Scott's graph model is a lambda-algebra based on the observation that continuous endofunctions on the lattice of sets of natural numbers can be represented via their graphs. A graph is a relation mapping finite sets of input values to output values. We consider a similar model based on relations whose input values are finite sequences rather than sets. This alteration means that we are taking into account the order in which observations are made. This new notion of graph gives rise to a model of affine lambda-calculus that admits an interpretation of imperative constructs including variable assignment, dereferencing and allocation. Extending this untyped model, we construct a category that provides a model of typed higher-order imperative computation with an affine type system. An appropriate language of this kind is Reynolds's Syntactic Control of Interference. Our model turns out to be fully abstract for this language. At a concrete level, it is the same as Reddy's object spaces model, which was the first "state-free" model of a higher-order imperative programming language and an important precursor of games models. The graph model can therefore be seen as a universal domain for Reddy's model.
The utility of a universal type for establishing properties of a model is well-known, and was explained in detail by Longley @cite_8 . The central idea of this paper, of modifying Scott's graph model to record slightly different information, has also been used by Longley in @cite_22 to obtain a model of fresh name generation. A similar model construction has been investigated by @cite_15 . We shall remark further on the connections between these papers and our present work below, although we leave closer investigation for future work.
@cite_15 @cite_22 @cite_8
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Motivated by the desirability of universal composability, we analyze in terms of L1 distinguishability the task of secret key generation from a joint random variable. Under this secrecy criterion, using the Renyi entropy of order 1+s for s ∈ [0,1], we derive a new upper bound of Eve's distinguishability under the application of the universal2 hash functions. It is also shown that this bound gives the tight exponential rate of decrease in the case of independent and identical distributions. The result is applied to the wiretap channel model and to secret key generation (distillation) by public discussion. Rapid movement generation models are described in the literature as an efficient tool to apprehend the handwriting behavior. Fields of application are diverse, including handwriting description, regeneration, and more recently OCR. In this paper, we propose a grapheme-based approach to offline Arabic writer identification and verification. Rather than extracting naturel graphemes from a training corpus using segmentation and clustering, it synthesizes its own graphemes based on the beta-elliptic model. Originality lies in the independence of the grapheme codebook from any training process, and the use of a model instead. One full and four partial codebooks are generated and tested. Using feature selection, raw codebooks are reduced in size with respect to FDR, FDR and cross-correlation, and random subsampling criteria. A total of 60 feature vectors are extracted using template matching, and evaluated with 411 individual writers from the IFN ENIT database. The results presented in this study demonstrated the wide representativity and the good generalization capability of synthetic codebooks. We obtained a top1 rate=90.02 and a top5 rate=96.35 for writer identification, and an EER=2.1 for writer verification. Our approach showed better properties than most of the surveyed techniques in terms of supported corpus size and identification rates. To the best of our knowledge, this study is among the first to exploit the concept of model-based synthetic codebooks in writer identification and verification. HighlightsUniversal synthetic codebooks are used for writer identification and verification.The beta-elliptic handwriting generation model is used to create the codebooks.Neither corpus-driven training nor prior segmentation is needed in this approach.Synthetic codebook demonstrated good generalization capabilities for Arabic. We consider the problem of using a large unlabeled sample to boost performance of a learning algorit,hrn when only a small set of labeled examples is available. In particular, we consider a problem setting motivated by the task of learning to classify web pages, in which the description of each example can be partitioned into two distinct views. For example, the description of a web page can be partitioned into the words occurring on that page, and the words occurring in hyperlinks t,hat point to that page. We assume that either view of the example would be sufficient for learning if we had enough labeled data, but our goal is to use both views together to allow inexpensive unlabeled data to augment, a much smaller set of labeled examples. Specifically, the presence of two distinct views of each example suggests strategies in which two learning algorithms are trained separately on each view, and then each algorithm’s predictions on new unlabeled examples are used to enlarge the training set of the other. Our goal in this paper is to provide a PAC-style analysis for this setting, and, more broadly, a PAC-style framework for the general problem of learning from both labeled and unlabeled data. We also provide empirical results on real web-page data indicating that this use of unlabeled examples can lead to significant improvement of hypotheses in practice. *This research was supported in part by the DARPA HPKB program under contract F30602-97-1-0215 and by NSF National Young investigator grant CCR-9357793. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. TO copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and or a fee. COLT 98 Madison WI USA Copyright ACM 1998 l-58113-057--0 98 7... 5.00 92 Tom Mitchell School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213-3891 mitchell+@cs.cmu.edu We consider homogeneous factor models on uniformly sparse graph sequences converging locally to a (unimodular) random tree T, and study the existence of the free energy density ϕ, the limit of the log-partition function divided by the number of vertices n as n tends to infinity. We provide a new interpolation scheme and use it to prove existence of, and to explicitly compute, the quantity ϕ subject to uniqueness of a relevant Gibbs measure for the factor model on T. By way of example we compute ϕ for the independent set (or hard-core) model at low fugacity, for the ferromagnetic Ising model at all parameter values, and for the ferromagnetic Potts model with both weak enough and strong enough interactions. Even beyond uniqueness regimes our interpolation provides useful explicit bounds on ϕ. In the regimes in which we establish existence of the limit, we show that it coincides with the Bethe free energy functional evaluated at a suitable fixed point of the belief propagation (Bethe) recursions on T. In the special case that T has a Galton–Watson law, this formula coincides with the nonrigorous “Bethe prediction” obtained by statistical physicists using the “replica” or “cavity” methods. Thus our work is a rigorous generalization of these heuristic calculations to the broader class of sparse graph sequences converging locally to trees. We also provide a variational characterization for the Bethe prediction in this general setting, which is of independent interest.