Additive cellular automata and algebraic series

A cellular automaton is an array of regularly interconnected identical cells. We study here the special case of automata where each cell depends in additive manner on its neighbours. The successives states of a given cell form a sequence whose generating series proved to be always an algebric series. We also examplify the realization of a given algebraic series by means of an automaton. As a by product we obtain a relation between additive cellular automata and certain "automatic sequences" like the paper folding sequence

Health impact of US military service in a large population-based military cohort: findings of the Millennium Cohort Study, 2001-2008

<p>Abstract</p> <p>Background</p> <p>Combat-intense, lengthy, and multiple deployments in Iraq and Afghanistan have characterized the new millennium. The US military's all-volunteer force has never been better trained and technologically equipped to engage enemy combatants in multiple theaters of operations. Nonetheless, concerns over potential lasting effects of deployment on long-term health continue to mount and are yet to be elucidated. This report outlines how findings from the first 7 years of the Millennium Cohort Study have helped to address health concerns related to military service including deployments.</p> <p>Methods</p> <p>The Millennium Cohort Study was designed in the late 1990s to address veteran and public concerns for the first time using prospectively collected health and behavioral data.</p> <p>Results</p> <p>Over 150 000 active-duty, reserve, and National Guard personnel from all service branches have enrolled, and more than 70% of the first 2 enrollment panels submitted at least 1 follow-up survey. Approximately half of the Cohort has deployed in support of operations in Iraq and Afghanistan.</p> <p>Conclusion</p> <p>The Millennium Cohort Study is providing prospective data that will guide public health policymakers for years to come by exploring associations between military exposures and important health outcomes. Strategic studies aim to identify, reduce, and prevent adverse health outcomes that may be associated with military service, including those related to deployment.</p

Population and Environmental Correlates of Maize Yields in Mesoamerica: a Test of Boserup’s Hypothesis in the Milpa

Using a sample of 40 sources reporting milpa and mucuna-intercropped maize yields in Mesoamerica, we test Boserup’s (1965) prediction that fallow is reduced as a result of growing population density. We further examine direct and indirect effects of population density on yield. We find only mixed support for Boserupian intensification. Fallow periods decrease slightly with increasing population density in this sample, but the relationship is weak. Controlling for other covariates, fallow-unadjusted maize yields first rise then fall with population density. Fallow-adjusted maize yields peak at 390 kg/ha/yr for low population densities (8 persons / km2) and decline to around 280 kg/ha/yr for the highest population densities observed in our dataset. Fallow practices do not appear to mediate the relationship between population density and yield. The multi-level modeling methods we adopt allow for data clustering, accurate estimates of group-level variation, and they generate conditional predictions, all features essential to the comparative study of prehistoric and contemporary agricultural yields

A Note on the Discrete Convolution Theorem

We report on an obstruction to naturally extending the discrete convolution theorem from polynomials to power series. The basis of discrete Fourier transforms is the discrete convolution theorem (DCT) for polynomials. In fact, the DCT establishes a connection between polynomial multiplication and Hadamard product of polynomials. It asserts that there exist invertible tranformations T , which take polynomials to polynomials and are linear in polynomial addition such that f \Delta g = T \Gamma1 (Tf fi Tg) ; where p \Delta q is the usual product of polynomials and p fi q is the Hadamard product. If we drop the requirement that T be invertible, we get the weak DCT. That is, there exist transformations T , linear in polynomial addition such that T (f \Delta g) = Tf fi Tg : The weak DCT extends directly to power series, however the natural formulation of the DCT fails in this case. We write p(a) to indicate the evaluation of p at a. All polynomials and series involve the indeterminate..

A Simple Subexponential Time Algorithm for Hamiltonian Circuit

Let ff satisfy OE = p 5 + 1 2 ! ff ! 2 : We present an algorithm which counts the number of Hamiltonian circuits in a graph and which runs in time 2 O((log(n)) 3 \Deltan log ff ) : Logarithms are binary. The constant implied by O(\Delta) notation behaves like 1=ffl, where ffl = ff \Gamma OE. 1 Introduction Motivation At present, except for the trivial containment of NP in DTIME( S c?0 2 n c ), nothing is known about the minimum time needed to solve NP-complete problems. This paper does not contribute to this important open problem. However, it does show that a relatively straightforward method yields time upper bounds of the form 2 n a , for 0 ! a ! 1 for some NP-complete problems. In particular, Hamiltonian circuit and any problem that can be reduced to it in linear time have time bounds of this type. We note that, so far as standard reductions go, this type of bound cannot be extended in this way to SAT since its reductions to Hamiltonian circuit appear to requi..

Weakly Bounded Probabilistic Polytime is Contained in POLYSIZE

It is known that bounded error probabilistic polynomial time (BPP) languages are accepted by polynomial size circuit families (POLYSIZE). We sharpen and extend this result to WBPP for which the BPP error bound ffl ? 0 is weakened to ffl(n) =\Omega\Gamma3 =n O(1) ) for length n inputs. The WBPP result is obtained by using Turing randomness to avoid involved counting arguments. 1 Introduction Complexity theory is the part of computer science that identifies computing resources and establishes quantitative relationships among them. In this way, one resource can be measured in terms of others. We will be concerned with measuring randomness in terms of Boolean circuit size. Additional details about the notions used here may be obtained from [2]. It will be convenient to express computation in terms of language acceptance. Languages will be subsets of f0; 1g + . The output of a Turing machine M on input x will be designated by M(x). If a Turing machine M with inputs over f0; 1g + ha..

A note on commutative multivariate rational series

Direct arguments are presented showing that for rational series in several commuting variables, the rational series problem is undecidable, and closure under Hadamard product fails

On sums of roots of unity

We make two remarks on linear forms over Z in complex roots of unity. First we show that a Liouville type lower bound on\ud the absolute value of a nonvanishing form can be derived from the time complexity upper bound on Tarski algbera. Second we exhibit an efficient randomized algorithm for deciding whether a given form vanishes. In the special case where the periods of the roots of unity are mutually coprime, we can eliminate randomization. This efficiency is surprising given the doubly exponential smallness of the Liouville bound

On Hadamard Square Roots of Unity

A series all of whose coefficients have unit modulus is called an Hadamard square root of unity. We investigate and partially characterise the algebraic Hadamard square roots of unity

A special case of a unary regular language containment

Given an n-state unary finite automaton accepting a language T, and an ultimately periodic set S given as a union of arithmetic progressions that can be represented using n^{O(1)} bits, and whose periods are mutually coprime, deciding whether T is a subset of S is in n^{O(log n)} time. Dropping the mutual coprimality condition, this containment problem becomes NP-hard