Dynamical Arguments Research Articles

Global dynamics of a non-local delayed differential equation in the half plane

In this paper, we first derive an equationfor a single species population with two age stages and a fixedmaturation period living in the half plane such as ocean andbig lakes.By adopting the compact open topology, we establish some a prioriestimate for nontrivial solutions after describing asymptotic propertiesof the nonlocal delayed effect, which enables us to show thepermanence of the equation. Then we can employ standard dynamical system theoretical arguments to establish the globaldynamics of the equation under appropriate conditions. Applyingthe main results to the model with Ricker's birth function andMackey-Glass's hematopoiesis function, we obtain threshold resultsfor the global dynamics of these two models.

Seedbeds of insurgency

Studies of insurgency and collective action are divided between structural and dynamic explanations. Structural theories address the presence of insurgency while dynamic theories focus on the frequency of insurgent actions. Yet prior studies often treat these arguments additively, leaving unclear how structural and dynamic processes affect these different aspects of insurgency. This study addresses this division by using zero-inflated negative binomial regression to examine in a single equation both the presence and the count of Islamist insurgency in Egyptian governorates between 1986 and 1999. We test political economy, moral economy, and cultural clash explanations of the presence of insurgency alongside political dynamics arguments about repression and exclusion to explain the count of attacks. Looking at the structural side of this equation, we find that communities with high rates of poverty, child mortality, cultural conservatism in terms of low contraceptive prevalence, and greater urban density are more likely to support insurgency. Looking at the dynamic side, parliamentary exclusion, security sweeps, and executions affect the count of attacks along with spatial diffusion from neighboring governorates. The culturally conservative region of Upper Egypt, which has a history of social and political marginality and opposition, provided a seedbed of insurgent support but this challenge broke down over time as repression intensified and exclusion was relaxed. These findings underscore the point that the presence of and the intensity of insurgency are distinct and driven by different factors. There are notable methodological and theoretical advantages to distinguishing between presence and count to better understand when and where insurgencies develop and their level of collective action.

Revisiting Zariski Main Theorem from a constructive point of view

This paper deals with the Peskine version of Zariski Main Theorem published in 1965 and discusses some applications. It is written in the style of Bishop's constructive mathematics. Being constructive, each proof in this paper can be interpreted as an algorithm for constructing explicitly the conclusion from the hypothesis. The main non-constructive argument in the proof of Peskine is the use of minimal prime ideals. Essentially we substitute this point by two dynamical arguments; one about gcd's, using subresultants, and another using our notion of strong transcendence. In particular we obtain algorithmic versions for the Multivariate Hensel Lemma and the structure theorem of quasi-finite algebras.

Shortfall Risk Minimization in Discrete Time Financial Market Models

In this paper, we study theoretical and computational aspects of risk minimization in financial market models operating in discrete time. To define the risk, we consider a class of convex risk measures defined on $L^{p}(\mathbb{P})$ in terms of shortfall risk. Under mild assumptions, namely, the absence of arbitrage opportunity and the nondegeneracy of the price process, we prove the existence of an optimal strategy by performing a dynamic programming argument in a non-Markovian framework. In a Markovian framework, the shortfall risk and optimal dynamic strategies are estimated using three main tools: Newton--Raphson Monte Carlo--based procedure, stochastic approximation algorithm, and Markovian quantization scheme. Finally, we illustrate our approach by considering several shortfall risk measures and portfolios inspired by energy and financial markets.

On the molecular mechanism of ion specific Hofmeister series

Hofmeister series ranks the ability of salt ions in influencing a variety of properties and processes in aqueous solutions. In this review, we reexamine how these ions and some other small molecules affect water structure and thermodynamic properties, such as surface tension and protein backbone solvation. We illustrate the difficulties in interpreting the thermodynamic information based on structural and dynamic arguments. As an alternative, we show that the solvation properties of ions and proteins/small molecules can be used to explain the salt effects on the thermodynamic properties of the solutions. Our analysis shows that the often neglected cation-anion cooperativity plays a very important role in these effects. We also argue that the change of hydrogen donor/acceptor equilibrium by added cosolutes/cosolvents can be used to explain their effects on protein secondary structure denaturation/protection: those increase hydrogen donor concentrations such as urea and salts with strongly solvated cations/weakly hydrated anions tend to dissolve protein backbone acting as secondary structure denaturants, whereas those lack of hydrogen donors but rich in acceptors have the opposite effect.

