On Learning Counting Functions With Queries

We investigate the problem of learning disjunctions of counting functions, which are general cases of parity and modulo functions, with equivalence and membership queries. We prove that, for any prime number p, the class of disjunctions of integer-weighted counting functions with modulus p over the domain Znq (or Zn) for any given integer q ≥ 2 is polynomial time learnable using at most n + 1 equivalence queries, where the hypotheses issued by the learner are disjunctions of at most n counting functions with weights from Zp. The result is obtained through learning linear systems over an arbitrary field. In general a counting function may have a composite modulus. We prove that, for any given integer q ≥ 2, over the domain Zn2, the class of read-once disjunctions of Boolean-weighted counting functions with modulus q is polynomial time learnable with only one equivalence query, and the class of disjunctions of log log n Boolean-weighted counting functions with modulus q is polynomial time learnable. Finally, we present an algorithm for learning graph-based counting functions.

Type Reconstruction in the Presence of Polymorphic Recursion and the Recursive Types

We establish the equivalence of type reconstruction with polymorphic recursion and recursive types is equivalent to regular semi-unification which proves the undecidability of the corresponding type reconstruction problem. We also establish the equivalence of type reconstruction with polymorphic recursion and positive recursive types to a special case of regular semi-unification which we call positive regular semi-unification. The decidability of positive regular semi-unification is an open problem.

Recursive Estimation of Motion and Planar Structure

A specialized formulation of Azarbayejani and Pentland's framework for recursive recovery of motion, structure and focal length from feature correspondences tracked through an image sequence is presented. The specialized formulation addresses the case where all tracked points lie on a plane. This planarity constraint reduces the dimension of the original state vector, and consequently the number of feature points needed to estimate the state. Experiments with synthetic data and real imagery illustrate the system performance. The experiments confirm that the specialized formulation provides improved accuracy, stability to observation noise, and rate of convergence in estimation for the case where the tracked points lie on a plane.

Efficient Hash-Consing of Recursive Types

Efficient storage of types within a compiler is necessary to avoid large blowups in space during compilation. Recursive types in particular are important to consider, as naive representations of recursive types may be arbitrarily larger than necessary through unfolding. Hash-consing has been used to efficiently store non-recursive types. Deterministic finite automata techniques have been used to efficiently perform various operations on recursive types. We present a new system for storing recursive types combining hash-consing and deterministic finite automata techniques. The space requirements are linear in the number of distinct types. Both update and lookup operations take polynomial time and linear space and type equality can be checked in constant time once both types are in the system.

Type Inference For Recursive Definitions

We consider type systems that combine universal types, recursive types, and object types. We study type inference in these systems under a rank restriction, following Leivant's notion of rank. To motivate our work, we present several examples showing how our systems can be used to type programs encountered in practice. We show that type inference in the rank-k system is decidable for k ≤ 2 and undecidable for k ≥ 3. (Similar results based on different techniques are known to hold for System F, without recursive types and object types.) Our undecidability result is obtained by a reduction from a particular adaptation (which we call "regular") of the semi-unification problem and whose undecidability is, interestingly, obtained by methods totally different from those used in the case of standard (or finite) semi-unification.

A Neural Theory of Visual Search: Recursive Attention to Segmentations and Surfaces

A neural theory is proposed in which visual search is accomplished by perceptual grouping and segregation, which occurs simultaneous across the visual field, and object recognition, which is restricted to a selected region of the field. The theory offers an alternative hypothesis to recently developed variations on Feature Integration Theory (Treisman, and Sato, 1991) and Guided Search Model (Wolfe, Cave, and Franzel, 1989). A neural architecture and search algorithm is specified that quantitatively explains a wide range of psychophysical search data (Wolfe, Cave, and Franzel, 1989; Cohen, and lvry, 1991; Mordkoff, Yantis, and Egeth, 1990; Treisman, and Sato, 1991).

