Capturability of augmented proportional navigation (APN) guidance with nonlinear engagement dynamics

Proportional Navigation (PN) and its variants are widely used guidance philosophies. However, in the presence of target maneuver, PN guidance law is effective only for a restrictive set of initial geometries. To account for target maneuvers, the concept of Augmented Proportional Navigation (APN) guidance law was introduced and analyzed in a linearized interceptor-target engagement framework presented in literature. However, there is no work in the literature, that addresses the capturability performance of the APN guidance law in a nonlinear engagement framework. This paper presents such an analysis and obtains the conditions for capturability. It also shows that a shorter time of interception is obtained when APN is formulated in the nonlinear framework as proposed in this paper. Simulation results are given to support the theoretical findings.

Energy loss due to adhesion in longitudinal impact of elastic cylinders

Adhesive interaction between impacting bodies can cause energy loss, even in an otherwise elastic impact. Adhesion force induces tensile stress in the bodies, which modifies the stress wave profile and influences the restitution behavior. We investigate this effect by developing a finite element framework, which incorporates a Lennard-Jones-type potential for modeling the adhesive interaction between volume elements. With this framework, the classical problems in contact mechanics can be revisited without the restrictive surface-force approximation. In this paper, we study the longitudinal impact of an elastic cylinder on a rigid half-space with adhesion. In the absence of adhesion, this problem reduces to the impact between two identical cylinders in which there is no energy loss. Adhesion causes a fraction of energy in the stress waves to remain in the cylinder as residual stress waves. This apparent loss in kinetic energy is shown to be a unique function of maximum tensile strain energy. We have developed a 1-D model in terms of interaction force parameters, velocity and material properties to estimate the tensile stain energy. We show that this model can be used to predict practically important phenomena like capture wherein the impacting bodies stick together. (C) 2013 Elsevier Masson SAS. All rights reserved.

Subexponential Algorithm for d-Cluster Edge Deletion: Exception or Rule?

The correlation clustering problem is a fundamental problem in both theory and practice, and it involves identifying clusters of objects in a data set based on their similarity. A traditional modeling of this question as a graph theoretic problem involves associating vertices with data points and indicating similarity by adjacency. Clusters then correspond to cliques in the graph. The resulting optimization problem, Cluster Editing (and several variants) are very well-studied algorithmically. In many situations, however, translating clusters to cliques can be somewhat restrictive. A more flexible notion would be that of a structure where the vertices are mutually ``not too far apart'', without necessarily being adjacent. One such generalization is realized by structures called s-clubs, which are graphs of diameter at most s. In this work, we study the question of finding a set of at most k edges whose removal leaves us with a graph whose components are s-clubs. Recently, it has been shown that unless Exponential Time Hypothesis fail (ETH) fails Cluster Editing (whose components are 1-clubs) does not admit sub-exponential time algorithm STACS, 2013]. That is, there is no algorithm solving the problem in time 2 degrees((k))n(O(1)). However, surprisingly they show that when the number of cliques in the output graph is restricted to d, then the problem can be solved in time O(2(O(root dk)) + m + n). We show that this sub-exponential time algorithm for the fixed number of cliques is rather an exception than a rule. Our first result shows that assuming the ETH, there is no algorithm solving the s-Club Cluster Edge Deletion problem in time 2 degrees((k))n(O(1)). We show, further, that even the problem of deleting edges to obtain a graph with d s-clubs cannot be solved in time 2 degrees((k))n(O)(1) for any fixed s, d >= 2. This is a radical contrast from the situation established for cliques, where sub-exponential algorithms are known.