Mass entrainment and turbulence-driven acceleration of ultra-high energy cosmic rays in Centaurus A

Observations of the FR I radio galaxy Centaurus A in radio, X-ray and gamma-ray bands provide evidence for lepton acceleration up to several TeV and clues about hadron acceleration to tens of EeV. Synthesising the available observational constraints on the physical conditions and particle content in the jets, inner lobes and giant lobes of Centaurus A, we aim to evaluate its feasibility as an ultra-high-energy cosmic-ray source. We apply several methods of determining jet power and affirm the consistency of various power estimates of ~ 1 x 10^43 erg s^-1. Employing scaling relations based on previous results for 3C 31, we estimate particle number densities in the jets, encompassing available radio through X-ray observations. Our model is compatible with the jets ingesting ~ 3 x 10^21 g s^-1 of matter via external entrainment from hot gas and ~ 7 x 10^22 g s^-1 via internal entrainment from jet-contained stars. This leads to an imbalance between the internal lobe pressure available from radiating particles and magnetic field, and our derived external pressure. Based on knowledge of the external environments of other FR I sources, we estimate the thermal pressure in the giant lobes as 1.5 x 10^-12 dyn cm^-2, from which we deduce a lower limit to the temperature of ~ 1.6 x 10^8 K. Using dynamical and buoyancy arguments, we infer ~ 440-645 Myr and ~ 560 Myr as the sound-crossing and buoyancy ages of the giant lobes respectively, inconsistent with their spectral ages. We re-investigate the feasibility of particle acceleration via stochastic processes in the lobes, placing new constraints on the energetics and on turbulent input to the lobes. The same 'very hot' temperatures that allow self-consistency between the entrainment calculations and the missing pressure also allow stochastic UHECR acceleration models to work.

The Judiciary Is a They, Not an It: Two Fallacies of Interpretive Theory

In the theory of constitutional and statutory interpretation, dynamic arguments point to the beneficial effects on legislative behavior that will result if or courts adopt a particular approach to interpretation. In this paper I claim that such arguments are conceptually confused, and thus do not count as valid arguments at all. Dynamic arguments commit the fundamental mistake of overlooking the collective character of judicial institutions - of overlooking that the judiciary, like Congress, is a they, not an it. That mistake produces the critical, and erroneous, assumption that coordinated judicial adoption of some particular approach to legal interpretation is both feasible and desirable. That assumption commits two logical fallacies simultaneously. The fallacy of division arises when a claim that is true of, or justified for, a whole set is taken to apply to any particular member of the set. The fallacy of composition arises when a claim that is true of, or justified for, any particular member of a set is taken to apply to the whole set. Both fallacies infect dynamic interpretive arguments. First, the claim that a given approach would be best for the whole court or judiciary does not entail that it would be best for any given judge taken alone. The inference from the group-level claim to the individual-level claim fails if judicial coordination on a particular approach is infeasible or unlikely. Second, the claim that a particular approach is best for any given judge need not entail that it would be best for the whole court (or judiciary). If a diversity of approaches is desirable for systemic and institutional reasons, then it would be an affirmative bad for all judges to coordinate on a particular approach. To overlook the first point is to commit the division fallacy; to overlook the second is to commit the composition fallacy. The same reasoning applies from the standpoint of every judge in the system. In the language of moral philosophy, dynamic theorists have overlooked essential questions of non-ideal theory, which asks what obligations people have when others will not or cannot comply with their (identical) obligations. In the language of economics and consequentialist political theory, the interpretive theorist has overlooked essential questions of the second-best, which arise when a general or collective equilibrium cannot be attained. It is an irony of interpretive theory that so much emphasis has been given to exploring the consequences of the legislature's collective character, while inadequate attention has been paid to the same problem in judicial institutions.