Fuzzy ART Choice Functions

Adaptive Resonance Theory (ART) models are real-time neural networks for category learning, pattern recognition, and prediction. Unsupervised fuzzy ART and supervised fuzzy ARTMAP networks synthesize fuzzy logic and ART by exploiting the formal similarity between tile computations of fuzzy subsethood and the dynamics of ART category choice, search, and learning. Fuzzy ART self-organizes stable recognition categories in response to arbitrary sequences of analog or binary input patterns. It generalizes the binary ART 1 model, replacing the set-theoretic intersection (∩) with the fuzzy intersection(∧), or component-wise minimum. A normalization procedure called complement coding leads to a symmetric theory in which the fuzzy intersection and the fuzzy union (∨), or component-wise maximum, play complementary roles. A geometric interpretation of fuzzy ART represents each category as a box that increases in size as weights decrease. This paper analyzes fuzzy ART models that employ various choice functions for category selection. One such function minimizes total weight change during learning. Benchmark simulations compare peformance of fuzzy ARTMAP systems that use different choice functions.

Hippocampal Modulation of Recognition, Conditioning, Timing, and Space: Why So Many Functions?

Advanced Research Projects Agency (ONR N00014-92-J-4015); National Science Foundation (IRI-90-24877); Office of Naval Research (N00014-91-J-1309)

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

A novel syndrome of severe neutrophil dysfunction: unresponsiveness confined to chemotaxin-induced functions.

We have identified a patient with a number of neutrophil dysfunctions. The patient was a female baby who lived for 8 months. During her life, she developed severe bacterial infections and showed omphalitis, impaired wound healing, and a pronounced leukocytosis. She was not a patient with leukocyte adhesion deficiency, because all leukocyte CD18 complex proteins were expressed at normal levels. Yet, neutrophil polarization and chemotaxis to platelet-activating factor, leukotriene B4, or formyl-methionyl-leucyl-phenylalanine (FMLP) were completely absent. We found a strong defect in actin polymerization in response to chemotactic stimuli, but only a retarded or even normal reaction with other stimuli. This indicates that the cellular dysfunctions were not due to an intrinsic defect in actin metabolism. Instead, the regulation of actin polymerization with chemotactic stimuli seemed to be defective. We concentrated on FMLP-induced responses in the patient's neutrophils. Functions dependent on activation of complement receptor type 3, such as aggregation or adherence to endothelial cells, were normally induced. Binding to serum-coated coverslips was normal in cell number; however, spreading was not observed. Exocytosis from the specific granules was readily induced. In contrast, FMLP failed to induce a respiratory burst activity or degranulation of the azurophil granules. FMLP induced a normal increase in free intracellular Ca2+, but a decreased formation of diglycerides (especially the 1-O-alkyl,2-acyl compounds). Thus, we have described a patient whose neutrophils show a severe defect in functional activation via chemotaxin receptors, resulting in a selective absence of NADPH oxidase activity, exocytosis from the azurophil granules, and actin polymerization. Our findings show that actin polymerization for neutrophil spreading and locomotion is regulated differently from that for phagocytosis. Also, the release of azurophil and specific granule contents is clearly shown to be regulated in a different way.

Distinct functions of POT1 at telomeres.

The mammalian protein POT1 binds to telomeric single-stranded DNA (ssDNA), protecting chromosome ends from being detected as sites of DNA damage. POT1 is composed of an N-terminal ssDNA-binding domain and a C-terminal protein interaction domain. With regard to the latter, POT1 heterodimerizes with the protein TPP1 to foster binding to telomeric ssDNA in vitro and binds the telomeric double-stranded-DNA-binding protein TRF2. We sought to determine which of these functions-ssDNA, TPP1, or TRF2 binding-was required to protect chromosome ends from being detected as DNA damage. Using separation-of-function POT1 mutants deficient in one of these three activities, we found that binding to TRF2 is dispensable for protecting telomeres but fosters robust loading of POT1 onto telomeric chromatin. Furthermore, we found that the telomeric ssDNA-binding activity and binding to TPP1 are required in cis for POT1 to protect telomeres. Mechanistically, binding of POT1 to telomeric ssDNA and association with TPP1 inhibit the localization of RPA, which can function as a DNA damage sensor, to telomeres.