Compiler/Runtime Framework for Dynamic Dataflow Parallelization of Tiled Programs

Task-parallel languages are increasingly popular. Many of them provide expressive mechanisms for intertask synchronization. For example, OpenMP 4.0 will integrate data-driven execution semantics derived from the StarSs research language. Compared to the more restrictive data-parallel and fork-join concurrency models, the advanced features being introduced into task-parallelmodels in turn enable improved scalability through load balancing, memory latency hiding, mitigation of the pressure on memory bandwidth, and, as a side effect, reduced power consumption. In this article, we develop a systematic approach to compile loop nests into concurrent, dynamically constructed graphs of dependent tasks. We propose a simple and effective heuristic that selects the most profitable parallelization idiom for every dependence type and communication pattern. This heuristic enables the extraction of interband parallelism (cross-barrier parallelism) in a number of numerical computations that range from linear algebra to structured grids and image processing. The proposed static analysis and code generation alleviates the burden of a full-blown dependence resolver to track the readiness of tasks at runtime. We evaluate our approach and algorithms in the PPCG compiler, targeting OpenStream, a representative dataflow task-parallel language with explicit intertask dependences and a lightweight runtime. Experimental results demonstrate the effectiveness of the approach.

Deformation pathways and breakup modes in acoustically levitated bicomponent droplets under external heating

Controlled breakup of droplets using heat or acoustics is pivotal in applications such as pharmaceutics, nanoparticle production, and combustion. In the current work we have identified distinct thermal acoustics-induced deformation regimes (ligaments and bubbles) and breakup dynamics in externally heated acoustically levitated bicomponent (benzene-dodecane) droplets with a wide variation in volatility of the two components (benzene is significantly more volatile than dodecane). We showcase the physical mechanism and universal behavior of droplet surface caving in leading to the inception and growth of ligaments. The caving of the top surface is governed by a balance between the acoustic pressure field and the restrictive surface tension of the droplet. The universal collapse of caving profiles for different benzene concentration (<70% by volume) is shown by using an appropriate time scale obtained from force balance. Continuous caving leads to the formation of a liquid membrane-type structure which undergoes radial extension due to inertia gained during the precursor phase. The membrane subsequently closes at the rim and the kinetic energy leads to ligament formation and growth. Subsequent ligament breakup is primarily Rayleigh-Plateau type. The breakup mode shifts to diffusional entrapment-induced boiling with an increase in concentration of the volatile component (benzene >70% by volume). The findings are portable to any similar bicomponent systems with differential volatility.

La calidad de vida y salud desde una antropología cristiana

Resumen: Este trabajo examina con atento discernimiento los términos “calidad de vida” y “promoción de la salud” que identifican uno de los principales objetivos de las sociedades contemporáneas. En el mismo se cita la encíclica Evangelium vitae que dice “La llamada ‘calidad de vida’ se interpreta principal o exclusivamente como eficiencia económica, consumismo desordenado, belleza y goce de la vida física, olvidando las dimensiones más profundas -relacionales, espirituales y religiosas- de la existencia” (n. 23). Todas las dimensiones de la persona -la corpórea, la psicológica, la espiritual y la moral- han de promoverse en armonía. Esto supone la presencia de condiciones sociales y ambientales aptas para favorecer ese desarrollo armonioso. En la actualidad la expresión “calidad de vida” no está fundada en una antropología filosófica y teológica, favoreciendo una noción restrictiva y selectiva. En referencia al concepto de salud también ha sufrido una desviación análoga. Se debe proteger y cuidar la salud como equilibrio físico, psíquico y espiritual del ser humano. Se analiza, asimismo, el concepto de “bien común” en relación a la sociedad, la democracia y el trabajo de la política en la construcción del mismo. En el texto se discute sobre la priorización de intervenciones de salud y se presentan posibles respuestas. Se muestran criterios de decisión al momento de distribuir recursos entre las distintas necesidades de salud, buscando definir principios éticos relevantes para una priorización de intervenciones.

El caso Artavia Murillo y otros vs. Costa Rica (fecundación in vitro) : la redefinición del derecho a la vida desde la concepción, reconocido en la Convención Americana

Resumen: El Artículo 4(1) de la Convención Americana protege la vida de la persona por nacer desde el momento de la concepción. Esta nota analiza críticamente la interpretación restrictiva de este artículo realizada por la Corte Interamericana de Derechos Humanos en el caso Artavia Murillo y otros vs. Costa Rica, sobre la prohibición de la fecundación in vitro en ese país. La nota describe cómo la Corte revirtió parcialmente el reconocimiento del derecho a la vida del niño no nacido, qué hicieron los Estados latinoamericanos, al adoptar la Convención Americana, a través de una aplicación distorsionada de sus propias técnicas de interpretación y de las normas internacionales de interpretación de los tratados.