In Defense of Reflection

I discuss two ways of justifying reflection principles. First, I propose that an undogmatic reading of dynamic Dutch book arguments provides them with a sound foundation. Second, I show also that minimizing expected inaccuracy leads to a novel argument for reflection principles. The required inaccuracy measures comprise a natural class of functions that can be derived from a generalization of a condition known as propriety or immodesty. This shows that reflection principles are an essential feature not just of consistent degrees of belief but also of degrees of belief that approximate truth.

Diagnosing Surface Mixed Layer Dynamics from High-Resolution Satellite Observations: Numerical Insights

Abstract High-resolution numerical experiments of ocean mesoscale eddy turbulence show that the wind-driven mixed layer (ML) dynamics affects mesoscale motions in the surface layers at scales lower than O(60 km). At these scales, surface horizontal currents are still coherent to, but weaker than, those derived from sea surface height using geostrophy. Vertical motions, on the other hand, are stronger than those diagnosed using the adiabatic quasigeotrophic (QG) framework. An analytical model, based on a scaling analysis and on simple dynamical arguments, provides a physical understanding and leads to a parameterization of these features in terms of vertical mixing. These results are valid when the wind-driven velocity scale is much smaller than that associated with eddies and the Ekman number (related to the ratio between the Ekman and ML depth) is not small. This suggests that, in these specific situations, three-dimensional ML motions (including the vertical velocity) can be diagnosed from high-resolution satellite observations combined with a climatological knowledge of ML conditions and interior stratification.

Inference to the Best Explanation, Dutch Books, and Inaccuracy Minimisation

Bayesians have traditionally taken a dim view of the Inference to the Best Explanation (IBE), arguing that, if IBE is at variance with Bayes' rule, then it runs afoul of the dynamic Dutch book argument. More recently, Bayes' rule has been claimed to be superior on grounds of conduciveness to our epistemic goal. The present paper aims to show that neither of these arguments succeeds in undermining IBE.

IDENTIFICATION OF OUTFLOWS AND CANDIDATE DUAL ACTIVE GALACTIC NUCLEI IN SDSS QUASARS ATz= 0.8-1.6

We present a sample of 131 quasars from the Sloan Digital Sky Survey at redshifts 0.8 < z < 1.6 with double peaks in either of the high-ionization narrow emission lines [Ne v] λ3426 or [Ne iii] λ3869. These sources were selected with the intention of identifying high-redshift analogs of the z < 0.8 active galactic nuclei (AGNs) with double-peaked [O iii] λ5007 lines, which might represent AGN outflows or dual AGNs. Lines of high ionization potential are believed to originate in the inner, highly photoionized portion of the narrow line region, and we exploit this assumption to investigate the possible kinematic origins of the double-peaked lines. For comparison, we measure the [Ne v] λ3426 and [Ne iii] λ3869 double peaks in low-redshift (z < 0.8) [O iii]-selected sources. We find that [Ne v] λ3426 and [Ne iii] λ3869 show a correlation between line splitting and line width similar to that of [O iii] λ5007 in other studies, and the velocity splittings are correlated with the quasar Eddington ratio. These results suggest an outflow origin for at least a subset of the double peaks, allowing us to study the high-ionization gas kinematics around quasars. However, we find that a non-negligible fraction of our sample show no evidence for an ionization stratification. For these sources, the outflow scenario is less compelling, leaving the dual AGN scenario as a viable possibility. Finally, we find that our sample shows an anti-correlation between the velocity-offset ratio and luminosity ratio of the components, which is a potential dynamical argument for the presence of dual AGNs. Therefore, this study serves as a first attempt at extending the selection of candidate dual AGNs to higher redshifts.

The Evolving Impact of Combinatorial Opportunities and Exhaustion on Innovation by Business Groups as Market Development Increases: The Case of Taiwan

Business groups are key sources of innovation in emerging market economies, but we understand little about why innovativeness differs across groups and over time. Variation in the density of intragroup buyer–supplier ties, which are common structural linkages among group affiliates, can help explain both cross-sectional and temporal heterogeneity of group innovativeness. We argue that greater buyer–supplier density within a group initially creates combinatorial opportunities that contribute to group innovativeness but ultimately generates combinatorial exhaustion that constrains innovation. Combinatorial exhaustion will set in at lower levels of density as the market environment becomes more developed because the opportunity costs of local search increase. The research introduces a dynamic argument to studies of business-group innovation.This paper was accepted by Bruno Cassiman, business strategy.

