Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Capping computation time and storage requirements for appearance-based localization with CAT-SLAM

Appearance-based localization is increasingly used for loop closure detection in metric SLAM systems. Since it relies only upon the appearance-based similarity between images from two locations, it can perform loop closure regardless of accumulated metric error. However, the computation time and memory requirements of current appearance-based methods scale linearly not only with the size of the environment but also with the operation time of the platform. These properties impose severe restrictions on longterm autonomy for mobile robots, as loop closure performance will inevitably degrade with increased operation time. We present a set of improvements to the appearance-based SLAM algorithm CAT-SLAM to constrain computation scaling and memory usage with minimal degradation in performance over time. The appearance-based comparison stage is accelerated by exploiting properties of the particle observation update, and nodes in the continuous trajectory map are removed according to minimal information loss criteria. We demonstrate constant time and space loop closure detection in a large urban environment with recall performance exceeding FAB-MAP by a factor of 3 at 100% precision, and investigate the minimum computational and memory requirements for maintaining mapping performance.

Effort-release public-key encryption from cryptographic puzzles

Timed-release cryptography addresses the problem of “sending messages into the future”: information is encrypted so that it can only be decrypted after a certain amount of time, either (a) with the help of a trusted third party time server, or (b) after a party performs the required number of sequential operations. We generalise the latter case to what we call effort-release public key encryption (ER-PKE), where only the party holding the private key corresponding to the public key can decrypt, and only after performing a certain amount of computation which may or may not be parallelisable. Effort-release PKE generalises both the sequential-operation-based timed-release encryption of Rivest, Shamir, and Wagner, and also the encapsulated key escrow techniques of Bellare and Goldwasser. We give a generic construction for ER-PKE based on the use of moderately hard computational problems called puzzles. Our approach extends the KEM/DEM framework for public key encryption by introducing a difficulty notion for KEMs which results in effort-release PKE. When the puzzle used in our generic construction is non-parallelisable, we recover timed-release cryptography, with the addition that only the designated receiver (in the public key setting) can decrypt.

Fully private revocable predicate encryption

We introduce the concept of Revocable Predicate Encryption (RPE), which extends current predicate encryption setting with revocation support: private keys can be used to decrypt an RPE ciphertext only if they match the decryption policy (defined via attributes encoded into the ciphertext and predicates associated with private keys) and were not revoked by the time the ciphertext was created. We formalize the notion of attribute hiding in the presence of revocation and propose an RPE scheme, called AH-RPE, which achieves attribute-hiding under the Decision Linear assumption in the standard model. We then present a stronger privacy notion, termed full hiding, which further cares about privacy of revoked users. We propose another RPE scheme, called FH-RPE, that adopts the Subset Cover Framework and offers full hiding under the Decision Linear assumption in the standard model. The scheme offers very flexible privacy-preserving access control to encrypted data and can be used in sender-local revocation scenarios.

What health problems overcrowd hospital emergency departments in Queensland and has this changed over time? A case study of two hospitals in Queensland 2001 - 2009

Aim: to describe what health problems patients attending emergency department with and whether this changed over time. Methods: Electronic data was retrieved from EDIS (Emergency Department Information System) and HBCIS (Hospital Based Clinical Information System) in two hospitals in Queensland in the period 2001-2009. The ICD-10 code of patient's diagnosis was then extrapolated and then group into ICD-10 chapters, such that the health problem can be presented. Results: Among the specific health problems, Chapter XIX 'Injury and poisoning' ranked number one consistently (ranging from 22.1% to 31.2% of the total presentations) in both the urban and remote hospitals in Queensland. The top ten specific presenting health problems in both the urban and remote hospital include Chapter XI 'Digestive system', Chapter XIV 'Genitourinary system', Chapter IX 'Circulatory system', and Chapter XIII 'Musculoskeletal system and connective tissue'. Chapter X 'Respiratory system' made the top ten presenting Chapters in both hospitals, but ranked much higher (number four consistently for the eight years, ranging from 6.8% to 8.3%) in the remote hospital. Chapter XV 'Pregnancy childbirth and puerperium' made to the top ten in the urban hospital only while Chapter XII 'Skin and subcutaneous tissue', Chapter I 'Infectious and parasitic diseases' made the top ten in the remote hospital only. Conclusion: The number one health problem presenting to both the urban and remote hospitals in Queensland is Chapter XIX 'Injury and poisoning', and it did not change in the period 211 - 2009.