Reduction Theorems for Optimal Unambiguous State Discrimination of Density Matrices

We present reduction theorems for the problem of optimal unambiguous state discrimination (USD) of two general density matrices. We show that this problem can be reduced to that of two density matrices that have the same rank $n$ and are described in a Hilbert space of dimensions $2n$. We also show how to use the reduction theorems to discriminate unambiguously between N mixed states (N \ge 2).Comment: 6 pages, 1 figur

Unambiguous quantum state filtering

In this paper, we consider the generalized measurement where one particular quantum signal is unambiguously extracted from a set of non-commutative quantum signals and the other signals are filtered out. Simple expressions for the maximum detection probability and its POVM are derived. We applyl such unambiguous quantum state filtering to evaluation of the sensing of decoherence channels. The bounds of the precision limit for a given quantum state of probes and possible device implementations are discussed.Comment: 7 pages, 5 figure

The Neural Network Pushdown Automaton: Model, Stack and Learning Simulations

In order for neural networks to learn complex languages or grammars, they must have sufficient computational power or resources to recognize or generate such languages. Though many approaches have been discussed, one obvious approach to enhancing the processing power of a recurrent neural network is to couple it with an external stack memory - in effect creating a neural network pushdown automata (NNPDA). This paper discusses in detail this NNPDA - its construction, how it can be trained and how useful symbolic information can be extracted from the trained network. In order to couple the external stack to the neural network, an optimization method is developed which uses an error function that connects the learning of the state automaton of the neural network to the learning of the operation of the external stack. To minimize the error function using gradient descent learning, an analog stack is designed such that the action and storage of information in the stack are continuous. One interpretation of a continuous stack is the probabilistic storage of and action on data. After training on sample strings of an unknown source grammar, a quantization procedure extracts from the analog stack and neural network a discrete pushdown automata (PDA). Simulations show that in learning deterministic context-free grammars - the balanced parenthesis language, 1n0n, and the deterministic Palindrome - the extracted PDA is correct in the sense that it can correctly recognize unseen strings of arbitrary length. In addition, the extracted PDAs can be shown to be identical or equivalent to the PDAs of the source grammars which were used to generate the training strings. (Also cross-referenced as UMIACS-TR-93-77.

In vitro shoot induction and plant regeneration from flower buds in Paphiopedilum orchids

Paphiopedilum species are recalcitrant in tissue culture, and no explant from mature plants has been successfully mass propagated in vitro. This study was aimed at inducing shoots and regenerating plants from the flowering plants of a sequentially flowering Paphiopedilum Deperle and a single floral Paphiopedilum Armeni White. By using cross-sectioned flower buds (FBs), we found that in both species, only sections that contained the base tissue of FBs were able to produce shoots and plants. We have also found that sections of FBs between 1.5 and 3.0 cm from Paphiopedilum Deperle were able to produce shoots, but only sections of FBs > 2.5 cm from Paphiopedilum Armeni White were regenerable. Our microscopic observations revealed that the small bract at the FB base harbored a new miniature FB, which further harbored a primitive FB with dome-shaped meristem-like tissues that presumably led to the plant induction. The reiteration of this pattern resulted in a scorpioid cyme inflorescence architecture in the multifloral Paphiopedilum species, and its failure to reiterate resulted in a single flower. The induction rates were 57-75%, and all plants survived in a greenhouse. This method is potentially applicable for the micropropagation and conservation of slipper orchids

Patterns of plant invasions in China: Taxonomic, biogeographic, climatic approaches and anthropogenic effects

This study was aimed to determine the patterns as well as the effects of biological, anthropogenic, and climatic factors on plant invasions in China. About 270 volumes of national and regional floras were employed to compile a naturalized flora of China. Habit, life form, origin, distribution, and uses of naturalized plants were also analyzed to determine patterns on invasion. Correlations between biological, anthropogenic and climatic parameters were estimated at province and regional scales. Naturalized species represent 1% of the flora of China. Asteraceae, Fabaceae, and Poaceae are the dominant families, but Euphorbiaceae and Cactaceae have the largest ratios of naturalized species to their global numbers. Oenothera, Euphorbia, and Crotalaria were the dominant genera. Around 50% of exotic species were introduced intentionally for medicinal purposes. Most of the naturalized species originated in tropical America, followed by Asia and Europe. Number of naturalized species was significantly correlated to the number of native species/log area. The intensity of plant invasion showed a pattern along climate zones from mesic to xeric, declining with decreasing temperature and precipitation across the nation. Anthropogenic factor, such as distance of transportation, was significantly correlated to plant invasions at a regional scale. Although anthropogenic factors were largely responsible for creating opportunities for exotic species to spread and establish, the local biodiversity and climate factors were the major factors shaping the pattern of plant invasions in China. The warm regions, which are the hot spots of local biodiversity, and relatively developed areas of China, furthermore, require immediate attentions

