Asymptotics of orthogonal polynomials via the Koosis theorem

The main aim of this short paper is to advertize the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a new theorem about asymptotics of orthogonal polynomi- als for which the Koosis theorem seems to be the most natural tool. Namely, we consider the case when a SzegÄo measure on the unit circumference is perturbed by an arbitrary measure inside the unit disk and an arbitrary Blaschke sequence of point masses outside the unit disk.

Musical actions of dihedral groups

The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor triads. We illustrate both geometrically and algebraically how these two actions are dual. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.

Resurgence of inner solutions for perturbations of the McMillan map

A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove here all the results relative to these equations which are necessary to complete the proof of the main result of [MSS09]. The present work relies on ideas from resurgence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use ´Ecalle’s alien derivations to measure the discrepancy between different Borel-Laplace sums.

On Cooperative solutions of a generalized assignment game: limit theorems to the set of competitive equilibria

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We first establish that the Set-wise stable set is contained in the Core and it contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Second, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff.

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

Multiple non-collinear TF-map alignments of promoter regions

Background: The analysis of the promoter sequence of genes with similar expression patterns isa basic tool to annotate common regulatory elements. Multiple sequence alignments are on thebasis of most comparative approaches. The characterization of regulatory regions from coexpressedgenes at the sequence level, however, does not yield satisfactory results in manyoccasions as promoter regions of genes sharing similar expression programs often do not shownucleotide sequence conservation.Results: In a recent approach to circumvent this limitation, we proposed to align the maps ofpredicted transcription factors (referred as TF-maps) instead of the nucleotide sequence of tworelated promoters, taking into account the label of the corresponding factor and the position in theprimary sequence. We have now extended the basic algorithm to permit multiple promotercomparisons using the progressive alignment paradigm. In addition, non-collinear conservationblocks might now be identified in the resulting alignments. We have optimized the parameters ofthe algorithm in a small, but well-characterized collection of human-mouse-chicken-zebrafishorthologous gene promoters.Conclusion: Results in this dataset indicate that TF-map alignments are able to detect high-levelregulatory conservation at the promoter and the 3'UTR gene regions, which cannot be detectedby the typical sequence alignments. Three particular examples are introduced here to illustrate thepower of the multiple TF-map alignments to characterize conserved regulatory elements inabsence of sequence similarity. We consider this kind of approach can be extremely useful in thefuture to annotate potential transcription factor binding sites on sets of co-regulated genes fromhigh-throughput expression experiments.

SelenoDB 1.0 : a database of selenoprotein genes, proteins and SECIS elements

Selenoproteins are a diverse group of proteinsusually misidentified and misannotated in sequencedatabases. The presence of an in-frame UGA (stop)codon in the coding sequence of selenoproteingenes precludes their identification and correctannotation. The in-frame UGA codons are recodedto cotranslationally incorporate selenocysteine,a rare selenium-containing amino acid. The developmentof ad hoc experimental and, more recently,computational approaches have allowed the efficientidentification and characterization of theselenoproteomes of a growing number of species.Today, dozens of selenoprotein families have beendescribed and more are being discovered in recentlysequenced species, but the correct genomic annotationis not available for the majority of thesegenes. SelenoDB is a long-term project that aims toprovide, through the collaborative effort of experimentaland computational researchers, automaticand manually curated annotations of selenoproteingenes, proteins and SECIS elements. Version 1.0 ofthe database includes an initial set of eukaryoticgenomic annotations, with special emphasis on thehuman selenoproteome, for immediate inspectionby selenium researchers or incorporation into moregeneral databases. SelenoDB is freely available athttp://www.selenodb.org.

Transcription factor map alignment of promoter regions

We address the problem of comparing and characterizing the promoter regions of genes with similar expression patterns. This remains a challenging problem in sequence analysis, because often the promoter regions of co-expressed genes do not show discernible sequence conservation. In our approach, thus, we have not directly compared the nucleotide sequence of promoters. Instead, we have obtained predictions of transcription factor binding sites, annotated the predicted sites with the labels of the corresponding binding factors, and aligned the resulting sequences of labels—to which we refer here as transcription factor maps (TF-maps). To obtain the global pairwise alignment of two TF-maps, we have adapted an algorithm initially developed to align restriction enzyme maps. We have optimized the parameters of the algorithm in a small, but well-curated, collection of human–mouse orthologous gene pairs. Results in this dataset, as well as in an independent much larger dataset from the CISRED database, indicate that TF-map alignments are able to uncover conserved regulatory elements, which cannot be detected by the typical sequence alignments.

Free-and open source software for a course on network management: authoring and enactment of scripts based on collaborative learning strategies

This paper describes a Computer-Supported Collaborative Learning (CSCL) case study in engineering education carried out within the context of a network management course. The case study shows that the use of two computing tools developed by the authors and based on Free- and Open-Source Software (FOSS) provide significant educational benefits over traditional engineering pedagogical approaches in terms of both concepts and engineering competencies acquisition. First, the Collage authoring tool guides and supports the course teacher in the process of authoring computer-interpretable representations (using the IMS Learning Design standard notation) of effective collaborative pedagogical designs. Besides, the Gridcole system supports the enactment of that design by guiding the students throughout the prescribed sequence of learning activities. The paper introduces the goals and context of the case study, elaborates onhow Collage and Gridcole were employed, describes the applied evaluation methodology, anddiscusses the most significant findings derived from the case study.

