Assembling genes from predicted exons in linear time with dynamic programming

In a number of programs for gene structure prediction in higher eukaryotic genomic sequences, exon prediction is decoupled from gene assembly: a large pool of candidate exons is predicted and scored from features located in the query DNA sequence, and candidate genes are assembled from such a pool as sequences of nonoverlapping frame-compatible exons. Genes are scored as a function of the scores of the assembled exons, and the highest scoring candidate gene is assumed to be the most likely gene encoded by the query DNA sequence. Considering additive gene scoring functions, currently available algorithms to determine such a highest scoring candidate gene run in time proportional to the square of the number of predicted exons. Here, we present an algorithm whose running time grows only linearly with the size of the set of predicted exons. Polynomial algorithms rely on the fact that, while scanning the set of predicted exons, the highest scoring gene ending in a given exon can be obtained by appending the exon to the highest scoring among the highest scoring genes ending at each compatible preceding exon. The algorithm here relies on the simple fact that such highest scoring gene can be stored and updated. This requires scanning the set of predicted exons simultaneously by increasing acceptor and donor position. On the other hand, the algorithm described here does not assume an underlying gene structure model. Indeed, the definition of valid gene structures is externally defined in the so-called Gene Model. The Gene Model specifies simply which gene features are allowed immediately upstream which other gene features in valid gene structures. This allows for great flexibility in formulating the gene identification problem. In particular it allows for multiple-gene two-strand predictions and for considering gene features other than coding exons (such as promoter elements) in valid gene structures.

Characterization of myocardial deformation in patients with different etiologies of left ventricular hypertrophy by using strain distribution from Magnetic Resonance Imaging

Introducción y objetivos. Se ha señalado que, en la miocardiopatía hipertrófica (MCH), la desorganización de las fibras regionales da lugar a segmentos en los que la deformación es nula o está gravemente reducida, y que estos segmentos tienen una distribución no uniforme en el ventrículo izquierdo (VI). Esto contrasta con lo observado en otros tipos de hipertrofia como en el corazón de atleta o la hipertrofia ventricular izquierda hipertensiva (HVI-HT), en los que puede haber una deformación cardiaca anormal, pero nunca tan reducida como para que se observe ausencia de deformación. Así pues, proponemos el empleo de la distribución de los valores de strain para estudiar la deformación en la MCH. Métodos. Con el empleo de resonancia magnética marcada (tagged), reconstruimos la deformación sistólica del VI de 12 sujetos de control, 10 atletas, 12 pacientes con MCH y 10 pacientes con HVI-HT. La deformación se cuantificó con un algoritmo de registro no rígido y determinando los valores de strain sistólico máximo radial y circunferencial en 16 segmentos del VI. Resultados. Los pacientes con MCH presentaron unos valores medios de strain significativamente inferiores a los de los demás grupos. Sin embargo, aunque la deformación observada en los individuos sanos y en los pacientes con HVI-HT se concentraba alrededor del valor medio, en la MCH coexistían segmentos con contracción normal y segmentos con una deformación nula o significativamente reducida, con lo que se producía una mayor heterogeneidad de los valores de strain. Se observaron también algunos segmentos sin deformación incluso en ausencia de fibrosis o hipertrofia. Conclusiones. La distribución de strain caracteriza los patrones específicos de deformación miocárdica en pacientes con diferentes etiologías de la HVI. Los pacientes con MCH presentaron un valor medio de strain significativamente inferior, así como una mayor heterogeneidad de strain (en comparación con los controles, los atletas y los pacientes con HVI-HT), y tenían regiones sin deformación.

On codes, matroids, and secure multiparty computation from linear secret-sharing schemes

