Multilevel Training of Binary Morphological Operators

The design of binary morphological operators that are translation-invariant and locally defined by a finite neighborhood window corresponds to the problem of designing Boolean functions. As in any supervised classification problem, morphological operators designed from a training sample also suffer from overfitting. Large neighborhood tends to lead to performance degradation of the designed operator. This work proposes a multilevel design approach to deal with the issue of designing large neighborhood-based operators. The main idea is inspired by stacked generalization (a multilevel classifier design approach) and consists of, at each training level, combining the outcomes of the previous level operators. The final operator is a multilevel operator that ultimately depends on a larger neighborhood than of the individual operators that have been combined. Experimental results show that two-level operators obtained by combining operators designed on subwindows of a large window consistently outperform the single-level operators designed on the full window. They also show that iterating two-level operators is an effective multilevel approach to obtain better results.

Insights on eukaryotic translation initiation factor 5A (eIF5A) in the brain and aging

Long-term memory, a persistent form of synaptic plasticity, requires translation of a subset of mRNA present in neuronal dendrites during a short and critical period through a mechanism not yet fully elucidated. Western blotting analysis revealed a high content of eukaryotic translation initiation factor 5A (eIF5A) in the brain of neonatal rats, a period of intense neurogenesis rate, differentiation and synaptic establishment, when compared to adult rats. Immunohistochemistry analysis revealed that eIF5A is present in the whole brain of adult rats showing a variable content among the cells from different areas (e.g. cortex, hippocampus and cerebellum). A high content of eIF5A in the soma and dendrites of Purkinje cells, key neurons in the control of motor long-term memory in the cerebellum, was observed. Detection of high eIF5A content was revealed in dendritic varicosities of Purkinje cells. Evidence is presented herein that a reduction of eIF5A content is associated to brain aging. (C) 2008 Elsevier B.V. All rights reserved.

T3 acutely increases GH mRNA translation rate and GH secretion in hypothyroid rats

Cytoskeleton controls the stability of transcripts, by mechanisms that involve mRNAs and eEF1A attachment to it. Besides, it plays a key role in protein synthesis and secretion, which seems to be impaired in somatotrophs of hypothyroid rats, whose cytoskeleton is disarranged. This study investigated the: eEF1A and GH mRNA binding to cytoskeleton plus GH mRNA translation rate and GH secretion, in sham-operated and thyroidectomized rats treated with T3 or saline, and killed 30 min thereafter. Thyroidectomy reduced: (a) pituitary F-actin content, and eEF1A plus GH mRNA binding to it; (b) GH mRNA recruitment to polysome; and (c) liver IGF-1 mRNA expression, indicating that GH mRNA stability and translation rate, as well as GH secretion were impaired. T3 acutely reversed all these changes, which points toward a nongenomic action of T3 on cytoskeleton rearrangement, which might contribute to the increase on GH mRNA translation rate and GH secretion. (C) 2009 Elsevier Ireland Ltd. All rights reserved.

Involvement of Eukaryotic Translation Initiation Factor 5A (eIF5A) in Skeletal Muscle Stem Cell Differentiation

The eukaryotic translation initiation factor 5A (eIF5A) contains a special amino acid residue named hypusine that is required for its activity, being produced by a post-translational modification using spermidine as substrate. Stem cells from rat skeletal muscles (satellite cells) were submitted to differentiation and an increase of eIF5A gene expression was observed. Higher content of eIF5A protein was found in satellite cells on differentiation in comparison to non-differentiated satellite cells and skeletal muscle. The treatment with NI-guanyl- 1,7-diaminoheptane (GC7), a hypusination inhibitor, reversibly abolished the differentiation process. In association with the differentiation blockage, an increase of glucose consumption and lactate production and a decrease of glucose and palmitic acid oxidation were observed. A reduction in cell proliferation and protein synthesis was also observed. L-Arginine, a spermidine precursor and partial suppressor of muscle dystrophic phenotype, partially abolished the GC7 inhibitory effect on satellite cell differentiation. These results reveal a new physiological role for eIF5A and contribute to elucidate the molecular mechanisms involved in muscle regeneration.

Cyclic Maximal Ideals of Rings of Differential Operators over Power Series Rings

In [3], Bratti and Takagi conjectured that a first order differential operator S=11 +...+ nn+ with 1,..., n, {x1,..., xn} does not generate a cyclic maximal left (or right) ideal of the ring of differential operators. This is contrary to the case of the Weyl algebra, i.e., the ring of differential operators over the polynomial ring [x1,..., xn]. In this case, we know that such cyclic maximal ideals do exist. In this article, we prove several special cases of the conjecture of Bratti and Takagi.

Non-autonomous semilinear evolution equations with almost sectorial operators

Inspired by the theory of semigroups of growth a, we construct an evolution process of growth alpha. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that. under natural assumptions. a reasonable concept of solution can be given to Such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Holder continuous functions and to a parabolic problem in a domain Omega subset of R(n) with a one dimensional handle.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

CONSTRUCTING QUANTUM OBSERVABLES AND SELF-ADJOINT EXTENSIONS OF SYMMETRIC OPERATORS. III. SELF-ADJOINT BOUNDARY CONDITIONS

This paper completes the review of the theory of self-adjoint extensions of symmetric operators for physicists as a basis for constructing quantum-mechanical observables. It contains a comparative presentation of the well-known methods and a newly proposed method for constructing ordinary self-adjoint differential operators associated with self-adjoint differential expressions in terms of self-adjoint boundary conditions. The new method has the advantage that it does not require explicitly evaluating deficient subspaces and deficiency indices (these latter are determined in passing) and that boundary conditions are of explicit character irrespective of the singularity of a differential expression. General assertions and constructions are illustrated by examples of well-known quantum-mechanical operators like momentum and Hamiltonian.