La gestión de la innovación como la gestión de un ecosistema heterogéneo y estructurado

[ES] Este artículo aborda la innovación como un proceso evolutivo que toma lugar en un ecosistema heterogéneo estructurado. Esto permite entender la gestión de la innovación como la gestión de las interacciones en un ecosistema que se quiere modificar.

New variational principles for systems of partial differential equations

The question of finding variational principles for coupled systems of first order partial differential equations is considered. Using a potential representation for solutions of the first order system a higher order system is obtained. Existence of a variational principle follows if the original system can be transformed to a self-adjoint higher order system. Existence of variational principles for all linear wave equations with constant coefficients having real dispersion relations is established. The method of adjoining some of the equations of the original system to a suitable Lagrangian function by the method of Lagrange multipliers is used to construct new variational principles for a class of linear systems. The equations used as side conditions must satisfy highly-restrictive integrability conditions. In the more difficult nonlinear case the system of two equations in two independent variables can be analyzed completely. For systems determined by two conservation laws the side condition must be a conservation law in addition to satisfying the integrability conditions.

Del miedo a la obesidad a la obsesión por la delgadez; actitudes y dieta

Este trabajo se encuentra bajo la licencia Creative Commons Attribution 3.0.

Cell-targeted regulation of gene expression through synthetic RNA devices

The ability to interface with and program cellular function remains a challenging research frontier in biotechnology. Although the emerging field of synthetic biology has recently generated a variety of gene-regulatory strategies based on synthetic RNA molecules, few strategies exist through which to control such regulatory effects in response to specific exogenous or endogenous molecular signals. Here, we present the development of an engineered RNA-based device platform to detect and act on endogenous protein signals, linking these signals to the regulation of genes and thus cellular function.

We describe efforts to develop an RNA-based device framework for regulating endogenous genes in human cells. Previously developed RNA control devices have demonstrated programmable ligand-responsive genetic regulation in diverse cell types, and we attempted to adapt this class of cis-acting control elements to function in trans. We divided the device into two strands that reconstitute activity upon hybridization. Device function was optimized using an in vivo model system, and we found that device sequence is not as flexible as previously reported. After verifying the in vitro activity of our optimized design, we attempted to establish gene regulation in a human cell line using additional elements to direct device stability, structure, and localization. The significant limitations of our platform prevented endogenous gene regulation.

We next describe the development of a protein-responsive RNA-based regulatory platform. Employing various design strategies, we demonstrated functional devices that both up- and downregulate gene expression in response to a heterologous protein in a human cell line. The activity of our platform exceeded that of a similar, small-molecule-responsive platform. We demonstrated the ability of our devices to respond to both cytoplasmic- and nuclear-localized protein, providing insight into the mechanism of action and distinguishing our platform from previously described devices with more restrictive ligand localization requirements. Finally, we demonstrated the versatility of our device platform by developing a regulatory device that responds to an endogenous signaling protein.

The foundational tool we present here possesses unique advantages over previously described RNA-based gene-regulatory platforms. This genetically encoded technology may find future applications in the development of more effective diagnostic tools and targeted molecular therapy strategies.

The Art of Madness

The nineteenth century was not an entirely kind time for the female artist. Coming of age as the 1800’s bridged into its latter half, literary artists Elizabeth Stuart Phelps Ward, Charlotte Perkins Gilman, and Kate Chopin were all well aware of their uncharitable culture. Equipped with firm feminist bents and creative visions, each of three women produced a seminal work – The Story of Avis, “The Yellow Wallpaper,” and The Awakening, respectively – taking that atmosphere to task. In these stories, each of the three women produces a female protagonist who struggles for having been born simultaneously an artist and a woman. The writers pit their women’s desires against the restrictive latitude of their time and show how such conditions drive women to madness, as a result of which they are forced to either escape into the blind mind of insanity or deal daily with their pain and inescapable societal condemnation. In an age where “hysteria” was a frequent hit in the vernacular, Phelps, Gilman and Chopin use art and literature as mediums to show that, indeed, there is a method behind the madness.