Error-correcting codes and matroids have been widely used in the study of ordinary secret sharing schemes. In this paper, the connections between codes, matroids, and a special class of secret sharing schemes, namely, multiplicative linear secret sharing schemes (LSSSs), are studied. Such schemes are known to enable multiparty computation protocols secure against general (nonthreshold) adversaries.Two open problems related to the complexity of multiplicative LSSSs are considered in this paper. The first one deals with strongly multiplicative LSSSs. As opposed to the case of multiplicative LSSSs, it is not known whether there is an efficient method to transform an LSSS into a strongly multiplicative LSSS for the same access structure with a polynomial increase of the complexity. A property of strongly multiplicative LSSSs that could be useful in solving this problem is proved. Namely, using a suitable generalization of the well-known Berlekamp–Welch decoder, it is shown that all strongly multiplicative LSSSs enable efficient reconstruction of a shared secret in the presence of malicious faults. The second one is to characterize the access structures of ideal multiplicative LSSSs. Specifically, the considered open problem is to determine whether all self-dual vector space access structures are in this situation. By the aforementioned connection, this in fact constitutes an open problem about matroid theory, since it can be restated in terms of representability of identically self-dual matroids by self-dual codes. A new concept is introduced, the flat-partition, that provides a useful classification of identically self-dual matroids. Uniform identically self-dual matroids, which are known to be representable by self-dual codes, form one of the classes. It is proved that this property also holds for the family of matroids that, in a natural way, is the next class in the above classification: the identically self-dual bipartite matroids.

A systolic array for linear MIMO detection based on an all-swap lattice reduction algorithm

A systolic array to implement lattice-reduction-aided lineardetection is proposed for a MIMO receiver. The lattice reductionalgorithm and the ensuing linear detections are operated in the same array, which can be hardware-efficient. All-swap lattice reduction algorithm (ASLR) is considered for the systolic design.ASLR is a variant of the LLL algorithm, which processes all lattice basis vectors within one iteration. Lattice-reduction-aided linear detection based on ASLR and LLL algorithms have very similarbit-error-rate performance, while ASLR is more time efficient inthe systolic array, especially for systems with a large number ofantennas.

Determinants of linear judgment: A meta-analysis of lens model studies

The mathematical representation of Brunswik s lens model has been usedextensively to study human judgment and provides a unique opportunity to conduct ameta-analysis of studies that covers roughly five decades. Specifically, we analyzestatistics of the lens model equation (Tucker, 1964) associated with 259 different taskenvironments obtained from 78 papers. In short, we find on average fairly high levelsof judgmental achievement and note that people can achieve similar levels of cognitiveperformance in both noisy and predictable environments. Although overall performancevaries little between laboratory and field studies, both differ in terms of components ofperformance and types of environments (numbers of cues and redundancy). An analysisof learning studies reveals that the most effective form of feedback is information aboutthe task. We also analyze empirically when bootstrapping is more likely to occur. Weconclude by indicating shortcomings of the kinds of studies conducted to date, limitationsin the lens model methodology, and possibilities for future research.

Fusion of data sets in multivariate linear regression with errors-in-variables

We consider the application of normal theory methods to the estimation and testing of a general type of multivariate regressionmodels with errors--in--variables, in the case where various data setsare merged into a single analysis and the observable variables deviatepossibly from normality. The various samples to be merged can differ on the set of observable variables available. We show that there is a convenient way to parameterize the model so that, despite the possiblenon--normality of the data, normal--theory methods yield correct inferencesfor the parameters of interest and for the goodness--of--fit test. Thetheory described encompasses both the functional and structural modelcases, and can be implemented using standard software for structuralequations models, such as LISREL, EQS, LISCOMP, among others. An illustration with Monte Carlo data is presented.

Equivalence of piecewise-linear approximation and Lagrangian relaxation for network revenue management

The network revenue management (RM) problem arises in airline, hotel, media,and other industries where the sale products use multiple resources. It can be formulatedas a stochastic dynamic program but the dynamic program is computationallyintractable because of an exponentially large state space, and a number of heuristicshave been proposed to approximate it. Notable amongst these -both for their revenueperformance, as well as their theoretically sound basis- are approximate dynamic programmingmethods that approximate the value function by basis functions (both affinefunctions as well as piecewise-linear functions have been proposed for network RM)and decomposition methods that relax the constraints of the dynamic program to solvesimpler dynamic programs (such as the Lagrangian relaxation methods). In this paperwe show that these two seemingly distinct approaches coincide for the network RMdynamic program, i.e., the piecewise-linear approximation method and the Lagrangianrelaxation method are one and the same.