Transactive Memory Systems: A Microfoundation of Dynamic Capabilities

A persistent puzzle in management research is competitive advantage and why certain firms excel in getting ahead while others falter (Knott, 2003). One explanation is the dynamic capability argument, which emphasizes a firm’s superior ability in sensing new opportunities in its environment and seeking those opportunities by continuously adapting, integrating, and reconfiguring its key assets and competences (Teece et al., 1997). Researchers have called for more work to identify the micro-processes or mechanisms through which firms develop dynamic capabilities (Argote and Ingram, 2000; Spender and Grant, 1996; Teece, 2007). In this paper, we present transactive memory as a microfoundation of dynamic capabilities and describe how an organizational system for collectively encoding, storing, and retrieving knowledge can facilitate the combinative integration and renovation of an organization’s knowledge assets.

A DERIVATION OF (HALF) THE DARK MATTER DISTRIBUTION FUNCTION

All dark matter structures appear to follow a set of universalities, such as phase-space density or velocity anisotropy profiles, however, the origin of these universalities remains a mystery. Any equilibrated dark matter structure can be fully described by two functions, namely the radial and the tangential velocity distribution functions (VDF), and when we will understand these two then we will understand all the observed universalities. Here we demonstrate that if we know the radial VDF, then we can derive and understand the tangential VDF. This is based on simple dynamical arguments about properties of collisionless systems. We use a range of controlled numerical simulations to demonstrate the accuracy of this result. We therefore boil the question of the dark matter structural properties down to understanding the radial VDF.

Dynamical and stationary critical behavior of the Ising ferromagnet in a thermal gradient

In this paper we present and discuss results of Monte Carlo numerical simulations of the two-dimensional Ising ferromagnet in contact with a heat bath that intrinsically has a thermal gradient. The extremes of the magnet are at temperatures $T_1<T_c<T_2$, where $T_c$ is the Onsager critical temperature. In this way one can observe a phase transition between an ordered phase ($T<T_c$) and a disordered one ($T>T_c$) by means of a single simulation. By starting the simulations with fully disordered initial configurations with magnetization $m\equiv 0$ corresponding to $T=\infty$, which are then suddenly annealed to a preset thermal gradient, we study the short-time critical dynamic behavior of the system. Also, by setting a small initial magnetization $m=m_0$, we study the critical initial increase of the order parameter. Furthermore, by starting the simulations from fully ordered configurations, which correspond to the ground state at T=0 and are subsequently quenched to a preset gradient, we study the critical relaxation dynamics of the system. Additionally, we perform stationary measurements ($t\rightarrow\infty$) that are discussed in terms of the standard finite-size scaling theory. We conclude that our numerical simulation results of the Ising magnet in a thermal gradient, which are rationalized in terms of both dynamic and standard scaling arguments, are fully consistent with well established results obtained under equilibrium conditions.

Global dynamics of delayed reaction–diffusion equations in unbounded domains

We consider a nonlocal delayed reaction–diffusion equation in an unbounded domain that includes some special cases arising from population dynamics. Due to the non-compactness of the spatial domain, the solution semiflow is not compact. We first show that, with respect to the compact open topology for the natural phase space, the solutions induce a compact and continuous semiflow $${\Phi}$$ on a bounded and positively invariant set Y in C + = C([−1, 0], X +) that attracts every solution of the equation, where X + is the set of all bounded and uniformly continuous functions from $${\mathbb{R}}$$ to [0, ∞). Then, to overcome the difficulty in describing the global dynamics, we establish a priori estimate for nontrivial solutions after describing the delicate asymptotic properties of the nonlocal delayed effect and the diffusion operator. The estimate enables us to show the permanence of the equation with respect to the compact open topology. With the help of the permanence, we can employ standard dynamical system theoretical arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated with the diffusive Nicholson’s blowfly equation and the diffusive Mackey–Glass equation.

