327,910 research outputs found
The topos of labelled trees : a categorical semantics for SCCS
No full textThe work presented in this paper starts from the observation that labelled trees together with labeland
parenthood-preserving morphisms form a topos: a slice category of the topos of sheaves over
the poset (!, ) for the topology generated by the empty cover for 0.
After a very well presented and easily accessible exposition of this idea two applications are
elaborated. First, it is shown how the use of topos theory simplifies the interpretation of SCCS
using labelled trees, in particular, the treatment of guarded recursion.
Second, a new characterisation of bisimulation in terms of morphisms is presented: two trees
S, T are bisimilar iff there are conflict-preserving morphisms f: S ! T and g: T ! S such that
fgf = f and gfg = g. In elementary terms (distilled from Propositions 6.1 and 6.2), a morphism
f: S !T is conflict-preserving if whenever x!a y in S and f(x) = f(x0) then x0 !a y0 for some y0
with f(y) = f(y0).
The proof of the characterisation of bisimulation in terms of conflict-preserving morphisms
makes essential use of the topos-theoretic view.
The presentation is very understandable and does not require prior knowledge of topos theory
Optimal time of annuitization in the decumulation phase of a defined contribution pension scheme
No full textIn this paper, we consider the problem of finding the optimal time of annuitization for a retiree of a defined contribution pension scheme having the possibility of choosing her own investment and consumption strategy. We exploit the model introduced by Højgaard - Vigna (2010), who formulate the problem as a combined stochastic control and optimal stopping problem. They select a quadratic loss function that penalizes both the deviance of the running consumption rate from a desired consumption rate and the deviance of the final wealth at the time of annuitization from a desired target. We make extensive numerical investigations to address relevant issues such as optimal annuitization time, size of final annuity upon annuitization, extent of improvement when annuitization is not immediate and comparison between optimal annuitization and immediate annuitization. We find that the optimal annuitization time depends on personal factors such as the retiree's risk aversion and her subjective perception of remaining lifetime. It also depends on the financial market, via the Sharpe ratio of the risky asset. Optimal annuitization should occur a few years after retirement with high risk aversion, low Sharpe ratio and/or short remaining lifetime, and many years after retirement with low risk aversion, high Sharpe ratio and/or long remaining lifetime. Moreover, we show rigorously that with typical values of the model's parameters, a pension system where immediate annuitization is compulsory for all individuals is sub-optimal within this model. We measure the cost of sub-optimality in terms of loss of expected present value of consumption from retirement to death, and we find that the cost of sub-optimality, in relative terms, varies between 6% and 40%, depending on the risk aversion. This result gives an idea about the extent of loss in wealth suffered by a retiree who cannot choose programmed withdrawals, but is obliged to annuitize immediately on retirement all her wealth.Dened contribution pension scheme, decumulation phase, optimal annuitization time, cost of sub-optimality.
Quasi-succinct indices
No full textCompressed inverted indices in use today are based on the idea of gap compression: documents pointers are stored in increasing order, and the gaps between successive document pointers are stored using suitable codes which represent smaller gaps using less bits. Additional data such as counts and positions is stored using similar techniques. A large body of research has been built in the last 30 years around gap compression, including theoretical modeling of the gap distribution, specialized instantaneous codes suitable for gap encoding, and ad hoc document reorderings which increase the efficiency of instantaneous codes. This paper proposes to represent an index using a different architecture based on quasi-succinct representation of monotone sequences. We show that, besides being theoretically elegant and simple, the new index provides expected constant-time operations, space savings, and, in practice, significant performance improvements on conjunctive, phrasal and proximity queries. © 2013 ACM
On the relations between distributive computability and the BSS model
No full textAbstractThis paper presents an equivalence result between computability in the BSS model and in a suitable distributive category. It is proved that the class of functions Rl → Rm (with l, m finite and R a commutative, ordered ring) computable in the BSS model and the functions distributively computable over a natural distributive graph based on the operations of R coincide. Using this result, a new structural characterization, based on iteration, of the same functions is given
Hydrogeological Prognosis With Regard to Realisation of the New Colle Di Tenda Road Tunnel
No full textAn experimental exploration of Marsaglia's xorshift Generators, Scrambled
No full textMarsaglia proposed xorshift generators are a class of very fast, good-quality pseudorandom number generators. Subsequent analysis by Panneton and L'Ecuyer has lowered the expectations raised by Marsaglia's article, showing several weaknesses of such generators. Nonetheless, many of the weaknesses of xorshift generators fade away if their result is scrambled by a nonlinear operation (as originally suggested by Marsaglia). In this article we explore the space of possible generators obtained by multiplying the result of a xorshift generator by a suitable constant. We sample generators at 100 points of their state space and obtain detailed statistics that lead us to choices of parameters that improve on the current ones. We then explore for the first time the space of high-dimensional xorshift generators, following another suggestion in Marsaglia's article, finding choices of parameters providing periods of length 21024 - 1 and 24096 - 1. The resulting generators are of extremely high quality, faster than current similar alternatives, and generate long-period sequences passing strong statistical tests using only eight logical operations, one addition, and one multiplication by a constant
Spectral ranking
No full textWe sketch the history of spectral ranking - a general umbrella name for techniques that apply the theory of linear maps (in particular, eigenvalues and eigenvectors) to matrices that do not represent geometric transformations, but rather some kind of relationship between entities. Albeit recently made famous by the ample press coverage of Google's PageRank algorithm, spectral ranking was devised more than 60 years ago, almost exactly in the same terms, and has been studied in psychology, social sciences, bibliometrics, economy, and choice theory. We describe the contribution given by previous scholars in precise and modern mathematical terms: Along the way, we show how to express in a general way damped rankings, such as Katz's index, as dominant eigenvectors of perturbed matrices, and then use results on the Drazin inverse to go back to the dominant eigenvectors by a limit process. The result suggests a regularized definition of spectral ranking that yields for a general matrix a unique vector depending on a boundary condition
fastutil 5.0
No full textfastutil extends the JavaTM Collections Framework by providing type-specific maps, sets, lists and queues with a small memory footprint and fast access and insertion; it also includes a fast I/O API for binary and text files
Further scramblings of Marsaglia's xorshift generators
No full textxorshift* generators are a variant of Marsaglia's xorshift generators that eliminate linear artifacts typical of generators based on Z/2Z-linear operations using multiplication by a suitable constant. Shortly after high-dimensional xorshift* generators were introduced, Saito and Matsumoto suggested a different way to eliminate linear artifacts based on addition in Z/232Z, leading to the XSadd generator. Starting from the observation that the lower bits of XSadd are very weak, as its reverse fails several statistical tests, we explore variants of XSadd using 64-bit operations, and describe in detail xorshift128+, an extremely fast generator that passes strong statistical tests using only three shifts, four xors and an addition
- …