A new compact linear programming formulation for choice network revenue management

The choice network revenue management model incorporates customer purchase behavioras a function of the offered products, and is the appropriate model for airline and hotel networkrevenue management, dynamic sales of bundles, and dynamic assortment optimization.The optimization problem is a stochastic dynamic program and is intractable. A certainty-equivalencerelaxation of the dynamic program, called the choice deterministic linear program(CDLP) is usually used to generate dyamic controls. Recently, a compact linear programmingformulation of this linear program was given for the multi-segment multinomial-logit (MNL)model of customer choice with non-overlapping consideration sets. Our objective is to obtaina tighter bound than this formulation while retaining the appealing properties of a compactlinear programming representation. To this end, it is natural to consider the affine relaxationof the dynamic program. We first show that the affine relaxation is NP-complete even for asingle-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a newcompact linear program that approximates the dynamic programming value function betterthan CDLP, provably between the CDLP value and the affine relaxation, and often comingclose to the latter in our numerical experiments. When the segment consideration sets overlap,we show that some strong equalities called product cuts developed for the CDLP remain validfor our new formulation. Finally we perform extensive numerical comparisons on the variousbounds to evaluate their performance.

Asymptotic robustness in multi-sample analysis of multivariate linear relations

Standard methods for the analysis of linear latent variable models oftenrely on the assumption that the vector of observed variables is normallydistributed. This normality assumption (NA) plays a crucial role inassessingoptimality of estimates, in computing standard errors, and in designinganasymptotic chi-square goodness-of-fit test. The asymptotic validity of NAinferences when the data deviates from normality has been calledasymptoticrobustness. In the present paper we extend previous work on asymptoticrobustnessto a general context of multi-sample analysis of linear latent variablemodels,with a latent component of the model allowed to be fixed across(hypothetical)sample replications, and with the asymptotic covariance matrix of thesamplemoments not necessarily finite. We will show that, under certainconditions,the matrix $\Gamma$ of asymptotic variances of the analyzed samplemomentscan be substituted by a matrix $\Omega$ that is a function only of thecross-product moments of the observed variables. The main advantage of thisis thatinferences based on $\Omega$ are readily available in standard softwareforcovariance structure analysis, and do not require to compute samplefourth-order moments. An illustration with simulated data in the context ofregressionwith errors in variables will be presented.

Finite sample nonparametric tests for linear regressions

We introduce several exact nonparametric tests for finite sample multivariatelinear regressions, and compare their powers. This fills an important gap inthe literature where the only known nonparametric tests are either asymptotic,or assume one covariate only.

Solving non-linear stochastic models by parameterizing expectations: An application to asset pricing with production

A new algorithm called the parameterized expectations approach(PEA) for solving dynamic stochastic models under rational expectationsis developed and its advantages and disadvantages are discussed. Thisalgorithm can, in principle, approximate the true equilibrium arbitrarilywell. Also, this algorithm works from the Euler equations, so that theequilibrium does not have to be cast in the form of a planner's problem.Monte--Carlo integration and the absence of grids on the state variables,cause the computation costs not to go up exponentially when the numberof state variables or the exogenous shocks in the economy increase. \\As an application we analyze an asset pricing model with endogenousproduction. We analyze its implications for time dependence of volatilityof stock returns and the term structure of interest rates. We argue thatthis model can generate hump--shaped term structures.

On the throughput-WIP trade-off in queueing systems, diminishing returns and the threshold property: A linear programming approach

We present a new unifying framework for investigating throughput-WIP(Work-in-Process) optimal control problems in queueing systems,based on reformulating them as linear programming (LP) problems withspecial structure: We show that if a throughput-WIP performance pairin a stochastic system satisfies the Threshold Property we introducein this paper, then we can reformulate the problem of optimizing alinear objective of throughput-WIP performance as a (semi-infinite)LP problem over a polygon with special structure (a thresholdpolygon). The strong structural properties of such polygones explainthe optimality of threshold policies for optimizing linearperformance objectives: their vertices correspond to the performancepairs of threshold policies. We analyze in this framework theversatile input-output queueing intensity control model introduced byChen and Yao (1990), obtaining a variety of new results, including (a)an exact reformulation of the control problem as an LP problem over athreshold polygon; (b) an analytical characterization of the Min WIPfunction (giving the minimum WIP level required to attain a targetthroughput level); (c) an LP Value Decomposition Theorem that relatesthe objective value under an arbitrary policy with that of a giventhreshold policy (thus revealing the LP interpretation of Chen andYao's optimality conditions); (d) diminishing returns and invarianceproperties of throughput-WIP performance, which underlie thresholdoptimality; (e) a unified treatment of the time-discounted andtime-average cases.