Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.

Drop penetration into porous powder beds

The kinetics of drop penetration were studied by filming single drops of several different fluids (water, PEG200, PEG600, and HPC solutions) as they penetrated into loosely packed beds of glass ballotini, lactose, zinc oxide, and titanium dioxide powders. Measured times ranged from 0.45 to 126 s and depended on the powder particle size,viscosity, surface tensions, and contact angle. The experimental drop penetration times were compared to existing theoretical predictions by M. Denesuk et al. (J. Colloid Interface Sci. 158, 114, 1993) and S. Middleman (Modeling Axisymmetric Flows: Dynamics of Films, Jets, and Drops, Academic Press, San Diego, 1995) but did not agree. Loosely packed powder beds tend to have a heterogeneous bed structure containing large macrovoids which do not participate in liquid flow but are included implicitly in the existing approach to estimating powder pore size. A new two-phase model was proposed where the total volume of the macrovoids was assumed to be the difference between the bed porosity and the tap porosity. A new parameter, the effective porosity (epsilon)eff, was defined as the tap porosity multiplied by the fraction of pores that terminate at a macrovoid and are effectively blocked pores. The improved drop penetration model was much more successful at estimating the drop penetration time on all powders and the predicted times were generally within an order of magnitude of the experimental results. (C) 2002 Elsevier Science (USA).

On learning context-free and context-sensitive languages

The long short-term memory (LSTM) is not the only neural network which learns a context sensitive language. Second-order sequential cascaded networks (SCNs) are able to induce means from a finite fragment of a context-sensitive language for processing strings outside the training set. The dynamical behavior of the SCN is qualitatively distinct from that observed in LSTM networks. Differences in performance and dynamics are discussed.

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.

Tillering in grain sorghum over a wide range of population densities: Modelling dynamics of tiller fertility

The prediction of tillering is poor or absent in existing sorghum crop models even though fertile tillers contribute significantly to grain yield. The objective of this study was to identify general quantitative relationships underpinning tiller dynamics of sorghum for a broad range of assimilate availabilities. Emergence, phenology, leaf area development and fertility of individual main calms and tillers were quantified weekly in plants grown at one of four plant densities ranging from two to 16 plants m(-2). On any given day, a tiller was considered potentially fertile (a posteriori) if its number of leaves continued to increase thereafter. The dynamics of potentially fertile tiller number per plant varied greatly with plant density, but could generally be described by three determinants, stable across plant densities: tiller emergence rate aligned with leaf ligule appearance rate; cessation of tiller emergence occurred at a stable leaf area index; and rate of decrease in potentially fertile tillers was linearly related to the ratio of realized to potential leaf area growth. Realized leaf area growth is the measured increase in leaf area, whereas potential leaf area growth is the estimated increase in leaf area if all potentially fertile tillers were to continue to develop. Procedures to predict this ratio, by estimating realized leaf area per plant from intercepted radiation and potential leaf area per plant from the number and type of developing axes, are presented. While it is suitable for modelling tiller dynamics in grain sorghum, this general framework needs to be validated by testing it in different environments and for other cultivars. (C) 2002 Annals of Botany Company.

Simulation of the influence of rate- and state-dependent friction on the macroscopic behavior of complex fault zones with the lattice solid model

In order to understand the earthquake nucleation process, we need to understand the effective frictional behavior of faults with complex geometry and fault gouge zones. One important aspect of this is the interaction between the friction law governing the behavior of the fault on the microscopic level and the resulting macroscopic behavior of the fault zone. Numerical simulations offer a possibility to investigate the behavior of faults on many different scales and thus provide a means to gain insight into fault zone dynamics on scales which are not accessible to laboratory experiments. Numerical experiments have been performed to investigate the influence of the geometric configuration of faults with a rate- and state-dependent friction at the particle contacts on the effective frictional behavior of these faults. The numerical experiments are designed to be similar to laboratory experiments by DIETERICH and KILGORE (1994) in which a slide-hold-slide cycle was performed between two blocks of material and the resulting peak friction was plotted vs. holding time. Simulations with a flat fault without a fault gouge have been performed to verify the implementation. These have shown close agreement with comparable laboratory experiments. The simulations performed with a fault containing fault gouge have demonstrated a strong dependence of the critical slip distance D-c on the roughness of the fault surfaces and are in qualitative agreement with laboratory experiments.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

