Dynamical Arguments Research Articles

Strong Convexity and Smoothness of Solutions to Geometric Optics Problems via Dynamic Programming

In this letter, a formulation of Fermat’s principle as an optimization problem over a finite number of stages is used to prove strong convexity and smoothness of the solutions to certain geometric optics problems. The class of problems considered in this letter consists in the determination of the trajectory followed by a ray between a light source and a final fixed point, separated by a finite number of layered homogeneous media, characterized by their refractive indices. To obtain the theoretical results, a dynamic programming argument is used in the analysis. Then, strong convexity and smoothness are exploited to get an error bound valid when an exact solution is replaced by an approximate solution. Numerical results are provided to validate the theoretical achievements.

Global dynamics of a nonlocal delayed reaction–diffusion equation on a half plane

We consider a delayed reaction–diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson’s blowfly equation and the diffusive Mackey–Glass equation.

Constrained stochastic differential games with additive structure: Average and discount payoffs

This paper deals with two-person nonzero-sum stochastic differential games (SDGs) with an additive structure, subject to constraints that are additive also. Our main objective is to give conditions for the existence of constrained Nash equilibria for the case of infinite-horizon discounted payoff. This is done by means of the Lagrange multipliers approach combined with dynamic programming arguments. Then, following the vanishing discount approach, the results in the discounted case are used to obtain constrained Nash equilibria in the case of long-run average payoff.

Abstract allocation as a unified approach to polyvariance in control-flow analyses

AbstractIn higher order settings, control-flow analysis aims to model the propagation of both data and control by finitely approximating program behaviors across all possible executions. The polyvariance of an analysis describes the number of distinct abstract representations, or variants, for each syntactic entity (e.g., functions, variables, or intermediate expressions). Monovariance, one of the most basic forms of polyvariance, maintains only a single abstract representation for each variable or expression. Other polyvariant strategies allow a greater number of distinct abstractions and increase analysis complexity with the aim of increasing analysis precision. For example,k-call sensitivity distinguishes flows by the most recentkcall sites,k-object sensitivity by a history of allocation points, and argument sensitivity by a tuple of dynamic argument types. From this perspective, even a concrete operational semantics may be thought of as an unboundedly polyvariant analysis. In this paper, we develop a unified methodology that fully captures this design space. It is easily tunable and guarantees soundness regardless of how tuned. We accomplish this by extending the method of abstracting abstract machines, a systematic approach to abstract interpretation of operational abstract-machine semantics. Our approach permits arbitrary instrumentation of the underlying analysis and arbitrary tuning of an abstract-allocation function. We show that the design space of abstract allocators both unifies and generalizes existing notions of polyvariance. Simple changes to the behavior of this function recapitulate classic styles of analysis and yield novel combinations and variants.

External Potential Modifies Friction of Molecular Solutes in Water

Stokes’s law for the friction of a sphere in water has been argued to work down to molecular scales, provided the effective hydrodynamic radius includes the hydration layer. In interpretations of experiments and in theoretical models, it is tacitly assumed that the solvent friction experienced by a solute does not depend on whether an external confinement potential acts on the solute. Using a novel method to extract the friction memory function from molecular dynamics simulations, we show that the solvent friction of a strongly harmonically confined methane molecule in water increases by 60% compared to its free-solution value, which is caused by an amplification of the slowest component of the memory function. The friction enhancement occurs for potential strengths typical of physical and chemical bonds and is accompanied by a significant slowing-down of the hydration water dynamics. Thus, the solvent friction acting on molecular solutes is not determined by solvent properties and solute-solvent interactions alone but results from the coupling between solute and solvent dynamics and thereby can be tuned by an external potential acting on the solute. This also explains why simulations of positionally constrained solutes do not reproduce free-solution diffusivities. Dynamic scaling arguments suggest similar effects also for macromolecular solutes provided the solution viscosity is sufficiently enhanced.

