Variable Stars: which Nyquist Frequency ?

In the analysis of variable stars, the problem of sampling is central. This article focusses on the determination of the Nyquist frequency. It is well defined in the case of regular sampling. However, the time series of variable stars observations are generally unevenly sampled. Fourier analysis using the spectral window furnishes some clues about the equivalent Nyquist frequency in the irregular case. Often it is pushed very high, and thus very short periods can be detected. A specific example is shown, drawn from MACHO databases.Comment: 4 pages, 5 figures, submitted to A&

Branch Rings, Thinned Rings, Tree Enveloping Rings

We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field k we construct a k-algebra K which (1) is finitely generated and infinite-dimensional, but has only finite-dimensional quotients; (2) has a subalgebra of finite codimension, isomorphic to $M_2(K)$; (3) is prime; (4) has quadratic growth, and therefore Gelfand-Kirillov dimension 2; (5) is recursively presented; (6) satisfies no identity; (7) contains a transcendental, invertible element; (8) is semiprimitive if k has characteristic $\neq2$; (9) is graded if k has characteristic 2; (10) is primitive if k is a non-algebraic extension of GF(2); (11) is graded nil and Jacobson radical if k is an algebraic extension of GF(2).Comment: 35 pages; small changes wrt previous versio

Complexity of Manipulative Actions When Voting with Ties

Most of the computational study of election problems has assumed that each voter's preferences are, or should be extended to, a total order. However in practice voters may have preferences with ties. We study the complexity of manipulative actions on elections where voters can have ties, extending the definitions of the election systems (when necessary) to handle voters with ties. We show that for natural election systems allowing ties can both increase and decrease the complexity of manipulation and bribery, and we state a general result on the effect of voters with ties on the complexity of control.Comment: A version of this paper will appear in ADT-201

Combinatorial Voter Control in Elections

Voter control problems model situations such as an external agent trying to affect the result of an election by adding voters, for example by convincing some voters to vote who would otherwise not attend the election. Traditionally, voters are added one at a time, with the goal of making a distinguished alternative win by adding a minimum number of voters. In this paper, we initiate the study of combinatorial variants of control by adding voters: In our setting, when we choose to add a voter~$v$, we also have to add a whole bundle $\kappa(v)$ of voters associated with $v$. We study the computational complexity of this problem for two of the most basic voting rules, namely the Plurality rule and the Condorcet rule.Comment: An extended abstract appears in MFCS 201

On Property (FA) for wreath products

We characterize permutational wreath products with Property (FA). For instance, the standard wreath product A wr B of two nontrivial countable groups A,B, has Property (FA) if and only if B has Property (FA) and A is a finitely generated group with finite abelianisation. We also prove an analogous result for hereditary Property (FA). On the other hand, we prove that many wreath products with hereditary Property (FA) are not quotients of finitely presented groups with the same property.Comment: 12 pages, 0 figur

Search for high-amplitude Delta Scuti and RR Lyrae stars in Sloan Digital Sky Survey Stripe 82 using principal component analysis

We propose a robust principal component analysis (PCA) framework for the exploitation of multi-band photometric measurements in large surveys. Period search results are improved using the time series of the first principal component due to its optimized signal-to-noise ratio.The presence of correlated excess variations in the multivariate time series enables the detection of weaker variability. Furthermore, the direction of the largest variance differs for certain types of variable stars. This can be used as an efficient attribute for classification. The application of the method to a subsample of Sloan Digital Sky Survey Stripe 82 data yielded 132 high-amplitude Delta Scuti variables. We found also 129 new RR Lyrae variables, complementary to the catalogue of Sesar et al., 2010, extending the halo area mapped by Stripe 82 RR Lyrae stars towards the Galactic bulge. The sample comprises also 25 multiperiodic or Blazhko RR Lyrae stars.Comment: 23 pages, 17 figure

Algorithmic decidability of Engel's property for automaton groups

We consider decidability problems associated with Engel's identity ($[\cdots[[x,y],y],\dots,y]=1$ for a long enough commutator sequence) in groups generated by an automaton. We give a partial algorithm that decides, given $x,y$, whether an Engel identity is satisfied. It succeeds, importantly, in proving that Grigorchuk's $2$-group is not Engel. We consider next the problem of recognizing Engel elements, namely elements $y$ such that the map $x\mapsto[x,y]$ attracts to $\{1\}$. Although this problem seems intractable in general, we prove that it is decidable for Grigorchuk's group: Engel elements are precisely those of order at most $2$. Our computations were implemented using the package FR within the computer algebra system GAP

Search for high-amplitude δ Scuti and RR Lyrae stars in Sloan Digital Sky Survey Stripe 82 using principal component analysis

We propose a robust principal component analysis framework for the exploitation of multiband photometric measurements in large surveys. Period search results are improved using the time-series of the first principal component due to its optimized signal-to-noise ratio. The presence of correlated excess variations in the multivariate time-series enables the detection of weaker variability. Furthermore, the direction of the largest variance differs for certain types of variable stars. This can be used as an efficient attribute for classification. The application of the method to a subsample of Sloan Digital Sky Survey Stripe 82 data yielded 132 high-amplitude δ Scuti variables. We also found 129 new RR Lyrae variables, complementary to the catalogue of Sesar et al., extending the halo area mapped by Stripe 82 RR Lyrae stars towards the Galactic bulge. The sample also comprises 25 multiperiodic or Blazhko RR Lyrae star

On a conjecture of Goodearl: Jacobson radical non-nil algebras of Gelfand-Kirillov dimension 2

For an arbitrary countable field, we construct an associative algebra that is graded, generated by finitely many degree-1 elements, is Jacobson radical, is not nil, is prime, is not PI, and has Gelfand-Kirillov dimension two. This refutes a conjecture attributed to Goodearl