Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final time and hence the excitation probability. Using this method, which can reproduce the well-known expression for the LZ transition probability, we solve a variant of the LZ problem, which involves waiting at the minimum gap for a time t(w); we find an exact expression for the excitation probability as a function of t(w). We provide numerical results to support our analytical expressions. We then discuss the problem of waiting at the quantum critical point of a many-body system and calculate the residual energy generated by the time-dependent Hamiltonian. Finally, we discuss possible experimental realizations of this work.

Isoperimetric Problem and Meta-fibonacci Sequences

Let G = (V,E) be a simple, finite, undirected graph. For S ⊆ V, let $\delta(S,G) = \{ (u,v) \in E : u \in S \mbox { and } v \in V-S \}$ and $\phi(S,G) = \{ v \in V -S: \exists u \in S$ , such that (u,v) ∈ E} be the edge and vertex boundary of S, respectively. Given an integer i, 1 ≤ i ≤ ∣ V ∣, the edge and vertex isoperimetric value at i is defined as b e (i,G) =  min S ⊆ V; |S| = i |δ(S,G)| and b v (i,G) =  min S ⊆ V; |S| = i |φ(S,G)|, respectively. The edge (vertex) isoperimetric problem is to determine the value of b e (i, G) (b v (i, G)) for each i, 1 ≤ i ≤ |V|. If we have the further restriction that the set S should induce a connected subgraph of G, then the corresponding variation of the isoperimetric problem is known as the connected isoperimetric problem. The connected edge (vertex) isoperimetric values are defined in a corresponding way. It turns out that the connected edge isoperimetric and the connected vertex isoperimetric values are equal at each i, 1 ≤ i ≤ |V|, if G is a tree. Therefore we use the notation b c (i, T) to denote the connected edge (vertex) isoperimetric value of T at i. Hofstadter had introduced the interesting concept of meta-fibonacci sequences in his famous book “Gödel, Escher, Bach. An Eternal Golden Braid”. The sequence he introduced is known as the Hofstadter sequences and most of the problems he raised regarding this sequence is still open. Since then mathematicians studied many other closely related meta-fibonacci sequences such as Tanny sequences, Conway sequences, Conolly sequences etc. Let T 2 be an infinite complete binary tree. In this paper we related the connected isoperimetric problem on T 2 with the Tanny sequences which is defined by the recurrence relation a(i) = a(i − 1 − a(i − 1)) + a(i − 2 − a(i − 2)), a(0) = a(1) = a(2) = 1. In particular, we show that b c (i, T 2) = i + 2 − 2a(i), for each i ≥ 1. We also propose efficient polynomial time algorithms to find vertex isoperimetric values at i of bounded pathwidth and bounded treewidth graphs.

A FEM-Based Forward Solver for Studying the Forward Problem of Electrical Impedance Tomography (EIT) with A Practical Biological Phantom

A Finite Element Method based forward solver is developed for solving the forward problem of a 2D-Electrical Impedance Tomography. The Method of Weighted Residual technique with a Galerkin approach is used for the FEM formulation of EIT forward problem. The algorithm is written in MatLAB7.0 and the forward problem is studied with a practical biological phantom developed. EIT governing equation is numerically solved to calculate the surface potentials at the phantom boundary for a uniform conductivity. An EIT-phantom is developed with an array of 16 electrodes placed on the inner surface of the phantom tank filled with KCl solution. A sinusoidal current is injected through the current electrodes and the differential potentials across the voltage electrodes are measured. Measured data is compared with the differential potential calculated for known current and solution conductivity. Comparing measured voltage with the calculated data it is attempted to find the sources of errors to improve data quality for better image reconstruction.

On a Special Co-cycle Basis of Graphs

In this paper we consider the problems of computing a minimum co-cycle basis and a minimum weakly fundamental co-cycle basis of a directed graph G. A co-cycle in G corresponds to a vertex partition (S,V ∖ S) and a { − 1,0,1} edge incidence vector is associated with each co-cycle. The vector space over ℚ generated by these vectors is the co-cycle space of G. Alternately, the co-cycle space is the orthogonal complement of the cycle space of G. The minimum co-cycle basis problem asks for a set of co-cycles that span the co-cycle space of G and whose sum of weights is minimum. Weakly fundamental co-cycle bases are a special class of co-cycle bases, these form a natural superclass of strictly fundamental co-cycle bases and it is known that computing a minimum weight strictly fundamental co-cycle basis is NP-hard. We show that the co-cycle basis corresponding to the cuts of a Gomory-Hu tree of the underlying undirected graph of G is a minimum co-cycle basis of G and it is also weakly fundamental.