LOFAR reveals the giant: a low-frequency radio continuum study of the outflow in the nearby FR I radio galaxy 3C 31

We present a deep, low-frequency radio continuum study of the nearby Fanaroff--Riley class I (FR I) radio galaxy 3C 31 using a combination of LOw Frequency ARray (LOFAR; 30--85 and 115--178 MHz), Very Large Array (VLA; 290--420 MHz), Westerbork Synthesis Radio Telescope (WSRT; 609 MHz) and Giant Metre Radio Telescope (GMRT; 615 MHz) observations. Our new LOFAR 145-MHz map shows that 3C 31 has a largest physical size of $1.1$ Mpc in projection, which means 3C 31 now falls in the class of giant radio galaxies. We model the radio continuum intensities with advective cosmic-ray transport, evolving the cosmic-ray electron population and magnetic field strength in the tails as functions of distance to the nucleus. We find that if there is no in-situ particle acceleration in the tails, then decelerating flows are required that depend on radius $r$ as $v\propto r^{\beta}$ ($\beta\approx -1$). This then compensates for the strong adiabatic losses due to the lateral expansion of the tails. We are able to find self-consistent solutions in agreement with the entrainment model of Croston & Hardcastle, where the magnetic field provides $\approx$$1/3$ of the pressure needed for equilibrium with the surrounding intra-cluster medium (ICM). We obtain an advective time-scale of $\approx$$190$ Myr, which, if equated to the source age, would require an average expansion Mach number ${\cal M} \approx 5$ over the source lifetime. Dynamical arguments suggest that instead, either the outer tail material does not represent the oldest jet plasma or else the particle ages are underestimated due to the effects of particle acceleration on large scales.

Compactness and existence results for an elliptic PDE with zero Dirichlet boundary condition

We prove compactness and existence results for a scalar curvature-type equation on a bounded domain of . The problem has a variational structure with lack of compactness. Using an asymptotic analysis and dynamical arguments, we characterize the accumulation points of all non-compact flow-lines of the gradient vector field, the so-called critical points at infinity. We then associate to each critical point at infinity a Morse index, which enables us to derive a Bahri–Coron index type criteria and to establish the existence.

Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity

In this paper we prove the existence of an exponentially localized stationary solution for a two-dimensional cubic Dirac equation. It appears as an effective equation in the description of nonlinear waves for some Condensed Matter (Bose–Einstein condensates) and Nonlinear Optics (optical fibers) systems. The nonlinearity is of Kerr-type, that is of the form |ψ|2ψ and thus not Lorenz-invariant. We solve compactness issues related to the critical Sobolev embedding H12(R2,C2)↪L4(R2,C4) thanks to a particular radial ansatz. Our proof is then based on elementary dynamical systems arguments.

A Multi-planet System Transiting the V = 9 Rapidly Rotating F-Star HD 106315

Abstract We report the discovery of a multi-planet system orbiting HD 106315, a rapidly rotating mid F-type star, using data from the K2 mission. HD 106315 hosts a 2.51 ± 0.12 R ⊕ sub-Neptune in a 9.5-day orbit and a super-Neptune in a 21-day orbit. The projected rotational velocity of HD 106315 (12.9 km s−1) likely precludes precise measurements of the planets’ masses but could enable a measurement of the sky-projected spin–orbit obliquity for the outer planet via Doppler tomography. The eccentricities of both planets were constrained to be consistent with 0, following a global modeling of the system that includes a Gaia distance and dynamical arguments. The HD 106315 system is one of few multi-planet systems hosting a Neptune-sized planet for which orbital obliquity measurements are possible, making it an excellent test-case for formation mechanisms of warm-Neptunian systems. The brightness of the host star also makes HD 106315 c a candidate for future transmission spectroscopic follow-up studies.

Low‐mode internal tides and balanced dynamics disentanglement in altimetric observations: Synergy with surface density observations

AbstractThe performance of a tentative method that disentangles the contributions of a low‐mode internal tide on sea level from that of the balanced mesoscale eddies is examined using an idealized high resolution numerical simulation. This disentanglement is essential for proper estimation from sea level of the ocean circulation related to balanced motions. The method relies on an independent observation of the sea surface water density whose variations are 1/dominated by the balanced dynamics and 2/correlate with variations of potential vorticity at depth for the chosen regime of surface‐intensified turbulence. The surface density therefore leads via potential vorticity inversion to an estimate of the balanced contribution to sea level fluctuations. The difference between instantaneous sea level (presumably observed with altimetry) and the balanced estimate compares moderately well with the contribution from the low‐mode tide. Application to realistic configurations remains to be tested. These results aim at motivating further developments of reconstruction methods of the ocean dynamics based on potential vorticity dynamics arguments. In that context, they are particularly relevant for the upcoming wide‐swath high resolution altimetric missions (SWOT).