Nash and Stackelberg differential games

A large class of stochastic differential games for several players is considered in this paper. The class includes Nash differential games as well as Stackelberg differential games. A mix is possible. The existence of feedback strategies under general conditions is proved. The limitations concern the functionals in which the state and the controls appear separately. This is also true for the state equations. The controls appear in a quadratic form for the payoff and linearly in the state equation. The most serious restriction is the dimension of the state equation, which cannot exceed 2. The reason comes from PDE (partial differential equations) techniques used in studying the system of Bellman equations obtained by Dynamic Programming arguments. In the authors’ previous work in 2002, there is not such a restriction, but there are serious restrictions on the structure of the Hamiltonians, which are violated in the applications dealt with in this article.

Global model of differential rotation in the Sun

The isorotation contours of the solar convective zone (SCZ) show three distinct morphologies, corresponding to two boundary layers (inner and outer), and the bulk of the interior. Previous work has shown that the thermal wind equation together with informal arguments on the nature of convection in a rotating fluid could be used to deduce the shape of the isorotation surfaces in the bulk of the SCZ with great fidelity, and that the tachocline contours could also be described by relatively simple phenomenology. In this paper, we show that the form of these surfaces can be understood more broadly as a mathematical consequence of the thermal wind equation and a narrow convective shell. The analysis does not yield the angular velocity function directly, an additional surface boundary condition is required. But much can already be deduced without constructing the entire rotation profile. The mathematics may be combined with dynamical arguments put forth in previous works to the mutual benefit of each. An important element of our approach is to regard the constant angular velocity surfaces as an independent coordinate variable for what is termed the "residual entropy," a quantity that plays a key role in the equation of thermal wind balance. The difference between the dynamics of the bulk of the SCZ and the tachocline is due to a different functional form of the residual entropy in each region. We develop a unified theory for the rotational behavior of both the SCZ and the tachocline, using the solutions for the characteristics of the thermal wind equation. These characteristics are identical to the isorotation contours in the bulk of the SCZ, but the two deviate in the tachocline. The outer layer may be treated, at least descriptively, by similar mathematical techniques, but this region probably does not obey thermal wind balance.

Dynamical detection of a magnetocentrifugal wind driven by a 20 M⊙ YSO

AbstractWe have tracked the proper motions of ground-state λ7mm SiO maser emission excited by radio Source I in the Orion BN/KL region. Based on dynamical arguments, Source I is believed to be a hard 20 M⊙ binary. The SiO masers trace a linear bipolar outflow (NE-SW) 100 to 1000 AU from the binary. The median 3D velocity is 18 km s−1. An overlying distribution of 1.3 cm H2O masers betrays similar characteristics. The outflow is aligned with the rotation axis of an edge-on disk and wide angle flow known inside 100 AU. Gas dynamics and emission morphology traced by masers around Source I provide dynamical evidence of a magnetocentrifugal disk-wind around this massive YSO, notably a measured gradient in line-of-sight velocity perpendicular to the flow axis, in the same direction as the disk rotation and with comparable speed. The linearity of the flow, despite the high proper motion of Source I and the proximity of dense gas associated with the Orion Hot Core, is also more readily explained for a magnetized flow. The extended arcs of ground-state maser emission bracketing Source I are a striking feature, in particular since dust formation occurs at smaller radii. We propose that the arcs mark two C-type shocks at the transition radius to super-Alfvénic flow.

Optimal Investment with High-watermark Performance Fee

We consider the problem of optimal investment and consumption when the investment opportunity is represented by a hedge fund charging proportional fees on profit. The value of the fund evolves as a geometric Brownian motion and the performance of the investment and consumption strategy is measured using discounted power utility from consumption on infinite horizon. The resulting stochastic control problem is solved using dynamic programming arguments. We show by analytical methods that the associated Hamilton–Jacobi–Bellman equation has a smooth solution and then obtain the existence and representation of the optimal control in feedback form using verification arguments.