Generic Reduction Research Articles

Reduced attentional capacity, but normal processing speed and shifting of attention in developmental dyslexia: Evidence from a serial task

We report the performance of a group of adult dyslexics and matched controls in an array-matching task where two strings of either consonants or symbols are presented side by side and have to be judged to be the same or different. The arrays may differ either in the order or identity of two adjacent characters. This task does not require naming – which has been argued to be the cause of dyslexics’ difficulty in processing visual arrays – but, instead, has a strong serial component as demonstrated by the fact that, in both groups, Reaction times (RTs) increase monotonically with position of a mismatch. The dyslexics are clearly impaired in all conditions and performance in the identity conditions predicts performance across orthographic tasks even after age, performance IQ and phonology are partialled out. Moreover, the shapes of serial position curves are revealing of the underlying impairment. In the dyslexics, RTs increase with position at the same rate as in the controls (lines are parallel) ruling out reduced processing speed or difficulties in shifting attention. Instead, error rates show a catastrophic increase for positions which are either searched later or more subject to interference. These results are consistent with a reduction in the attentional capacity needed in a serial task to bind together identity and positional information. This capacity is best seen as a reduction in the number of spotlights into which attention can be split to process information at different locations rather than as a more generic reduction of resources which would also affect processing the details of single objects.

An Epigenetic Approach to Cancer Etiology

The practice of clinical oncology historically has been rooted in therapy for established cancers, and over the past decade, early detection of the malignancy has occurred increasingly, allowing an increasing chance of cure by surgical intervention. Cancer prevention has been targeted largely to generic reduction of exposure to environmental carcinogens, such as smoking reduction. However, targeted identification of patients at increased risk and therapeutic tailored intervention in those patients have not taken hold in oncology, despite the enormous success of that approach in preventive cardiology. A paradigm of such a strategy for oncology may be the identification of patients with epigenetic alterations in progenitor cells and intervention before the development of the earliest identifiable neoplasms. We review studies of loss of imprinting of insulin-like growth factor 2 in colorectal cancer as an example of such a target for preventive oncology.

Approximation Algorithms and Online Mechanisms for Item Pricing

$ \newcommand{\val}{w} \newcommand{\expect}[1]{{\mathbf E}\left[ #1 \right]} \newcommand{\setsize}[1]{\left| #1\right|} \newcommand{\nitems}{n} \newcommand{\ncust}{m} $ We present approximation and online algorithms for problems of pricing a collection of items for sale so as to maximize the seller's revenue in an unlimited supply setting. Our first result is an $O(k)$-approximation algorithm for pricing items to single-minded bidders who each want at most $k$ items. This improves over work of Briest and Krysta (2006) who achieve an $O(k^2)$ bound. For the case $k=2$, where we obtain a $4$-approximation, this can be viewed as the following graph vertex pricing problem: given a (multi) graph $G$ with valuations $\val_{ij}$ on the edges, find prices $p_i \geq 0$ for the vertices to maximize $$\sum\limits_{\{(i,j):\val_{ij} \geq p_i+p_j\}} \left(p_i + p_j \right)\,.$$ We also improve the approximation of Guruswami et al. (2005) for the “highway problem” in which all desired subsets are intervals on a line, from $O(\log {\ncust} + \log {\nitems})$ to $O(\log {\nitems})$, where $\ncust$ is the number of bidders and $\nitems$ is the number of items. Our approximation algorithms can be fed into the generic reduction of Balcan et al. (2005) to yield an incentive-compatible auction with nearly the same performance guarantees so long as the number of bidders is sufficiently large. In addition, we show how our algorithms can be combined with results of Blum and Hartline (2005) and Kalai and Vempala (2003) to achieve good performance in the online setting, where customers arrive one at a time and each must be presented a set of item prices based only on knowledge of the customers seen so far.

The most nonelementary theory

We give a direct proof by generic reduction that testing validity of formulas in a decidable rudimentary theory Ω of finite typed sets (Henkin, Fundamenta Mathematicæ 52 (1963) 323–344) requires space and time exceeding infinitely often(1)2···2exp∞(exp(cn))=2height2cmforsomeconstantc>0, where n denotes the length of input. This gives the highest currently known lower bound for a decidable logical theory and affirmatively settles Problem 10.13 from (Compton and Henson, Ann. Pure Applied Logic 48 (1990) 1–79): Is there a “natural” decidable theory with a lower bound of the form exp∞(f(n)), where f is not linearly bounded? The highest previously known lower (and upper) bounds for “natural” decidable theories, like WS1S, S2S, are of the form exp∞(dn), with just linearly growing stacks of twos. Originally, the lower bound (1) for Ω was settled in (12th Annual IEEE Symposium on Logic in Computer Science (LICS’97), 1997, 294–305) using the powerful uniform lower bounds method due to Compton and Henson, and probably would never be discovered otherwise. Although very concise, the original proof has certain gaps, because the method was pushed out of the limits it was originally designed and intended for, and some hidden assumptions were violated. This results in slightly weaker bounds—the stack of twos in (1) grows subexponentially, but superpolynomially, namely, as 2cn for formulas with fixed quantifier prefix, or as 2cn/log(n) for formulas with varying prefix. The independent direct proof presented in this paper closes the gaps and settles the originally claimed lower bound (1) for the minimally typed, succinct version of Ω.