Market orientation, buyer-supplier relationship and firm performance with dynamic capabilities as an intervening variable: a research model

In most of the studies on market orientation it has been proven that the market orientation has a positive effect on firm performance. It is important to know the mediation effect of market orientation on business performance. The perspective buyer-supplier relationship and dynamic capabilities are described in this paper. The view of market orientation is a business perspective that makes the customer as the focal point of total operating companies. The purpose of this study is to give an understanding of the conceptual advances, models of research on the impact of market orientation, buyer-supplier relationship to company performance and dynamic capabilities on firm performance are proposed and described. With the conceptual model developed, the author shows how market orientation and buyers-suppliers relationship can turn into dynamic capabilities and competitive value argument that market orientation and buyer-supplier relationship positively mediate the dynamic capability. Finally, some research hypothesis for research related to market orientation, buyer-supplier relationship to firm performance with the dynamic capabilities as an intervening variable in the future are discussed.

Market orientation, buyer-supplier relationship and firm performance with dynamic capabilities as an intervening variable: a research model

In most of the studies on market orientation it has been proven that the market orientation has a positive effect on firm performance. It is important to know the mediation effect of market orientation on business performance. The perspective buyer-supplier relationship and dynamic capabilities are described in this paper. The view of market orientation is a business perspective that makes the customer as the focal point of total operating companies. The purpose of this study is to give an understanding of the conceptual advances, models of research on the impact of market orientation, buyer-supplier relationship to company performance and dynamic capabilities on firm performance are proposed and described. With the conceptual model developed, the author shows how market orientation and buyers-suppliers relationship can turn into dynamic capabilities and competitive value argument that market orientation and buyer-supplier relationship positively mediate the dynamic capability. Finally, some research hypothesis for research related to market orientation, buyer-supplier relationship to firm performance with the dynamic capabilities as an intervening variable in the future are discussed.

Dynamic Argument Structure

This paper presents a new classification of verbs of change and modification, proposing a dynamic interpretation of the lexical semantics of the predicate and its arguments. Adopting the model of dynamic event structure proposed in Pustejovsky (2013), and extending the model of dynamic selection outlined in Pustejovsky and Jezek (2011), we define a verb class in terms of its Dynamic Argument Structure (DAS), a representation which encodes how the participants involved in the change behave as the event unfolds. We address how the logical resources and results of change predicates are realized syntactically, if at all, as well as how the exploitation of the resource results in the initiation or termination of a new object, i.e. the result. We show how DAS can be associated with a dynamically encoded event structure representation, which measures the change making reference to a scalar component, modelled in terms of assignment and/or testing of values of attributes of participants.

An approach to decision making based on dynamic argumentation systems

In this paper we introduce a formalism for single-agent decision making that is based on Dynamic Argumentation Frameworks. The formalism can be used to justify a choice, which is based on the current situation the agent is involved. Taking advantage of the inference mechanism of the argumentation formalism, it is possible to consider preference relations, and conflicts among the available alternatives for that reasoning. With this formalization, given a particular set of evidence, the justified conclusions supported by warranted arguments will be used by the agent's decision rules to determine which alternatives will be selected. We also present an algorithm that implements a choice function based on our formalization. Finally, we complete our presentation by introducing formal results that relate the proposed framework with approaches of classical decision theory.

Focal points and sup-norms of eigenfunctions II: the two-dimensional case

We use a purely dynamical argument on circle maps to improve a result in our accompanying article, [5], on real analytic surfaces possessing eigenfunctions that achieve maximal sup norm bounds. The improved result is that there exists a ‘pole’ p so that all geodesics emanating from p are smoothly closed.

Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning

An increase in the efficiency of sampling from Boltzmann distributions would have a significant impact on deep learning and other machine-learning applications. Recently, quantum annealers have been proposed as a potential candidate to speed up this task, but several limitations still bar these state-of-the-art technologies from being used effectively. One of the main limitations is that, while the device may indeed sample from a Boltzmann-like distribution, quantum dynamical arguments suggest it will do so with an {\it instance-dependent} effective temperature, different from its physical temperature. Unless this unknown temperature can be unveiled, it might not be possible to effectively use a quantum annealer for Boltzmann sampling. In this work, we propose a strategy to overcome this challenge with a simple effective-temperature estimation algorithm. We provide a systematic study assessing the impact of the effective temperatures in the learning of a special class of a restricted Boltzmann machine embedded on quantum hardware, which can serve as a building block for deep-learning architectures. We also provide a comparison to $k$-step contrastive divergence (CD-$k$) with $k$ up to 100. Although assuming a suitable fixed effective temperature also allows us to outperform one step contrastive divergence (CD-1), only when using an instance-dependent effective temperature do we find a performance close to that of CD-100 for the case studied here.

Digitalization and Boards of Directors: A New Era of Corporate Governance?

The ongoing megatrend of digitalization is significantly affecting societies and organizations. How organizations deal with the impact of digitalization may determine whether or not they will be competitive in the future. The board of directors may hereby play a key role for the organization to adapt to the changing strategic context. But based on various corporate failures, boards’ work and their effectiveness have recently been questioned. Are todays’ boards equipped to create values for organizations in the future? We address this important research question by introducing a framework where digitalization is predicted to influence boards in two areas. First, we argue that boards in the future consist of virtual networks of people where needs to monitor management diminish and shared leadership approaches are emphasized. Second, we suggest that boards work according to a dynamic board agenda based on organizational threats and opportunities. The agenda is built around learning and knowledge management and is reflected in the committee structure. Using dynamic capabilities arguments, we propose a framework with the ambition to contribute to the understanding of what makes boards fit future organizational needs. With such an approach, this is the first study that contributes to knowledge on boards by examining how boards need to adapt to meet the challenges in a digital world. The implications for theory and practice call for changed perspectives on what boards do and how they look like.

Periodic solitons for the elliptic–elliptic focussing Davey–Stewartson equations

We consider the elliptic–elliptic, focussing Davey–Stewartson equations, which have an explicit bright line soliton solution. The existence of a family of periodic solitons, which have the profile of the line soliton in the longitudinal spatial direction and are periodic in the transverse spatial direction, is established using dynamical systems arguments. We also show that the line soliton is linearly unstable with respect to perturbations in the transverse direction.

Dive in the cosmic web: voids with Delaunay triangulation from discrete matter tracer distributions

We present a novel parameter-free cosmological void finder (dive, Delaunay TrIangulation Void findEr) based on Delaunay Triangulation (DT), which efficiently computes the empty spheres constrained by a discrete set of tracers. We define the spheres as DT voids, and describe their properties, including a universal density profile together with an intrinsic scatter. We apply this technique on 100 halo catalogues with volumes of 2.5 h−1Gpc side each, with a bias and number density similar to the Baryon Oscillation Spectroscopic Survey CMASS luminous red galaxies, performed with the patchy code. Our results show that there are two main species of DT voids, which can be characterized by the radius: they have different responses to halo redshift space distortions, to number density of tracers, and reside in different dark matter environments. Based on dynamical arguments using the tidal field tensor, we demonstrate that large DT voids are hosted in expanding regions, whereas the haloes used to construct them reside in collapsing ones. Our approach is therefore able to efficiently determine the troughs of the density field from galaxy surveys, and can be used to study their clustering. We further study the power spectra of DT voids, and find that the bias of the two populations are different, demonstrating that the small DT voids are essentially tracers of groups of haloes.

The Lagrange and the vanishing discount techniques to controlled diffusions with cost constraints

In this paper we introduce two useful methods to compute optimal control policies for either the discounted or the average payoff criterion with cost constraints when the dynamic system evolves as a n-dimensional diffusion processes. As for the attribute “cost constraints” we mean the coexistence of a given cost function that in general is dominated above by another function (in particular by a constant) playing the role of an extra constraint in the control model. To deduce optimality results for the discounted case, we employ the Lagrange multipliers technique along with dynamic programming arguments. Then, the vanishing discount method is applied to easily obtain average optimal policies. We support our theory by providing an example on pollution accumulation problem.