On the exchange of intersection and supremum of sigma-fields in filtering theory

We construct a stationary Markov process with trivial tail sigma-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not uniquely ergodic. This settles in the negative a conjecture of the author in the ergodic theory of nonlinear filters arising from an erroneous proof in the classic paper of H. Kunita (1971), wherein an exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page

Sliding mode control of quantum systems

This paper proposes a new robust control method for quantum systems with uncertainties involving sliding mode control (SMC). Sliding mode control is a widely used approach in classical control theory and industrial applications. We show that SMC is also a useful method for robust control of quantum systems. In this paper, we define two specific classes of sliding modes (i.e., eigenstates and state subspaces) and propose two novel methods combining unitary control and periodic projective measurements for the design of quantum sliding mode control systems. Two examples including a two-level system and a three-level system are presented to demonstrate the proposed SMC method. One of main features of the proposed method is that the designed control laws can guarantee desired control performance in the presence of uncertainties in the system Hamiltonian. This sliding mode control approach provides a useful control theoretic tool for robust quantum information processing with uncertainties.Comment: 18 pages, 4 figure

Tur\'an numbers for Ks,tK_{s,t}-free graphs: topological obstructions and algebraic constructions

We show that every hypersurface in $\R^s\times \R^s$ contains a large grid, i.e., the set of the form $S\times T$, with $S,T\subset \R^s$. We use this to deduce that the known constructions of extremal $K_{2,2}$-free and $K_{3,3}$-free graphs cannot be generalized to a similar construction of $K_{s,s}$-free graphs for any $s\geq 4$. We also give new constructions of extremal $K_{s,t}$-free graphs for large $t$.Comment: Fixed a small mistake in the application of Proposition

A Quantum Langevin Formulation of Risk-Sensitive Optimal Control

In this paper we formulate a risk-sensitive optimal control problem for continuously monitored open quantum systems modelled by quantum Langevin equations. The optimal controller is expressed in terms of a modified conditional state, which we call a risk-sensitive state, that represents measurement knowledge tempered by the control purpose. One of the two components of the optimal controller is dynamic, a filter that computes the risk-sensitive state. The second component is an optimal control feedback function that is found by solving the dynamic programming equation. The optimal controller can be implemented using classical electronics. The ideas are illustrated using an example of feedback control of a two-level atom

Probabilistic transition of condition: render facades

The service life of cement-rendered facades is closely related to the environmental conditions that they are exposed to. The probability distribution is determined for the degradation condition of render facades considering different environmental exposures. A sample of 100 render facades was subjected to meticulous fieldwork to determine their condition. The analysis focuses on the environmental factors that most influence the overall degradation of the facades, evaluated through the condition level. Probabilistic models based on Markov chains are developed to predict the evolution of facade deterioration according to exposure to outdoor environmental conditions. The proposed model provides data on the synergy between the degradation agents and the degradation condition of render facades, the average time of permanence in each degradation level and indications of the effect of degradation on the durability of render that may be applied in the implementation and fine tuning of maintenance procedures. Better understanding the durability of render facades allows a more rational management of their maintenance, contributing to a reduction of their life cycle costs. The proposed stochastic model provides information that can be applied in the context of insurance policies, allowing an evaluation of the risk of failure of coatings

Quantum projection filter for a highly nonlinear model in cavity QED

Both in classical and quantum stochastic control theory a major role is played by the filtering equation, which recursively updates the information state of the system under observation. Unfortunately, the theory is plagued by infinite-dimensionality of the information state which severely limits its practical applicability, except in a few select cases (e.g. the linear Gaussian case.) One solution proposed in classical filtering theory is that of the projection filter. In this scheme, the filter is constrained to evolve in a finite-dimensional family of densities through orthogonal projection on the tangent space with respect to the Fisher metric. Here we apply this approach to the simple but highly nonlinear quantum model of optical phase bistability of a stongly coupled two-level atom in an optical cavity. We observe near-optimal performance of the quantum projection filter, demonstrating the utility of such an approach.Comment: 19 pages, 6 figures. A version with high quality images can be found at http://minty.caltech.edu/papers.ph

Relative luminosity measurement of the LHC with the ATLAS forward calorimeter

In this paper it is shown that a measurement of the relative luminosity changes at the LHC may be obtained by analysing the currents drawn from the high voltage power supplies of the electromagnetic section of the forward calorimeter of the ATLAS detector. The method was verified with a reproduction of a small section of the ATLAS forward calorimeter using proton beams of known beam energies and variable intensities at the U-70 accelerator at IHEP in Protvino, Russia. The experimental setup and the data taking during a test beam run in April 2008 are described in detail. A comparison of the measured high voltage currents with reference measurements from beam intensity monitors shows a linear dependence on the beam intensity. The non-linearities are measured to be less than 0.5 % combining statistical and systematic uncertainties.Comment: 16 page

Topology of Chaotic Mixing Patterns

A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically-complex motion guarantees at least a minimum amount of stretching of material lines, which is important for chaotic mixing. We use topological considerations to describe the nature of the injection of unmixed material into a central mixing region, which takes place at injection cusps. A topological index formula allow us to predict the possible types of unstable foliations that can arise for a fixed number of rods.Comment: 15 pages, 13 figures, RevTeX4 macros. Final versio

Understanding foot-and-mouth disease virus transmission biology: identification of the indicators of infectiousness

The control of foot-and-mouth disease virus (FMDV) outbreaks in non-endemic countries relies on the rapid detection and removal of infected animals. In this paper we use the observed relationship between the onset of clinical signs and direct contact transmission of FMDV to identify predictors for the onset of clinical signs and identify possible approaches to preclinical screening in the field. Threshold levels for various virological and immunological variables were determined using Receiver Operating Characteristic (ROC) curve analysis and then tested using generalized linear mixed models to determine their ability to predict the onset of clinical signs. In addition, concordance statistics between qualitative real time PCR test results and virus isolation results were evaluated. For the majority of animals (71%), the onset of clinical signs occurred 3–4 days post infection. The onset of clinical signs was associated with high levels of virus in the blood, oropharyngeal fluid and nasal fluid. Virus is first detectable in the oropharyngeal fluid, but detection of virus in the blood and nasal fluid may also be good candidates for preclinical indicators. Detection of virus in the air was also significantly associated with transmission. This study is the first to identify statistically significant indicators of infectiousness for FMDV at defined time periods during disease progression in a natural host species. Identifying factors associated with infectiousness will advance our understanding of transmission mechanisms and refine intra-herd and inter-herd disease transmission models

Vitamin D receptor ChIP-seq in primary CD4+ cells: relationship to serum 25-hydroxyvitamin D levels and autoimmune disease

PMCID: PMC3710212This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited