Quartically hyponormal weighted shifts need not be 3-hyponormal

We give the first example of a quartically hyponormal unilateral weighted shift which is not 3-hyponormal

A new approach to the 2-variable subnormal completion problem

We study the Subnormal Completion Problem (SCP) for 2-variable weighted shifts. We use tools and techniques from the theory of truncated moment problems to give a general strategy to solve SCP. We then show that when all quadratic moments are known (equivalently, when the initial segment of weights consists of five independent data points), the natural necessary conditions for the existence of a subnormal completion are also sufficient. To calculate explicitly the associated Berger measure, we compute the algebraic variety of the associated truncated moment problem; it turns out that this algebraic variety is precisely the support of the Berger measure of the subnormal completion

Why Optimal States Recruit Fewer Reactions in Metabolic Networks

The metabolic network of a living cell involves several hundreds or thousands of interconnected biochemical reactions. Previous research has shown that under realistic conditions only a fraction of these reactions is concurrently active in any given cell. This is partially determined by nutrient availability, but is also strongly dependent on the metabolic function and network structure. Here, we establish rigorous bounds showing that the fraction of active reactions is smaller (rather than larger) in metabolic networks evolved or engineered to optimize a specific metabolic task, and we show that this is largely determined by the presence of thermodynamically irreversible reactions in the network. We also show that the inactivation of a certain number of reactions determined by irreversibility can generate a cascade of secondary reaction inactivations that propagates through the network. The mathematical results are complemented with numerical simulations of the metabolic networks of the bacterium Escherichia coli and of human cells, which show, counterintuitively, that even the maximization of the total reaction flux in the network leads to a reduced number of active reactions.Comment: Contribution to the special issue in honor of John Guckenheimer on the occasion of his 65th birthda

Hyponormality and subnormality for powers of commuting pairs of subnormal operators

Let H_0 (resp. H_\infty denote the class of commuting pairs of subnormal operators on Hilbert space (resp. subnormal pairs), and for an integer k>=1 let H_k denote the class of k-hyponormal pairs in H_0. We study the hyponormality and subnormality of powers of pairs in H_k. We first show that if (T_1,T_2) is in H_1, then the pair (T_1^2,T_2) may fail to be in H_1. Conversely, we find a pair (T_1,T_2) in H_0 such that (T_1^2,T_2) is in H_1 but (T_1,T_2) is not. Next, we show that there exists a pair (T_1,T_2) in H_1 such that T_1^mT_2^n is subnormal (all m,n >= 1), but (T_1,T_2) is not in H_\infty; this further stretches the gap between the classes H_1 and H_\infty. Finally, we prove that there exists a large class of 2-variable weighted shifts (T_1,T_2) (namely those pairs in H_0 whose cores are of tensor form) for which the subnormality of (T_1^2,T_2) and (T_1,T_2^2) does imply the subnormality of (T_1,T_2)

k-hyponormality of multivariable weighted shifts

We characterize joint k-hyponormality for 2-variable weighted shifts. Using this characterization we construct a family of examples which establishes and illustrates the gap between k-hyponormality and (k+1)-hyponormality for each k>=1. As a consequence, we obtain an abstract solution to the Lifting Problem for Commuting Subnormals.Comment: 13 pages; to appear in J. Funct. Ana

Development or Despair? The Intentions and Realities of South-South Migration

The literature on the motivations and the impacts of remittances sent by international migrants to their families and communities strongly focus on their economic impacts and the flows of money from the global North to the South. The driving factors for remittance sending, closely embedded in motivations for migration, often overlook the conditions in which remittances are not sent, where households do not prosper, and community development does not happen. This ethnographic study uses the case of Nicaraguan migration to Costa Rica to examine the lives of the families of migrants in the context of rural to rural and South to South migration. The paper examines the intentions and realities of South-South migration through the lens of migrants and their families, and illuminates the other side of migration often invisible in the migrant’s home communities and the migration and development literature. The paper also shows the disparity in physical, economic, and emotional distance as it illustrates the unique structural challenges of South-South and especially rural to rural migrants. These structural barriers that create an unbridgeable distance between migrants and their families embody the chasm between the intentions and the realities of migration for individuals on both sides of the border

Development or Despair? The Intentions and Realities of South-South Migration

The literature on the motivations and the impacts of remittances sent by international migrants to their families and communities strongly focus on their economic impacts and the flows of money from the global North to the South. The driving factors for remittance sending, closely embedded in motivations for migration, often overlook the conditions in which remittances are not sent, where households do not prosper, and community development does not happen. This ethnographic study uses the case of Nicaraguan migration to Costa Rica to examine the lives of the families of migrants in the context of rural to rural and South to South migration. The paper examines the intentions and realities of South-South migration through the lens of migrants and their families, and illuminates the other side of migration often invisible in the migrant’s home communities and the migration and development literature. The paper also shows the disparity in physical, economic, and emotional distance as it illustrates the unique structural challenges of South-South and especially rural to rural migrants. These structural barriers that create an unbridgeable distance between migrants and their families embody the chasm between the intentions and the realities of migration for individuals on both sides of the border

Particle-in-cell and weak turbulence simulations of plasma emission

The plasma emission process, which is the mechanism for solar type II and type III radio bursts phenomena, is studied by means of particle-in-cell and weak turbulence simulation methods. By plasma emission, it is meant as a loose description of a series of processes, starting from the solar flare associated electron beam exciting Langmuir and ion-acoustic turbulence, and subsequent partial conversion of beam energy into the radiation energy by nonlinear processes. Particle-in-cell (PIC) simulation is rigorous but the method is computationally intense, and it is difficult to diagnose the results. Numerical solution of equations of weak turbulence (WT) theory, termed WT simulation, on the other hand, is efficient and naturally lends itself to diagnostics since various terms in the equation can be turned on or off. Nevertheless, WT theory is based upon a number of assumptions. It is, therefore, desirable to compare the two methods, which is carried out for the first time in the present paper with numerical solutions of the complete set of equations of the WT theory and with two-dimensional electromagnetic PIC simulation. Upon making quantitative comparisons it is found that WT theory is largely valid, although some discrepancies are also found. The present study also indicates that it requires large computational resources in order to accurately simulate the radiation emission processes, especially for low electron beam speeds. Findings from the present paper thus imply that both methods may be useful for the study of solar radio emissions as they are complementary.Comment: 21 pages, 9 figure

Pascalammetry with operando microbattery probes: Sensing high stress in solid-state batteries.

Energy storage science calls for techniques to elucidate ion transport over a range of conditions and scales. We introduce a new technique, pascalammetry, in which stress is applied to a solid-state electrochemical device and induced faradaic current transients are measured and analyzed. Stress-step pascalammetry measurements are performed on operando microbattery probes (Li2O/Li/W) and Si cathodes, revealing stress-assisted Li+ diffusion. We show how non-Cottrellian lithium diffusional kinetics indicates stress, a prelude to battery degradation. An analytical solution to a diffusion/activation equation describes this stress signature, with spatiotemporal characteristics distinct from Cottrell's classic solution for unstressed systems. These findings create an unprecedented opportunity for quantitative detection of stress in solid-state batteries through the current signature. Generally, pascalammetry offers a powerful new approach to study stress-related phenomena in any solid-state electrochemical system