Efficient methods for stochastic optimal control

The Hamilton Jacobi Bellman (HJB) equation is central to stochastic optimal control (SOC) theory, yielding the optimal solution to general problems specified by known dynamics and a specified cost functional. Given the assumption of quadratic cost on the control input, it is well known that the HJB reduces to a particular partial differential equation (PDE). While powerful, this reduction is not commonly used as the PDE is of second order, is nonlinear, and examples exist where the problem may not have a solution in a classical sense. Furthermore, each state of the system appears as another dimension of the PDE, giving rise to the curse of dimensionality. Since the number of degrees of freedom required to solve the optimal control problem grows exponentially with dimension, the problem becomes intractable for systems with all but modest dimension.

In the last decade researchers have found that under certain, fairly non-restrictive structural assumptions, the HJB may be transformed into a linear PDE, with an interesting analogue in the discretized domain of Markov Decision Processes (MDP). The work presented in this thesis uses the linearity of this particular form of the HJB PDE to push the computational boundaries of stochastic optimal control.

This is done by crafting together previously disjoint lines of research in computation. The first of these is the use of Sum of Squares (SOS) techniques for synthesis of control policies. A candidate polynomial with variable coefficients is proposed as the solution to the stochastic optimal control problem. An SOS relaxation is then taken to the partial differential constraints, leading to a hierarchy of semidefinite relaxations with improving sub-optimality gap. The resulting approximate solutions are shown to be guaranteed over- and under-approximations for the optimal value function. It is shown that these results extend to arbitrary parabolic and elliptic PDEs, yielding a novel method for Uncertainty Quantification (UQ) of systems governed by partial differential constraints. Domain decomposition techniques are also made available, allowing for such problems to be solved via parallelization and low-order polynomials.

The optimization-based SOS technique is then contrasted with the Separated Representation (SR) approach from the applied mathematics community. The technique allows for systems of equations to be solved through a low-rank decomposition that results in algorithms that scale linearly with dimensionality. Its application in stochastic optimal control allows for previously uncomputable problems to be solved quickly, scaling to such complex systems as the Quadcopter and VTOL aircraft. This technique may be combined with the SOS approach, yielding not only a numerical technique, but also an analytical one that allows for entirely new classes of systems to be studied and for stability properties to be guaranteed.

The analysis of the linear HJB is completed by the study of its implications in application. It is shown that the HJB and a popular technique in robotics, the use of navigation functions, sit on opposite ends of a spectrum of optimization problems, upon which tradeoffs may be made in problem complexity. Analytical solutions to the HJB in these settings are available in simplified domains, yielding guidance towards optimality for approximation schemes. Finally, the use of HJB equations in temporal multi-task planning problems is investigated. It is demonstrated that such problems are reducible to a sequence of SOC problems linked via boundary conditions. The linearity of the PDE allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to satisfy a complex temporal logic specification.

A model for energy and morphology of crystalline grain boundaries with arbitrary geometric character

It has been well-established that interfaces in crystalline materials are key players in the mechanics of a variety of mesoscopic processes such as solidification, recrystallization, grain boundary migration, and severe plastic deformation. In particular, interfaces with complex morphologies have been observed to play a crucial role in many micromechanical phenomena such as grain boundary migration, stability, and twinning. Interfaces are a unique type of material defect in that they demonstrate a breadth of behavior and characteristics eluding simplified descriptions. Indeed, modeling the complex and diverse behavior of interfaces is still an active area of research, and to the author's knowledge there are as yet no predictive models for the energy and morphology of interfaces with arbitrary character. The aim of this thesis is to develop a novel model for interface energy and morphology that i) provides accurate results (especially regarding "energy cusp" locations) for interfaces with arbitrary character, ii) depends on a small set of material parameters, and iii) is fast enough to incorporate into large scale simulations.

