Conditioned Martingales

It is well known that upward conditioned Brownian motion is a three-dimensional Bessel process, and that a downward conditioned Bessel process is a Brownian motion. We give a simple proof for this result, which generalizes to any continuous local martingale and clarifies the role of finite versus infinite time in this setting. As a consequence, we can describe the law of regular diffusions that are conditioned upward or downward.Comment: Corrected several typos, improved formulations. Accepted by Electronic Communications in Probability; Electronic Communications in Probability, 2012, Volume 17, Issue 4

Conditioned Brownian trees

We consider a Brownian tree consisting of a collection of one-dimensional Brownian paths started from the origin, whose genealogical structure is given by the Continuum Random Tree (CRT). This Brownian tree may be generated from the Brownian snake driven by a normalized Brownian excursion, and thus yields a convenient representation of the so-called Integrated Super-Brownian Excursion (ISE), which can be viewed as the uniform probability measure on the tree of paths. We discuss different approaches that lead to the definition of the Brownian tree conditioned to stay on the positive half-line. We also establish a Verwaat-like theorem showing that this conditioned Brownian tree can be obtained by re-rooting the unconditioned one at the vertex corresponding to the minimal spatial position. In terms of ISE, this theorem yields the following fact: Conditioning ISE to put no mass on $]-\infty,-\epsilon[$ and letting $\epsilon$ go to 0 is equivalent to shifting the unconditioned ISE to the right so that the left-most point of its support becomes the origin. We derive a number of explicit estimates and formulas for our conditioned Brownian trees. In particular, the probability that ISE puts no mass on $]-\infty,-\epsilon[$ is shown to behave like $2\epsilon^4/21$ when $\epsilon$ goes to 0. Finally, for the conditioned Brownian tree with a fixed height $h$, we obtain a decomposition involving a spine whose distribution is absolutely continuous with respect to that of a nine-dimensional Bessel process on the time interval $[0,h]$, and Poisson processes of subtrees originating from this spine.Comment: 42 page

Air conditioned suit

An environmentally controlled suit is described consisting of an airtight outergarment attached by an airtight bellows to the wall of a sterile chamber, an undergarment providing for circulation of air near the skin of the wearer, and a circulation system comprised of air supply and distribution to the extremities of the undegarment and central collection and exhaust of air from the midsection of the undergarment. A workman wearing the undergarment and attached circulation system enters the outer garment through a tunnel in the chamber wall and the attached bellows to work in the chamber without any danger of spreading bacteria

ConSIT: A conditioned program slicer

Conditioned slicing is a powerful generalisation of static and dynamic slicing which has applications to many problems in software maintenance and evolution, including reuse, reengineering and program comprehension. However there has been relatively little work on the implementation of conditioned slicing. Algorithms for implementing conditioned slicing necessarily involve reasoning about the values of program predicates in certain sets of states derived from the conditioned slicing criterion, making implementation particularly demanding. The paper introduces ConSIT, a conditioned slicing system which is based upon conventional static slicing, symbolic execution and theorem proving. ConSIT is the first fully automated implementation of conditioned slicing. An implementation of ConSIT is available for experimentation at &http://www.mcs.gold.ac.uk/tilde/~mas01sd/consit.htm

Simulation of conditioned diffusions

In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of another diffusion which is easy for simulation, and the formula for the density is given explicitly

Domain Conditioned Adaptation Network

Tremendous research efforts have been made to thrive deep domain adaptation (DA) by seeking domain-invariant features. Most existing deep DA models only focus on aligning feature representations of task-specific layers across domains while integrating a totally shared convolutional architecture for source and target. However, we argue that such strongly-shared convolutional layers might be harmful for domain-specific feature learning when source and target data distribution differs to a large extent. In this paper, we relax a shared-convnets assumption made by previous DA methods and propose a Domain Conditioned Adaptation Network (DCAN), which aims to excite distinct convolutional channels with a domain conditioned channel attention mechanism. As a result, the critical low-level domain-dependent knowledge could be explored appropriately. As far as we know, this is the first work to explore the domain-wise convolutional channel activation for deep DA networks. Moreover, to effectively align high-level feature distributions across two domains, we further deploy domain conditioned feature correction blocks after task-specific layers, which will explicitly correct the domain discrepancy. Extensive experiments on three cross-domain benchmarks demonstrate the proposed approach outperforms existing methods by a large margin, especially on very tough cross-domain learning tasks.Comment: Accepted by AAAI 202

Apparatus for supplying conditioned air at a substantially constant temperature and humidity

The apparatus includes a supply duct coupled to a source of supply air for carrying the supply air therethrough. A return duct is coupled to the supply duct for carrying return conditioned air therethrough. A temperature reducing device is coupled to the supply duct for decreasing the temperature of the supply and return conditioned air. A by-pass duct is coupled to the supply duct for selectively directing portions of the supply and return conditioned air around the temperature reducing device. Another by-pass duct is coupled to the return duct for selectively directing portions of the return conditioned air around the supply duct and the temperature reduction device. Controller devices selectively control the flow and amount of mixing of the supply and return conditioned air

Conditioned Unitary Transformation on biphotons

A conditioned unitary transformation ($90^o$ polarization rotation) is performed at single-photon level. The transformation is realized by rotating polarization for one of the photons of a polarization-entangled biphoton state (signal photon) by means of a Pockel's cell triggered by the detection of the other (idler) photon after polarization selection. As a result, polarization degree for the signal beam changes from zero to the value given by the idler detector quantum efficiency. This result is relevant to practical realization of various quantum information schemes and can be used for developing a new method of absolute quantum efficiency calibration