The Swedish Code on health claims for foods. Revised version in action September 2004

The Swedish voluntary Code of Practice on health-related claims in the labelling and marketing of food products, originally introduced in 1990, has been revised, effective from September 2004. The Code addresses all claims related to health, performance and well-being. In addition to generic reduction of disease risk claims and product-specific physiological claims, nutrient function claims are now also clearly defined as health claims. Criteria regarding the nutritional composition of products eligible for marketing with generic reduction of disease risk claims are specified in the revised version. As before, product-specific health claims are subject to pre-marketing expert evaluation of the scientific documentation.

Application of modeling and simulation tools in costs and pollution monitoring

Summary. This paper presents the development and application of process modeling and simulation tools to aid in the monitoring and measuring of pollution from industry, and investigate a plant’s overall performance. A case study of a generic reduction plant is investigated, taking into account the underlying principles that determine the amount of fluoride emissions released from the plant’s processes. The simulation study includes the investigation of the gas cleaning system within the plant, such as the system’s operating relationships between the scrubbing efficiency, wear of the scrubber filter bags, maintenance costs and its response to the change of scrubbing circulation. Two sets of simulation runs are performed to seek a balance for the plant’s overall system performance, taking into account environmental issues (fluoride emissions) and cost. The final simulation result demonstrates that cost savings can be achieved when the plant operates in a cleaner manner.

On Interpolation and Automatization for Frege Systems

The interpolation method has been one of the main tools for proving lower bounds for propositional proof systems. Loosely speaking, if one can prove that a particular proof system has the feasible interpolation property, then a generic reduction can (usually) be applied to prove lower bounds for the proof system, sometimes assuming a (usually modest) complexity-theoretic assumption. In this paper, we show that this method cannot be used to obtain lower bounds for Frege systems, or even for TC0-Frege systems. More specifically, we show that unless factoring (of Blum integers) is feasible, neither Frege nor TC0-Frege has the feasible interpolation property. In order to carry out our argument, we show how to carry out proofs of many elementary axioms/theorems of arithmetic in polynomial-sized TC0-Frege. As a corollary, we obtain that TC0-Frege, as well as any proof system that polynomially simulates it, is not automatizable (under the assumption that factoring of Blum integers is hard). We also show under the same hardness assumption that the k-provability problem for Frege systems is hard.

Bubbles in modularity

We provide a global technique, called neatening, for the study of modularity of left-linear term rewriting systems. Objects called bubbles are identified as the responsibles of most of the problems occurring in modularity, and the concept of well-behaved (from the modularity point of view) reduction, called neat reduction, is introduced. Neatening consists of two steps: the first is proving a property is modular when only neat reductions are considered; the second is to ‘neaten’ a generic reduction so to obtain a neat one, thus showing that restricting to neat reductions is not limitative. This general technique is used to provide a unique, uniform method able to elegantly prove all the existing results on the modularity of every basic property of left-linear term rewriting systems, and also to provide new results on the modularity of termination.

Optimal parameterizations

The problem of exercising the freedoms of reparameterization of polynomial or rational curve segments to achieve a “parametric flow” closest to the unit-speed or arc-length representation is addressed. A quantitative measure of “closeness” to arc-length parameterization is formulated and, according to this measure, the problem of identifying the optimum rational reparameterization of a degree n polynomial curve is shown to be analytically reducible to the determination of the unique real root on (0, 1) of a quadratic equation. Examples indicate that, in practice, the algorithm can produce significantly more uniform parameter variation across the extent of typical Bézier curves. The generalization of the method to reparameterization of rational curves is more difficult, however, and does not admit generic reduction to a polynomial equation in even the simplest context (the conics).

Undecidable boundedness problems for datalog programs

A given Datalog program is bounded if its depth of recursion is independent of the input database. Deciding boundedness is a basic task for the analysis of database logic programs. The undecidability of Datalog boundedness was first demonstrated by Gaifman et al. [7]. We introduce new techniques for proving the undecidability of (various kinds of) boundedness, which allow us to considerably strengthen the results of Gaifman et al. [7]. In particular, (1) we use a new generic reduction technique to show that program boundedness is undecidable for arity 2 predicates, even with linear rules; (2) we use the mortality problem of Turing machines to show that uniform boundedness is undecidable for arity 3 predicates and for arity 1 predicates when ≠ is also allowed; (3) by encoding all possible transitions of a two-counter machine in a single rule, we show that program (resp., predicate) boundedness is undecidable for two linear rules (resp., one rule and a projection) and one initialization rule, where all predicates have small arities (6 or 7).

Experiments with a generic reduction computer

Experiments with a generic reduction computer

Nonlinear Reduced Models For RapidAssessment Of Effects

This study aims at integrating results from large-scale models into Decision Support Systems (DSSs), so that the effects of measures can be rapidly assessed for use in the design, evaluation, construction and maintenance of major civil engineering systems. To fulfil this aim these models must be reduced in size and computation time. In hydroscience, large-scale numerical models are often of order 100,000. Consequently, model simulations require long computation times. In this paper we apply a systematic, generic reduction tool, which can extract the essential patterns from a large data set of model results. The model reduction technique is used to significantly reduce computation time, while maintaining an acceptable level of accuracy. In an earlier paper [1], large-scale models were reduced to a general linear auto regressive model in reduced space. In this paper we extend this method to nonlinear models, by incorporating knowledge of the original model and of the governing physical processes. In order to reduce the dimension of the system, eigenvalue decomposition of the covariance matrix of the data set is carried out. Only the most important eigenmodes are taken into account. These eigenmodes represent the most significant dynamic spatial patterns in the output of the complex model. In this paper some interesting results are discussed.