A new proposal for the picture changing operators in the minimal pure spinor formalism

Using a new proposal for the ""picture lowering"" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude will be written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism. The natural language for relating these formalisms is the. Cech-Dolbeault isomorphism. Moreover, the Dolbeault cocycle corresponding to the tree-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space. Also, the. Cech-Dolbeault language plays a key role for proving the invariance of the scattering amplitude under BRST, Lorentz and supersymmetry transformations, as well as the decoupling of unphysical states. We also relate the Green`s function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders. In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.

Using metrics from complex networks to evaluate machine translation

Establishing metrics to assess machine translation (MT) systems automatically is now crucial owing to the widespread use of MT over the web. In this study we show that such evaluation can be done by modeling text as complex networks. Specifically, we extend our previous work by employing additional metrics of complex networks, whose results were used as input for machine learning methods and allowed MT texts of distinct qualities to be distinguished. Also shown is that the node-to-node mapping between source and target texts (English-Portuguese and Spanish-Portuguese pairs) can be improved by adding further hierarchical levels for the metrics out-degree, in-degree, hierarchical common degree, cluster coefficient, inter-ring degree, intra-ring degree and convergence ratio. The results presented here amount to a proof-of-principle that the possible capturing of a wider context with the hierarchical levels may be combined with machine learning methods to yield an approach for assessing the quality of MT systems. (C) 2010 Elsevier B.V. All rights reserved.

Structural modeling and mutational analysis of yeast eukaryotic translation initiation factor 5A reveal new critical residues and reinforce its involvement in protein synthesis

Eukaryotic translation initiation factor 5A (eIF5A) is a protein that is highly conserved and essential for cell viability. This factor is the only protein known to contain the unique and essential amino acid residue hypusine. This work focused on the structural and functional characterization of Saccharomyces cerevisiae eIF5A. The tertiary structure of yeast eIF5A was modeled based on the structure of its Leishmania mexicana homologue and this model was used to predict the structural localization of new site-directed and randomly generated mutations. Most of the 40 new mutants exhibited phenotypes that resulted from eIF-5A protein-folding defects. Our data provided evidence that the C-terminal alpha-helix present in yeast eIF5A is an essential structural element, whereas the eIF5A N-terminal 10 amino acid extension not present in archaeal eIF5A homologs, is not. Moreover, the mutants containing substitutions at or in the vicinity of the hypusine modification site displayed nonviable or temperature-sensitive phenotypes and were defective in hypusine modification. Interestingly, two of the temperature-sensitive strains produced stable mutant eIF5A proteins - eIF5A(K56A) and eIF5A(Q22H,L93F)- and showed defects in protein synthesis at the restrictive temperature. Our data revealed important structural features of eIF5A that are required for its vital role in cell viability and underscored an essential function of eIF5A in the translation step of gene expression.

An Information Theory framework for two-stage binary image operator design

The design of translation invariant and locally defined binary image operators over large windows is made difficult by decreased statistical precision and increased training time. We present a complete framework for the application of stacked design, a recently proposed technique to create two-stage operators that circumvents that difficulty. We propose a novel algorithm, based on Information Theory, to find groups of pixels that should be used together to predict the Output Value. We employ this algorithm to automate the process of creating a set of first-level operators that are later combined in a global operator. We also propose a principled way to guide this combination, by using feature selection and model comparison. Experimental results Show that the proposed framework leads to better results than single stage design. (C) 2009 Elsevier B.V. All rights reserved.

Spaces of compact operators on C(2(m) circle plus [0, alpha]) spaces

We classify up to isomorphism the spaces of compact operators K(E, F), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2(m) circle plus [0, alpha], the topological sum of Cantor cubes 2(m) and the intervals of ordinal numbers [0, alpha]. More precisely, we prove that if 2(m) and aleph(gamma) are not real-valued measurable cardinals and n >= aleph(0) is not sequential cardinal, then for every ordinals xi, eta, lambda and mu with xi >= omega(1), eta >= omega(1), lambda = mu < omega or lambda, mu is an element of [omega(gamma), omega(gamma+1)[, the following statements are equivalent: (a) K(C(2(m) circle plus [0, lambda]), C(2(n) circle plus [0, xi])) and K(C(2(m) circle plus [0, mu]), C(2(n) circle plus [0, eta]) are isomorphic. (b) Either C([0, xi]) is isomorphic to C([0, eta] or C([0, xi]) is isomorphic to C([0, alpha p]) and C([0, eta]) is isomorphic to C([0,alpha q]) for some regular cardinal alpha and finite ordinals p not equal q. Thus, it is relatively consistent with ZFC that this result furnishes a complete isomorphic classification of these spaces of compact operators. (C) 2010 Elsevier Inc. All rights reserved.