Applause identification and its relevance to archival of Carnatic music

A Carnatic music concert is made up of a sequence of pieces, where each piece corresponds to a particular genre and ra¯aga (melody). Unlike a western music concert, the artist may be applauded intra-performance inter-performance. Most Carnatic music that is archived today correspond to a single audio recordings of entire concerts.The purpose of this paper is to segment single audio recordings into a sequence of pieces using thecharacteristic features of applause and music. Spectral flux, spectral entropy change quite significantly from music to applause and vice-versa. The characteristics of these features for a subset of concerts was studied. A threshold based approach was used to segment the pieces into music fragments and applauses. Preliminary resultson recordings 19 concerts from matched microphones show that the EER is about 17% for a resolution of 0.25 seconds. Further, a parameter called CUSUM is estimatedfor the applause regions. The CUSUM values determine the strength of the applause. The CUSUM is used to characterise the highlights of a concert.

A global view of economic growth

This paper integrates in a unified and tractable framework some of the key insights of the field of international trade and economic growth. It examines a sequence of theoretical models that share a common description of technology and preferences but differ on their assumptions about trade frictions. By comparing the predictions of these models against each other, it is possible to identify a variety of channels through which trade affects the evolution of world income and its geographical distribution. By comparing the predictions of these models against the data, it is also possible to construct coherent explanations of income differences and long-run trends in economic growth.

Nonlinear models and small sample performance of the generalized method of moments

In this paper I explore the issue of nonlinearity (both in the datageneration process and in the functional form that establishes therelationship between the parameters and the data) regarding the poorperformance of the Generalized Method of Moments (GMM) in small samples.To this purpose I build a sequence of models starting with a simple linearmodel and enlarging it progressively until I approximate a standard (nonlinear)neoclassical growth model. I then use simulation techniques to find the smallsample distribution of the GMM estimators in each of the models.

Optimal taxation without state-contingent debt

To recover a version of Barro's (1979) `random walk'tax smoothing outcome, we modify Lucas and Stokey's (1983) economyto permit only risk--free debt. This imparts near unit root like behaviorto government debt, independently of the government expenditureprocess, a realistic outcome in the spirit of Barro's. We showhow the risk--free--debt--only economy confronts the Ramsey plannerwith additional constraints on equilibrium allocations thattake the form of a sequence of measurability conditions.We solve the Ramsey problem by formulating it in terms of a Lagrangian,and applying a Parameterized Expectations Algorithm tothe associated first--order conditions. The first--order conditions andnumerical impulse response functions partially affirmBarro's random walk outcome. Though the behaviors oftax rates, government surpluses, and government debts differ, allocationsare very close for computed Ramsey policies across incomplete and completemarkets economies.

A zero-delay sequential scheme for lossy coding of individual sequences

We consider adaptive sequential lossy coding of bounded individual sequences when the performance is measured by the sequentially accumulated mean squared distortion. Theencoder and the decoder are connected via a noiseless channel of capacity $R$ and both are assumed to have zero delay. No probabilistic assumptions are made on how the sequence to be encoded is generated. For any bounded sequence of length $n$, the distortion redundancy is defined as the normalized cumulative distortion of the sequential scheme minus the normalized cumulative distortion of the best scalarquantizer of rate $R$ which is matched to this particular sequence. We demonstrate the existence of a zero-delay sequential scheme which uses common randomization in the encoder and the decoder such that the normalized maximum distortion redundancy converges to zero at a rate $n^{-1/5}\log n$ as the length of the encoded sequence $n$ increases without bound.

What is what?: A simple time-domain test of long-memory vs. structural breaks

This paper proposes a new time-domain test of a process being I(d), 0 < d = 1, under the null, against the alternative of being I(0) with deterministic components subject to structural breaks at known or unknown dates, with the goal of disentangling the existing identification issue between long-memory and structural breaks. Denoting by AB(t) the different types of structural breaks in the deterministic components of a time series considered by Perron (1989), the test statistic proposed here is based on the t-ratio (or the infimum of a sequence of t-ratios) of the estimated coefficient on yt-1 in an OLS regression of ?dyt on a simple transformation of the above-mentioned deterministic components and yt-1, possibly augmented by a suitable number of lags of ?dyt to account for serial correlation in the error terms. The case where d = 1 coincides with the Perron (1989) or the Zivot and Andrews (1992) approaches if the break date is known or unknown, respectively. The statistic is labelled as the SB-FDF (Structural Break-Fractional Dickey- Fuller) test, since it is based on the same principles as the well-known Dickey-Fuller unit root test. Both its asymptotic behavior and finite sample properties are analyzed, and two empirical applications are provided.