New approximation algorithms for minimum cycle bases of graphs

We consider the problem of computing an approximate minimum cycle basis of an undirected edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k >= 1, we give (2k - 1)-approximation algorithms with expected running time 0(kmn(1+2/k) + mn((1+1/k)(omega-1))) and deterministic running time 0(n(3+2/k)), respectively. Here omega is the best exponent of matrix multiplication. It is presently known that omega < 2.376. Both algorithms are o(m(omega)) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the Theta(m(omega)) bound. We also present a 2-approximation algorithm with O(m(omega) root n log n) expected running time, a linear time 2-approximation algorithm for planar graphs and an O(n(3)) time 2.42-approximation algorithm for the complete Euclidean graph in the plane.

Robust joint precoder/receive filter designs for multiuser MIMO downlink

In this paper, we consider robust joint linear precoder/receive filter designs for multiuser multi-input multi-output (MIMO) downlink that minimize the sum mean square error (SMSE) in the presence of imperfect channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas, and each user terminal is equipped with one or more receive antennas. We consider a stochastic error (SE) model and a norm-bounded error (NBE) model for the CSIT error. In the case of CSIT error following SE model, we compute the desired downlink precoder/receive filter matrices by solving the simpler uplink problem by exploiting the uplink-downlink duality for the MSE region. In the case of the CSIT error following the NBE model, we consider the worst-case SMSE as the objective function, and propose an iterative algorithm for the robust transceiver design. The robustness of the proposed algorithms to imperfections in CSIT is illustrated through simulations.

Problem-based learning in an e-learning environment: A case study at Griffith University School of Medicine

Increasing numbers of medical schools in Australia and overseas have moved away from didactic teaching methodologies and embraced problem-based learning (PBL) to improve clinical reasoning skills and communication skills as well as to encourage self-directed lifelong learning. In January 2005, the first cohort of students entered the new MBBS program at the Griffith University School of Medicine, Gold Coast, to embark upon an exciting, fully integrated curriculum using PBL, combining electronic delivery, communication and evaluation systems incorporating cognitive principles that underpin the PBL process. This chapter examines the educational philosophies and design of the e-learning environment underpinning the processes developed to deliver, monitor and evaluate the curriculum. Key initiatives taken to promote student engagement and innovative and distinctive approaches to student learning at Griffith promoted within the conceptual model for the curriculum are (a) Student engagement, (b) Pastoral care, (c) Staff engagement, (d) Monitoring and (e) Curriculum/Program Review. © 2007 Springer-Verlag Berlin Heidelberg.

Selective attention in a synchronising bushcricket: physiology

Synchronising bushcricket males achieve synchrony by delaying their chirps in response to calling neighbours. In multi-male choruses, males that delay chirps in response to all their neighbours would remain silent most of the time and be unable to attract mates. This problem could be overcome if the afferent auditory system exhibited selective attention, and thus a male interacted only with a subset of neighbours. We investigated whether individuals of the bushcricket genus Mecopoda restricted their attention to louder chirps neurophysiologically, behaviourally and through spacing. We found that louder leading chirps were preferentially represented in the omega neuron but the representation of softer following chirps was not completely abolished. Following chirps that were 20 dB louder than leading chirps were better represented than leading chirps. During acoustic interactions, males synchronised with leading chirps even when the following chirps were 20 dB louder. Males did not restrict their attention to louder chirps during interactions but were affected by all chirps above a particular threshold. In the field, we found that males on average had only one or two neighbours whose calls were above this threshold. Selective attention is thus achieved in this bushcricket through spacing rather than neurophysiological filtering of softer signals.

