Bidirectional Classical Stochastic Processes with Measurements and Feedback

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox

BGRP: A Tree-Based Aggregation Protocol for Inter-domain Reservations

Resource reservation needs to accommodate the rapidly growing size and increasing service diversity of the Internet. Recently, hierarchical architectures have been proposed that provide domain-level reservation.However, it is not clear that these proposals can set up and maintain reservations in an efficient and scalable fashion. In this paper, we describe a distributed architecture and protocol,called the Border Gateway Reservation Protocol (BGRP), for inter-domain resource reservation that can scale in terms of message processing load. state storage and bandwidth. Each stub or transit domain may use its own intra-domain resource reservation protocol. BGRP builds a sink tree for each of the stub domains. Each sink tree aggregates bandwidth reservations from all data sources in the network.Since backbone routers only maintain the sink tree information, the total number of reservation states at each router scales, in the worst case, linearly with the number of domains in the Internet. BGRP relies on differentiated services for data forwarding. As a result, the number of packet classifier entries is small, not the number of micro-flows.To reduce the protocol message traffic, routers may reserve domain bandwidth beyond the current load so that sources can join or leave the tree or change their reservation without having to send messages all the way to the root for every such change. We use``soft state'' to maintain reservations. In contrast to RSVP, refresh messages are delivered reliably, allowing us to reduce the refresh frequency

A computational framework to emulate the human perspective in flow cytometric data analysis

Background: In recent years, intense research efforts have focused on developing methods for automated flow cytometric data analysis. However, while designing such applications, little or no attention has been paid to the human perspective that is absolutely central to the manual gating process of identifying and characterizing cell populations. In particular, the assumption of many common techniques that cell populations could be modeled reliably with pre-specified distributions may not hold true in real-life samples, which can have populations of arbitrary shapes and considerable inter-sample variation. <p/>Results: To address this, we developed a new framework flowScape for emulating certain key aspects of the human perspective in analyzing flow data, which we implemented in multiple steps. First, flowScape begins with creating a mathematically rigorous map of the high-dimensional flow data landscape based on dense and sparse regions defined by relative concentrations of events around modes. In the second step, these modal clusters are connected with a global hierarchical structure. This representation allows flowScape to perform ridgeline analysis for both traversing the landscape and isolating cell populations at different levels of resolution. Finally, we extended manual gating with a new capacity for constructing templates that can identify target populations in terms of their relative parameters, as opposed to the more commonly used absolute or physical parameters. This allows flowScape to apply such templates in batch mode for detecting the corresponding populations in a flexible, sample-specific manner. We also demonstrated different applications of our framework to flow data analysis and show its superiority over other analytical methods. <p/>Conclusions: The human perspective, built on top of intuition and experience, is a very important component of flow cytometric data analysis. By emulating some of its approaches and extending these with automation and rigor, flowScape provides a flexible and robust framework for computational cytomics

Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries

We extend the definition of generalized parity $P$, charge-conjugation $C$ and time-reversal $T$ operators to nondiagonalizable pseudo-Hermitian Hamiltonians, and we use these generalized operators to describe the full set of symmetries of a pseudo-Hermitian Hamiltonian according to a fourfold classification. In particular we show that $TP$ and $CTP$ are the generators of the antiunitary symmetries; moreover, a necessary and sufficient condition is provided for a pseudo-Hermitian Hamiltonian $H$ to admit a $P$-reflecting symmetry which generates the $P$-pseudounitary and the $P$-pseudoantiunitary symmetries. Finally, a physical example is considered and some hints on the $P$-unitary evolution of a physical system are also given.Comment: 20 page

Wind tunnel results of the high-speed NLF(1)-0213 airfoil

Wind tunnel tests were conducted to evaluate a natural laminar flow airfoil designed for the high speed jet aircraft in general aviation. The airfoil, designated as the High Speed Natural Laminar Flow (HSNLF)(1)-0213, was tested in two dimensional wind tunnels to investigate the performance of the basic airfoil shape. A three dimensional wing designed with this airfoil and a high lift flap system is also being evaluated with a full size, half span model

Strong quantum violation of the gravitational weak equivalence principle by a non-Gaussian wave-packet

The weak equivalence principle of gravity is examined at the quantum level in two ways. First, the position detection probabilities of particles described by a non-Gaussian wave-packet projected upwards against gravity around the classical turning point and also around the point of initial projection are calculated. These probabilities exhibit mass-dependence at both these points, thereby reflecting the quantum violation of the weak equivalence principle. Secondly, the mean arrival time of freely falling particles is calculated using the quantum probability current, which also turns out to be mass dependent. Such a mass-dependence is shown to be enhanced by increasing the non-Gaussianity parameter of the wave packet, thus signifying a stronger violation of the weak equivalence principle through a greater departure from Gaussianity of the initial wave packet. The mass-dependence of both the position detection probabilities and the mean arrival time vanish in the limit of large mass. Thus, compatibility between the weak equivalence principle and quantum mechanics is recovered in the macroscopic limit of the latter. A selection of Bohm trajectories is exhibited to illustrate these features in the free fall case.Comment: 11 pages, 7 figure