and decryption results, together with proofs of their correctness, are posted on the bulletin board throughout this process. In this paper, we present a verifiable shuffle and threshold decryption scheme in which, for security parameter k, L voters, M mix servers, and N decryption servers, the proof that the end tally corresponds to the original encrypted ballots is only O(k(L + M + N)) bits long. Previous verifiable shuffle constructions had proofs of size O(kLM + kLN), which, for elections with thousands of voters, mix servers, and decryption servers, meant that verifying an election on an ordinary computer in a reasonable amount of time was out of the question. The linchpin of each construction is a controlled-malleable proof (cm-NIZK), which allows each server, in turn, to take a current set of ciphertexts and a proof that the computation done by other servers has proceeded correctly so far. After shuffling or partially decrypting these ciphertexts, the server can also update the proof of correctness, obtaining as a result a cumulative proof that the computation is correct so far. In order to verify the end result, it is therefore sufficient to verify just the proof produced by the last server

Milagro Constraints on Very High Energy Emission from Short Duration Gamma-Ray Bursts

Recent rapid localizations of short, hard gamma-ray bursts (GRBs) by the Swift and HETE satellites have led to the observation of the first afterglows and the measurement of the first redshifts from this type of burst. Detection of >100 GeV counterparts would place powerful constraints on GRB mechanisms. Seventeen short duration (< 5 s) GRBs detected by satellites occurred within the field of view of the Milagro gamma-ray observatory between 2000 January and 2006 December. We have searched the Milagro data for >100 GeV counterparts to these GRBs and find no significant emission correlated with these bursts. Due to the absorption of high-energy gamma rays by the extragalactic background light (EBL), detections are only expected for redshifts less than ~0.5. While most long duration GRBs occur at redshifts higher than 0.5, the opposite is thought to be true of short GRBs. Lack of a detected VHE signal thus allows setting meaningful fluence limits. One GRB in the sample (050509b) has a likely association with a galaxy at a redshift of 0.225, while another (051103) has been tentatively linked to the nearby galaxy M81. Fluence limits are corrected for EBL absorption, either using the known measured redshift, or computing the corresponding absorption for a redshift of 0.1 and 0.5, as well as for the case of z=0.Comment: Accepted for publication in the Astrophysical Journa

Discovery of Localized Regions of Excess 10-TeV Cosmic Rays

An analysis of 7 years of Milagro data performed on a 10-degree angular scale has found two localized regions of excess of unknown origin with greater than 12 sigma significance. Both regions are inconsistent with gamma-ray emission with high confidence. One of the regions has a different energy spectrum than the isotropic cosmic-ray flux at a level of 4.6 sigma, and it is consistent with hard spectrum protons with an exponential cutoff, with the most significant excess at ~10 TeV. Potential causes of these excesses are explored, but no compelling explanations are found.Comment: Submitted to PhysRevLet

TeV Gamma-Ray Sources from a Survey of the Galactic Plane with Milagro

A survey of Galactic gamma-ray sources at a median energy of ~20 TeV has been performed using the Milagro Gamma Ray Observatory. Eight candidate sources of TeV emission are detected with pre-trials significance $>4.5\sigma$ in the region of Galactic longitude $l\in[30^\circ,220^\circ]$ and latitude $b\in[-10^\circ,10^\circ]$. Four of these sources, including the Crab nebula and the recently published MGRO J2019+37, are observed with significances $>4\sigma$ after accounting for the trials involved in searching the 3800 square degree region. All four of these sources are also coincident with EGRET sources. Two of the lower significance sources are coincident with EGRET sources and one of these sources is Geminga. The other two candidates are in the Cygnus region of the Galaxy. Several of the sources appear to be spatially extended. The fluxes of the sources at 20 TeV range from ~25% of the Crab flux to nearly as bright as the Crab.Comment: Submitted to Ap