Theory of coherent acoustic phonons in InGaN/GaN multi-quantum wells

A microscopic theory for the generation and propagation of coherent LA phonons in pseudomorphically strained wurzite (0001) InGaN/GaN multi-quantum well (MQW) p-i-n diodes is presented. The generation of coherent LA phonons is driven by photoexcitation of electron-hole pairs by an ultrafast Gaussian pump laser and is treated theoretically using the density matrix formalism. We use realistic wurzite bandstructures taking valence-band mixing and strain-induced piezo- electric fields into account. In addition, the many-body Coulomb ineraction is treated in the screened time-dependent Hartree-Fock approximation. We find that under typical experimental conditions, our microscopic theory can be simplified and mapped onto a loaded string problem which can be easily solved.Comment: 20 pages, 17 figure

Developing a methodology for three-dimensional correlation of PET–CT images and whole-mount histopathology in non-small-cell lung cancer

Background: Understanding the three-dimensional (3D) volumetric relationship between imaging and functional or histopathologic heterogeneity of tumours is a key concept in the development of image-guided radiotherapy. Our aim was to develop a methodologic framework to enable the reconstruction of resected lung specimens containing non-small-cell lung cancer (NSCLC), to register the result in 3D with diagnostic imaging, and to import the reconstruction into a radiation treatment planning system. Methods and Results: We recruited 12 patients for an investigation of radiology-pathology correlation (RPC) in NSCLC. Before resection, imaging by positron emission tomography (PET) or computed tomography (CT) was obtained. Resected specimens were formalin-fixed for 1-24 hours before sectioning at 3-mm to 10-mm intervals. To try to retain the original shape, we embedded the specimens in agar before sectioning. Consecutive sections were laid out for photography and manually adjusted to maintain shape. Following embedding, the tissue blocks underwent whole-mount sectioning (4-μm sections) and staining with hematoxylin and eosin. Large histopathology slides were used to whole-mount entire sections for digitization. The correct sequence was maintained to assist in subsequent reconstruction. Using Photoshop (Adobe Systems Incorporated, San Jose, CA, U.S.A.), contours were placed on the photographic images to represent the external borders of the section and the extent of macroscopic disease. Sections were stacked in sequence and manually oriented in Photoshop. The macroscopic tumour contours were then transferred to MATLAB (The Mathworks, Natick, MA, U.S.A.) and stacked, producing 3D surface renderings of the resected specimen and embedded gross tumour. To evaluate the microscopic extent of disease, customized "tile-based" and commercial confocal panoramic laser scanning (TISSUEscope: Biomedical Photometrics, Waterloo, ON) systems were used to generate digital images of whole-mount histopathology sections. Using the digital whole-mount images and imaging software, we contoured the gross and microscopic extent of disease. Two methods of registering pathology and imaging were used. First, selected PET and CT images were transferred into Photoshop, where they were contoured, stacked, and reconstructed. After importing the pathology and the imaging contours to MATLAB, the contours were reconstructed, manually rotated, and rigidly registered. In the second method, MATLAB tumour renderings were exported to a software platform for manual registration with the original PET and CT images in multiple planes. Data from this software platform were then exported to the Pinnacle radiation treatment planning system in DICOM (Digital Imaging and Communications in Medicine) format. Conclusions: There is no one definitive method for 3D volumetric RPC in NSCLC. An innovative approach to the 3D reconstruction of resected NSCLC specimens incorporates agar embedding of the specimen and whole-mount digital histopathology. The reconstructions can be rigidly and manually registered to imaging modalities such as CT and PET and exported to a radiation treatment planning system

Optimal discrimination of mixed quantum states involving inconclusive results

We propose a generalized discrimination scheme for mixed quantum states. In the present scenario we allow for certain fixed fraction of inconclusive results and we maximize the success rate of the quantum-state discrimination. This protocol interpolates between the Ivanovic-Dieks-Peres scheme and the Helstrom one. We formulate the extremal equations for the optimal positive operator valued measure describing the discrimination device and establish a criterion for its optimality. We also devise a numerical method for efficient solving of these extremal equations.Comment: 5 pages, 1 figur