In the first half of the work, a model for planar, immiscible grain boundary is formulated. By building on the assumption that anisotropic grain boundary energetics are dominated by geometry and crystallography, a construction on lattice density functions (referred to as "covariance") is introduced that provides a geometric measure of the order of an interface. Covariance forms the basis for a fully general model of the energy of a planar interface, and it is demonstrated by comparison with a wide selection of molecular dynamics energy data for FCC and BCC tilt and twist boundaries that the model accurately reproduces the energy landscape using only three material parameters. It is observed that the planar constraint on the model is, in some cases, over-restrictive; this motivates an extension of the model.

In the second half of the work, the theory of faceting in interfaces is developed and applied to the planar interface model for grain boundaries. Building on previous work in mathematics and materials science, an algorithm is formulated that returns the minimal possible energy attainable by relaxation and the corresponding relaxed morphology for a given planar energy model. It is shown that the relaxation significantly improves the energy results of the planar covariance model for FCC and BCC tilt and twist boundaries. The ability of the model to accurately predict faceting patterns is demonstrated by comparison to molecular dynamics energy data and experimental morphological observation for asymmetric tilt grain boundaries. It is also demonstrated that by varying the temperature in the planar covariance model, it is possible to reproduce a priori the experimentally observed effects of temperature on facet formation.

Finally, the range and scope of the covariance and relaxation models, having been demonstrated by means of extensive MD and experimental comparison, future applications and implementations of the model are explored.

Rings faithfully represented on their left socle

In 1964 A. W. Goldie [1] posed the problem of determining all rings with identity and minimal condition on left ideals which are faithfully represented on the right side of their left socle. Goldie showed that such a ring which is indecomposable and in which the left and right principal indecomposable ideals have, respectively, unique left and unique right composition series is a complete blocked triangular matrix ring over a skewfield. The general problem suggested above is very difficult. We obtain results under certain natural restrictions which are much weaker than the restrictive assumptions made by Goldie.

We characterize those rings in which the principal indecomposable left ideals each contain a unique minimal left ideal (Theorem (4.2)). It is sufficient to handle indecomposable rings (Lemma (1.4)). Such a ring is also a blocked triangular matrix ring. There exist r positive integers K₁,..., K_r such that the i,j^th block of a typical matrix is a K_i x K_j matrix with arbitrary entries in a subgroup D_ij of the additive group of a fixed skewfield D. Each D_ii is a sub-skewfield of D and D_ri = D for all i. Conversely, every matrix ring which has this form is indecomposable, faithfully represented on the right side of its left socle, and possesses the property that every principal indecomposable left ideal contains a unique minimal left ideal.

The principal indecomposable left ideals may have unique composition series even though the ring does not have minimal condition on right ideals. We characterize this situation by defining a partial ordering ρ on {i, 2,...,r} where we set iρj if D_ij ≠ 0. Every principal indecomposable left ideal has a unique composition series if and only if the diagram of ρ is an inverted tree and every D_ij is a one-dimensional left vector space over D_ii (Theorem (5.4)).

We show (Theorem (2.2)) that every ring A of the type we are studying is a unique subdirect sum of less complex rings A₁,...,A_s of the same type. Namely, each A_i has only one isomorphism class of minimal left ideals and the minimal left ideals of different A_i are non-isomorphic as left A-modules. We give (Theorem (2.1)) necessary and sufficient conditions for a ring which is a subdirect sum of rings A_i having these properties to be faithfully represented on the right side of its left socle. We show ((4.F), p. 42) that up to technical trivia the rings A_i are matrix rings of the form

[...]. Each Q_j comes from the faithful irreducible matrix representation of a certain skewfield over a fixed skewfield D. The bottom row is filled in by arbitrary elements of D.

In Part V we construct an interesting class of rings faithfully represented on their left socle from a given partial ordering on a finite set, given skewfields, and given additive groups. This class of rings contains the ones in which every principal indecomposable left ideal has a unique minimal left ideal. We identify the uniquely determined subdirect summands mentioned above in terms of the given partial ordering (Proposition (5.2)). We conjecture that this technique serves to construct all the rings which are a unique subdirect sum of rings each having the property that every principal-indecomposable left ideal contains a unique minimal left ideal.