Deterministic Polynomial-Time Algorithms for Designing Short DNA Words

Designing short DNA words is a problem of constructing a set (i.e., code) of n DNA strings (i.e., words) with the minimum length such that the Hamming distance between each pair of words is at least k and the n words satisfy a set of additional constraints. This problem has applications in, e.g., DNA self-assembly and DNA arrays. Previous works include those that extended results from coding theory to obtain bounds on code and word sizes for biologically motivated constraints and those that applied heuristic local searches, genetic algorithms, and randomized algorithms. In particular, Kao, Sanghi, and Schweller (2009) developed polynomial-time randomized algorithms to construct n DNA words of length within a multiplicative constant of the smallest possible word length (e.g., 9 max{log n, k}) that satisfy various sets of constraints with high probability. In this paper, we give deterministic polynomial-time algorithms to construct DNA words based on derandomization techniques. Our algorithms can construct n DNA words of shorter length (e.g., 2.1 log n + 6.28 k) and satisfy the same sets of constraints as the words constructed by the algorithms of Kao et al. Furthermore, we extend these new algorithms to construct words that satisfy a larger set of constraints for which the algorithms of Kao et al. do not work.Comment: 27 page

Co-expression of Gbeta 5 Enhances the Function of Two Ggamma Subunit-like Domain-containing Regulators of G Protein Signaling Proteins

Regulators of G protein signaling (RGS) stimulate the GTPase activity of G protein Galpha subunits and probably play additional roles. Some RGS proteins contain a Ggamma subunit-like (GGL) domain, which mediates a specific interaction with Gbeta 5. The role of such interactions in RGS function is unclear. RGS proteins can accelerate the kinetics of coupling of G protein-coupled receptors to G-protein-gated inwardly rectifying K+ (GIRK) channels. Therefore, we coupled m2-muscarinic acetylcholine receptors to GIRK channels in Xenopus oocytes to evaluate the effect of Gbeta 5 on RGS function. Co-expression of either RGS7 or RGS9 modestly accelerated GIRK channel kinetics. When Gbeta 5 was co-expressed with either RGS7 or RGS9, the acceleration of GIRK channel kinetics was strongly increased over that produced by RGS7 or RGS9 alone. RGS function was not enhanced by co-expression of Gbeta 1, and co-expression of Gbeta 5 alone had no effect on GIRK channel kinetics. Gbeta 5 did not modulate the function either of RGS4, an RGS protein that lacks a GGL domain, or of a functional RGS7 construct in which the GGL domain was omitted. Enhancement of RGS7 function by Gbeta 5 was not a consequence of an increase in the amount of plasma membrane or cytosolic RGS7 protein

A Link-Based Day-to-Day Traffic Assignment Model

Existing day-to-day traffic assignment models are all built upon path flow variables. This paper demonstrates two essential shortcomings of these path-based models. One is that their application requires a given initial path flow pattern, which is typically unidentifiable, i.e., mathematically nonunique and practically unobservable. In particular, we show that, for the path-based models, different initial path flow patterns constituting the same link flow pattern generally gives different day-to-day link flow evolutions. The other shortcoming of the path-based models is the path-overlapping problem. That is, the path-based models ignore the interdependence among paths and thus can give very unreasonable results for networks with paths overlapping with each other. These two path-based problems exist for most (if not all) deterministic day-to-day dynamics whose fixed points are the classic Wardrop user equilibrium. To avoid the two path-based problems, we propose a day-to-day traffic assignment model that directly deals with link flow variables. Our link-based model captures travelers\u27 cost-minimization behavior in their path finding as well as their inertia. The fixed point of our link-based dynamical system is the classic Wardrop user equilibrium

A Generalized Flow Splitting Model for Day-to-day Traffic Assignment

AbstractThe splitting rate model proposed by Smith and Mounce (2011) establishes a traffic evolution process on a link-node network representation, which overcomes the difficulties in applying traditional path-based models and provides the ease of implementing controls at nodes. While their model offers a new method for modeling traffic evolution, it contains an ad-hoc step of flow adjustment to preserve the flow conservation. This flow adjustment step leads to difficulties in analyzing the system properties. This paper proposes a generalized flow splitting model for day-to-day traffic assignment based on the concept of splitting flow at nodes. The proposed model preserves the flow conservation endogenously by introducing the inflow variable into the formulation. The generalized formulation provides the ease to construct a variety of day-to-day traffic assignment models, and serves as a framework for analyzing the models’ properties, such as the invariance property and the preservation of the Lipschitz continuity and strong monotonicity. Specifically, a proportional-adjustment model and a projection-type model are developed based on the proposed generalized formulation. A numerical example demonstrates the ease of implementing the proposed generalized model, as well as its convergence to user equilibrium

Stimulated emission and ultrafast carrier relaxation in AlGaN/GaN multiple quantum wells

Stimulated emission (SE) and ultrafast carrier relaxation dynamics were measured in two AlxGa1−xN/GaNmultiple-quantum-well(MQW) structures, grown in a Ga-rich environment with x=0.2 and 0.3, respectively. The threshold density for SE (Ith≃100 μJ/cm2) was found to be independent of x. Room-temperature, time-resolved, differential transmission measurements mapped the carrier relaxation mechanisms for above barrier energy excitation. Photoexcited carriers are observed to relax into the QWs in \u3c1 ps, while carrier recombination times as fast as 30 ps were measured. For excitation above Ith, SE is shown to deplete carriers in the barriers through a cascaded refilling of the QW state undergoing SE. Similar behavior is seen in an Al0.3Ga0.7N/GaNMQW grown with a N-rich atmosphere, but the relaxation phenomena of all AlGaN MQWs are significantly faster than observed in InGaN MQWs of similar structure

Labeled Partitions with Colored Permutations

In this paper, we extend the notion of labeled partitions with ordinary permutations to colored permutations in the sense that the colors are endowed with a cyclic structure. We use labeled partitions with colored permutations to derive the generating function of the $\mathrm{fmaj}_k$ indices of colored permutations. The second result is a combinatorial treatment of a relation on the q-derangement numbers with respect to colored permutations which leads to the formula of Chow for signed permutations and the formula of Faliharimalala and Zeng [10] on colored permutations. The third result is an involution on permutations that implies the generating function formula for the signed q-counting of the major indices due to Gessel and Simon. This involution can be extended to signed permutations. In this way, we obtain a combinatorial interpretation of a formula of Adin, Gessel and Roichman.Comment: 14 page

Adaptive Testing for Connected and Automated Vehicles with Sparse Control Variates in Overtaking Scenarios

Testing and evaluation is a critical step in the development and deployment of connected and automated vehicles (CAVs). Due to the black-box property and various types of CAVs, how to test and evaluate CAVs adaptively remains a major challenge. Many approaches have been proposed to adaptively generate testing scenarios during the testing process. However, most existing approaches cannot be applied to complex scenarios, where the variables needed to define such scenarios are high dimensional. Towards filling this gap, the adaptive testing with sparse control variates method is proposed in this paper. Instead of adaptively generating testing scenarios, our approach evaluates CAVs' performances by adaptively utilizing the testing results. Specifically, each testing result is adjusted using multiple linear regression techniques based on control variates. As the regression coefficients can be adaptively optimized for the CAV under test, using the adjusted results can reduce the estimation variance, compared with using the testing results directly. To overcome the high dimensionality challenge, sparse control variates are utilized only for the critical variables of testing scenarios. To validate the proposed method, the high-dimensional overtaking scenarios are investigated, and the results demonstrate that our approach can further accelerate the evaluation process by about 30 times