Selective attention in a synchronising bushcricket: physiology, behaviour and ecology

Synchronising bushcricket males achieve synchrony by delaying their chirps in response to calling neighbours. In multi-male choruses, males that delay chirps in response to all their neighbours would remain silent most of the time and be unable to attract mates. This problem could be overcome if the afferent auditory system exhibited selective attention, and thus a male interacted only with a subset of neighbours. We investigated whether individuals of the bushcricket genus Mecopoda restricted their attention to louder chirps neurophysiologically, behaviourally and through spacing. We found that louder leading chirps were preferentially represented in the omega neuron but the representation of softer following chirps was not completely abolished. Following chirps that were 20 dB louder than leading chirps were better represented than leading chirps. During acoustic interactions, males synchronised with leading chirps even when the following chirps were 20 dB louder. Males did not restrict their attention to louder chirps during interactions but were affected by all chirps above a particular threshold. In the field, we found that males on average had only one or two neighbours whose calls were above this threshold. Selective attention is thus achieved in this bushcricket through spacing rather than neurophysiological filtering of softer signals.

On the duality between rate and power optimizations

Sequence design problems are considered in this paper. The problem of sum power minimization in a spread spectrum system can be reduced to the problem of sum capacity maximization, and vice versa. A solution to one of the problems yields a solution to the other. Subsequently, conceptually simple sequence design algorithms known to hold for the white-noise case are extended to the colored noise case. The algorithms yield an upper bound of 2N - L on the number of sequences where N is the processing gain and L the number of non-interfering subsets of users. If some users (at most N - 1) are allowed to signal along a limited number of multiple dimensions, then N orthogonal sequences suffice.

Dacomitinib versus erlotinib in patients with EGFR-mutated advanced nonsmall-cell lung cancer (NSCLC): Pooled subset analyses from two randomized trials

Background: The irreversible epidermal growth factor receptor (EGFR) inhibitors have demonstrated efficacy in NSCLC patients with activating EGFR mutations, but it is unknown if they are superior to the reversible inhibitors. Dacomitinib is an oral, small-molecule irreversible inhibitor of all enzymatically active HER family tyrosine kinases. Methods: The ARCHER 1009 (NCT01360554) and A7471028 (NCT00769067) studies randomized patients with locally advanced/metastatic NSCLC following progression with one or two prior chemotherapy regimens to dacomitinib or erlotinib. EGFR mutation testing was performed centrally on archived tumor samples. We pooled patients with exon 19 deletion and L858R EGFR mutations from both studies to compare the efficacy of dacomitinib to erlotinib. Results: One hundred twenty-one patients with any EGFR mutation were enrolled; 101 had activating mutations in exon 19 or 21. For patients with exon19/21 mutations, the median progression-free survival was 14.6 months [95% confidence interval (CI) 9.0–18.2] with dacomitinib and 9.6 months (95% CI 7.4–12.7) with erlotinib [unstratified hazard ratio (HR) 0.717 (95% CI 0.458–1.124), two-sided log-rank, P = 0.146]. The median survival was 26.6 months (95% CI 21.6–41.5) with dacomitinib versus 23.2 months (95% CI 16.0–31.8) with erlotinib [unstratified HR 0.737 (95% CI 0.431–1.259), two-sided log-rank, P = 0.265]. Dacomitinib was associated with a higher incidence of diarrhea and mucositis in both studies compared with erlotinib. Conclusions: Dacomitinib is an active agent with comparable efficacy to erlotinib in the EGFR mutated patients. The subgroup with exon 19 deletion had favorable outcomes with dacomitinib. An ongoing phase III study will compare dacomitinib to gefitinib in first-line therapy of patients with NSCLC harboring common activating EGFR mutations (ARCHER 1050; NCT01774721). Clinical trials number: ARCHER 1009 (NCT01360554) and A7471028 (NCT00769067).

Mixed pixel analysis for flood mapping using extended support vector machine

This paper addresses the challenges of flood mapping using multispectral images. Quantitative flood mapping is critical for flood damage assessment and management. Remote sensing images obtained from various satellite or airborne sensors provide valuable data for this application, from which the information on the extent of flood can be extracted. However the great challenge involved in the data interpretation is to achieve more reliable flood extent mapping including both the fully inundated areas and the 'wet' areas where trees and houses are partly covered by water. This is a typical combined pure pixel and mixed pixel problem. In this paper, an extended Support Vector Machines method for spectral unmixing developed recently has been applied to generate an integrated map showing both pure pixels (fully inundated areas) and mixed pixels (trees and houses partly covered by water). The outputs were compared with the conventional mean based linear spectral mixture model, and better performance was demonstrated with a subset of Landsat ETM+ data recorded at the Daly River Basin, NT, Australia, on 3rd March, 2008, after a flood event.

