The Noether-Lefschetz theorem for the divisor class group

Let X be a normal projective threefold over a field of characteristic zero and vertical bar L vertical bar be a base-point free, ample linear system on X. Under suitable hypotheses on (X, vertical bar L vertical bar), we prove that for a very general member Y is an element of vertical bar L vertical bar, the restriction map on divisor class groups Cl(X) -> Cl(Y) is an isomorphism. In particular, we are able to recover the classical Noether-Lefschetz theorem, that a very general hypersurface X subset of P-C(3) of degree >= 4 has Pic(X) congruent to Z.

Automatic wildfire detection and simulation using optical information from unmanned aerial systems

In many parts of the world, uncontrolled fires in sparsely populated areas are a major concern as they can quickly grow into large and destructive conflagrations in short time spans. Detecting these fires has traditionally been a job for trained humans on the ground, or in the air. In many cases, these manned solutions are simply not able to survey the amount of area necessary to maintain sufficient vigilance and coverage. This paper investigates the use of unmanned aerial systems (UAS) for automated wildfire detection. The proposed system uses low-cost, consumer-grade electronics and sensors combined with various airframes to create a system suitable for automatic detection of wildfires. The system employs automatic image processing techniques to analyze captured images and autonomously detect fire-related features such as fire lines, burnt regions, and flammable material. This image recognition algorithm is designed to cope with environmental occlusions such as shadows, smoke and obstructions. Once the fire is identified and classified, it is used to initialize a spatial/temporal fire simulation. This simulation is based on occupancy maps whose fidelity can be varied to include stochastic elements, various types of vegetation, weather conditions, and unique terrain. The simulations can be used to predict the effects of optimized firefighting methods to prevent the future propagation of the fires and greatly reduce time to detection of wildfires, thereby greatly minimizing the ensuing damage. This paper also documents experimental flight tests using a SenseFly Swinglet UAS conducted in Brisbane, Australia as well as modifications for custom UAS.

Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.

Optimisation techniques for planning automatic under frequency load shedding in New Zealand’s power system

Electricity generation is vital in developed countries to power the many mechanical and electrical devices that people require. Unfortunately electricity generation is costly. Though electricity can be generated it cannot be stored efficiently. Electricity generation is also difficult to manage because exact demand is unknown from one instant to the next. A number of services are required to manage fluctuations in electricity demand, and to protect the system when frequency falls too low. A current approach is called automatic under frequency load shedding (AUFLS). This article proposes new methods for optimising AUFLS in New Zealand’s power system. The core ideas were developed during the 2015 Maths and Industry Study Group (MISG) in Brisbane, Australia. The problem has been motivated by Transpower Limited, a company that manages New Zealand’s power system and transports bulk electricity from where it is generated to where it is needed. The approaches developed in this article can be used in electrical power systems anywhere in the world.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Automatic Road Extraction using High Resolution Satellite Image Based on Texture Progressive Analysis and Normalized Cut Method

In this paper the approach for automatic road extraction for an urban region using structural, spectral and geometric characteristics of roads has been presented. Roads have been extracted based on two levels: Pre-processing and road extraction methods. Initially, the image is pre-processed to improve the tolerance by reducing the clutter (that mostly represents the buildings, parking lots, vegetation regions and other open spaces). The road segments are then extracted using Texture Progressive Analysis (TPA) and Normalized cut algorithm. The TPA technique uses binary segmentation based on three levels of texture statistical evaluation to extract road segments where as, Normalizedcut method for road extraction is a graph based method that generates optimal partition of road segments. The performance evaluation (quality measures) for road extraction using TPA and normalized cut method is compared. Thus the experimental result show that normalized cut method is efficient in extracting road segments in urban region from high resolution satellite image.

Automatic post-adoptive information technology use: The role of innovativeness goal

The business value of information technology (IT) is realized through the continuous use of IT subsequent to users’ adoption. Understanding post-adoptive IT usage is useful in realizing potential IT business value. Most previous research on post-adoptive IT usage, however, dismisses the unintentional and unconscious aspects of usage behavior. This paper advances understanding of the unintentional, unconscious, and thereby automatic usage of IT features during the post-adoptive stage. Drawing from Social Psychology literature, we argue human behaviors can be triggered by environmental cues and directed by the person’s mental goals, thereby operating without a person’s consciousness and intentional will. On this basis, we theorize the role of a user’s innovativeness goal, as the desired state of an act to innovate, in directing the user’s unintentional, unconscious, and automatic post-adoptive IT feature usage behavior. To test the hypothesized mechanisms, a human experiment employing a priming technique, is described.

Automatic text block separation in document images

Separation of printed text blocks from the non-text areas, containing signatures, handwritten text, logos and other such symbols, is a necessary first step for an OCR involving printed text recognition. In the present work, we compare the efficacy of some feature-classifier combinations to carry out this separation task. We have selected length-nomalized horizontal projection profile (HPP) as the starting point of such a separation task. This is with the assumption that the printed text blocks contain lines of text which generate HPP's with some regularity. Such an assumption is demonstrated to be valid. Our features are the HPP and its two transformed versions, namely, eigen and Fisher profiles. Four well known classifiers, namely, Nearest neighbor, Linear discriminant function, SVM's and artificial neural networks have been considered and efficiency of the combination of these classifiers with the above features is compared. A sequential floating feature selection technique has been adopted to enhance the efficiency of this separation task. The results give an average accuracy of about 96.

Dolezal's theorem revisited

This paper presents an improved version of Dolezal's theorem, in the area of linear algebra with continuously parametrized elements. An extension of the theorem is also presented, and applications of these results to system theory are indicated.

A Possible and Necessary Consistency Proof

After Gödel's incompleteness theorems and the collapse of Hilbert's programme Gerhard Gentzen continued the quest for consistency proofs of Peano arithmetic. He considered a finitistic or constructive proof still possible and necessary for the foundations of mathematics. For a proof to be meaningful, the principles relied on should be considered more reliable than the doubtful elements of the theory concerned. He worked out a total of four proofs between 1934 and 1939. This thesis examines the consistency proofs for arithmetic by Gentzen from different angles. The consistency of Heyting arithmetic is shown both in a sequent calculus notation and in natural deduction. The former proof includes a cut elimination theorem for the calculus and a syntactical study of the purely arithmetical part of the system. The latter consistency proof in standard natural deduction has been an open problem since the publication of Gentzen's proofs. The solution to this problem for an intuitionistic calculus is based on a normalization proof by Howard. The proof is performed in the manner of Gentzen, by giving a reduction procedure for derivations of falsity. In contrast to Gentzen's proof, the procedure contains a vector assignment. The reduction reduces the first component of the vector and this component can be interpreted as an ordinal less than epsilon_0, thus ordering the derivations by complexity and proving termination of the process.

A multiplier theorem for the sublaplacian on the Heisenberg group

A multiplier theorem for the sublaplacian on the Heisenberg group is proved using Littlewood-Paley-Stein theory of g-functions.

A Circuit-Based Proof of Toda′s Theorem

We present a simple proof of Toda′s result (Toda (1989), in "Proceedings, 30th Annual IEEE Symposium on Foundations of Computer Science," pp. 514-519), which states that circled plus P is hard for the Polynomial Hierarchy under randomized reductions. Our approach is circuit-based in the sense that we start with uniform circuit definitions of the Polynomial Hierarchy and apply the Valiant-Vazirani lemma on these circuits (Valiant and Vazirani (1986), Thoeret. Comput. Sci.47, 85-93).