The Galilean turn in population ecology

The standard mathematical models in population ecology assume that a population's growth rate is a function of its environment. In this paper we investigate an alternative proposal according to which the rate of change of the growth rate is a function of the environment and of environmental change. We focus on the philosophical issues involved in such a fundamental shift in theoretical assumptions, as well as on the explanations the two theories offer for some of the key data such as cyclic populations. We also discuss the relationship between this move in population ecology and a similar move from first-order to second-order differential equations championed by Galileo and Newton in celestial mechanics.

Dynamics of Gray Matter Loss in Alzheimer's Disease

We detected and mapped a dynamically spreading wave of gray matter loss in the brains of patients with Alzheimer's disease (AD). The loss pattern was visualized in four dimensions as it spread over time from temporal and limbic cortices into frontal and occipital brain regions, sparing sensorimotor cortices. The shifting deficits were asymmetric (left hemisphere >right hemisphere) and correlated with progressively declining cognitive status ( p 15% loss). The maps distinguished different phases of AD and differentiated AD from normal aging. Local gray matter loss rates (5.3 +/- 2.3% per year in AD v 0.9 +/- 0.9% per year in controls) were faster in the left hemisphere ( p < 0.029) than the right. Transient barriers to disease progression appeared at limbic/frontal boundaries. This degenerative sequence, observed in vivo as it developed, provides the first quantitative, dynamic visualization of cortical atrophic rates in normal elderly populations and in those with dementia.

The trans-membrane protein p25 forms highly specialized domains that regulate membrane composition and dynamics

Trans-membrane proteins of the p24 family are abundant, oligomeric proteins predominantly found in cis-Golgi membranes. They are not easily studied in vivo and their functions are controversial. We found that p25 can be targeted to the plasma membrane after inactivation of its canonical KKXX motif (KK to SS, p25SS), and that p25SS causes the co-transport of other p24 proteins beyond the Golgi complex, indicating that wild-type p25 plays a crucial role in retaining p24 proteins in cis-Golgi membranes. We then made use of these observations to study the intrinsic properties of these proteins, when present in a different membrane context. At the cell surface, the p25SS mutant segregates away from both the transferrin receptor and markers of lipid rafts, which are enriched in cholesterol and glycosphingolipids. This suggests that p25SS localizes to, or contributes to form, specialized membrane domains, presumably corresponding to oligomers of p25SS and other p24 proteins. Once at the cell surface, p25SS is endocytosed, together with other p24 proteins, and eventually accumulates in late endosomes, where it remains confined to well-defined membrane regions visible by electron microscopy. We find that this p25SS accumulation causes a concomitant accumulation of cholesterol in late endosomes, and an inhibition of their motility - two processes that are functionally linked. Yet, the p25SS-rich regions themselves seem to-exclude not only Lamp1 but also accumulated cholesterol. One may envision that p25SS accumulation, by excluding cholesterol from oligomers, eventually overloads neighboring late endosomal membranes with cholesterol beyond their capacity (see Discussion). In any case, our data show that p25 and presumably other p24 proteins are endowed with the intrinsic capacity to form highly specialized domains that control membrane composition and dynamics. We propose that p25 and other p24 proteins control the fidelity of membrane transport by maintaining cholesterol-poor membranes in the Golgi complex.

Learning the dynamics of embedded clauses

Recent work by Siegelmann has shown that the computational power of recurrent neural networks matches that of Turing Machines. One important implication is that complex language classes (infinite languages with embedded clauses) can be represented in neural networks. Proofs are based on a fractal encoding of states to simulate the memory and operations of stacks. In the present work, it is shown that similar stack-like dynamics can be learned in recurrent neural networks from simple sequence prediction tasks. Two main types of network solutions are found and described qualitatively as dynamical systems: damped oscillation and entangled spiraling around fixed points. The potential and limitations of each solution type are established in terms of generalization on two different context-free languages. Both solution types constitute novel stack implementations - generally in line with Siegelmann's theoretical work - which supply insights into how embedded structures of languages can be handled in analog hardware.