Robust heuristics for scalable optimization of complex SQL queries

Modern database systems incorporate a query optimizer to identify the most efficient "query execution plan" for executing the declarative SQL queries submitted by users. A dynamic-programming-based approach is used to exhaustively enumerate the combinatorially large search space of plan alternatives and, using a cost model, to identify the optimal choice. While dynamic programming (DP) works very well for moderately complex queries with up to around a dozen base relations, it usually fails to scale beyond this stage due to its inherent exponential space and time complexity. Therefore, DP becomes practically infeasible for complex queries with a large number of base relations, such as those found in current decision-support and enterprise management applications. To address the above problem, a variety of approaches have been proposed in the literature. Some completely jettison the DP approach and resort to alternative techniques such as randomized algorithms, whereas others have retained DP by using heuristics to prune the search space to computationally manageable levels. In the latter class, a well-known strategy is "iterative dynamic programming" (IDP) wherein DP is employed bottom-up until it hits its feasibility limit, and then iteratively restarted with a significantly reduced subset of the execution plans currently under consideration. The experimental evaluation of IDP indicated that by appropriate choice of algorithmic parameters, it was possible to almost always obtain "good" (within a factor of twice of the optimal) plans, and in the few remaining cases, mostly "acceptable" (within an order of magnitude of the optimal) plans, and rarely, a "bad" plan. While IDP is certainly an innovative and powerful approach, we have found that there are a variety of common query frameworks wherein it can fail to consistently produce good plans, let alone the optimal choice. This is especially so when star or clique components are present, increasing the complexity of th- e join graphs. Worse, this shortcoming is exacerbated when the number of relations participating in the query is scaled upwards.

Selective attention in a synchronising bushcricket: physiology, behaviour and ecology

Synchronising bushcricket males achieve synchrony by delaying their chirps in response to calling neighbours. In multi-male choruses, males that delay chirps in response to all their neighbours would remain silent most of the time and be unable to attract mates. This problem could be overcome if the afferent auditory system exhibited selective attention, and thus a male interacted only with a subset of neighbours. We investigated whether individuals of the bushcricket genus Mecopoda restricted their attention to louder chirps neurophysiologically, behaviourally and through spacing. We found that louder leading chirps were preferentially represented in the omega neuron but the representation of softer following chirps was not completely abolished. Following chirps that were 20 dB louder than leading chirps were better represented than leading chirps. During acoustic interactions, males synchronised with leading chirps even when the following chirps were 20 dB louder. Males did not restrict their attention to louder chirps during interactions but were affected by all chirps above a particular threshold. In the field, we found that males on average had only one or two neighbours whose calls were above this threshold. Selective attention is thus achieved in this bushcricket through spacing rather than neurophysiological filtering of softer signals.

Spectral unmixing with estimated adaptive endmember index using Extended Support Vector Machine

The most difficult operation in the flood inundation mapping using optical flood images is to separate fully inundated areas from the ‘wet’ areas where trees and houses are partly covered by water. This can be referred as a typical problem the presence of mixed pixels in the images. A number of automatic information extraction image classification algorithms have been developed over the years for flood mapping using optical remote sensing images. Most classification algorithms generally, help in selecting a pixel in a particular class label with the greatest likelihood. However, these hard classification methods often fail to generate a reliable flood inundation mapping because the presence of mixed pixels in the images. To solve the mixed pixel problem advanced image processing techniques are adopted and Linear Spectral unmixing method is one of the most popular soft classification technique used for mixed pixel analysis. The good performance of linear spectral unmixing depends on two important issues, those are, the method of selecting endmembers and the method to model the endmembers for unmixing. This paper presents an improvement in the adaptive selection of endmember subset for each pixel in spectral unmixing method for reliable flood mapping. Using a fixed set of endmembers for spectral unmixing all pixels in an entire image might cause over estimation of the endmember spectra residing in a mixed pixel and hence cause reducing the performance level of spectral unmixing. Compared to this, application of estimated adaptive subset of endmembers for each pixel can decrease the residual error in unmixing results and provide a reliable output. In this current paper, it has also been proved that this proposed method can improve the accuracy of conventional linear unmixing methods and also easy to apply. Three different linear spectral unmixing methods were applied to test the improvement in unmixing results. Experiments were conducted in three different sets of Landsat-5 TM images of three different flood events in Australia to examine the method on different flooding conditions and achieved satisfactory outcomes in flood mapping.