B-lymphocyte effector functions in health and disease.

B-lymphocytes have traditionally been thought to contribute to immunity and autoimmune disease through terminal differentiation into plasma cells that secrete antibody. However, studies in mice and recent clinical studies have demonstrated that genetically altered B-cell function and B-cell-targeted therapies can significantly affect autoimmune diseases that were predominantly thought to be T-cell-mediated. B-cell depletion in mouse models of disease has also led to the identification of alternative B-cell effector functions that regulate normal immune responses and autoimmune disease. This review highlights multiple B-cell effector mechanisms, including the promotion of cellular immunity, the negative regulation of immune responses, and the production of pathogenic antibodies.

Recursive directional ligation by plasmid reconstruction allows rapid and seamless cloning of oligomeric genes.

This paper reports a new strategy, recursive directional ligation by plasmid reconstruction (PRe-RDL), to rapidly clone highly repetitive polypeptides of any sequence and specified length over a large range of molecular weights. In a single cycle of PRe-RDL, two halves of a parent plasmid, each containing a copy of an oligomer, are ligated together, thereby dimerizing the oligomer and reconstituting a functional plasmid. This process is carried out recursively to assemble an oligomeric gene with the desired number of repeats. PRe-RDL has several unique features that stem from the use of type IIs restriction endonucleases: first, PRe-RDL is a seamless cloning method that leaves no extraneous nucleotides at the ligation junction. Because it uses type IIs endonucleases to ligate the two halves of the plasmid, PRe-RDL also addresses the major limitation of RDL in that it abolishes any restriction on the gene sequence that can be oligomerized. The reconstitution of a functional plasmid only upon successful ligation in PRe-RDL also addresses two other limitations of RDL: the significant background from self-ligation of the vector observed in RDL, and the decreased efficiency of ligation due to nonproductive circularization of the insert. PRe-RDL can also be used to assemble genes that encode different sequences in a predetermined order to encode block copolymers or append leader and trailer peptide sequences to the oligomerized gene.

Scale-wise evolution of rainfall probability density functions fingerprints the rainfall generation mechanism

© 2010 by the American Geophysical Union.The cross-scale probabilistic structure of rainfall intensity records collected over time scales ranging from hours to decades at sites dominated by both convective and frontal systems is investigated. Across these sites, intermittency build-up from slow to fast time-scales is analyzed in terms of heavy tailed and asymmetric signatures in the scale-wise evolution of rainfall probability density functions (pdfs). The analysis demonstrates that rainfall records dominated by convective storms develop heavier-Tailed power law pdfs toward finer scales when compared with their frontal systems counterpart. Also, a concomitant marked asymmetry build-up emerges at such finer time scales. A scale-dependent probabilistic description of such fat tails and asymmetry appearance is proposed based on a modified q-Gaussian model, able to describe the cross-scale rainfall pdfs in terms of the nonextensivity parameter q, a lacunarity (intermittency) correction and a tail asymmetry coefficient, linked to the rainfall generation mechanism.

Desensitization, internalization, and signaling functions of beta-arrestins demonstrated by RNA interference.

Beta-arrestins bind to activated G protein-coupled receptor kinase-phosphorylated receptors, which leads to their desensitization with respect to G proteins, internalization via clathrin-coated pits, and signaling via a growing list of "scaffolded" pathways. To facilitate the discovery of novel adaptor and signaling roles of beta-arrestins, we have developed and validated a generally applicable interfering RNA approach for selectively suppressing beta-arrestins 1 or 2 expression by up to 95%. Beta-arrestin depletion in HEK293 cells leads to enhanced cAMP generation in response to beta(2)-adrenergic receptor stimulation, markedly reduced beta(2)-adrenergic receptor and angiotensin II receptor internalization and impaired activation of the MAP kinases ERK 1 and 2 by angiotensin II. This approach should allow discovery of novel signaling and regulatory roles for the beta-arrestins in many seven-membrane-spanning receptor systems.