Non-existence of polar factorisations and polar inclusion of a vector-valued mapping

R.J. DOUGLAS, Non-existence of polar factorisations and polar inclusion of a vector-valued mapping. Intern. Jour. Of Pure and Appl. Math., (IJPAM) 41, no. 3 (2007).

Uniqueness of the polar factorisation and projection of a vector-valued mapping

G.R. BURTON and R.J. DOUGLAS, Uniqueness of the polar factorisation and projection of a vector-valued mapping. Ann. I.H. Poincare ? A.N. 20 (2003), 405-418.

From Parallel Sequence Representations to Calligraphic Control: A Conspiracy of Neural Circuits

Calligraphic writing presents a rich set of challenges to the human movement control system. These challenges include: initial learning, and recall from memory, of prescribed stroke sequences; critical timing of stroke onsets and durations; fine control of grip and contact forces; and letter-form invariance under voluntary size scaling, which entails fine control of stroke direction and amplitude during recruitment and derecruitment of musculoskeletal degrees of freedom. Experimental and computational studies in behavioral neuroscience have made rapid progress toward explaining the learning, planning and contTOl exercised in tasks that share features with calligraphic writing and drawing. This article summarizes computational neuroscience models and related neurobiological data that reveal critical operations spanning from parallel sequence representations to fine force control. Part one addresses stroke sequencing. It treats competitive queuing (CQ) models of sequence representation, performance, learning, and recall. Part two addresses letter size scaling and motor equivalence. It treats cursive handwriting models together with models in which sensory-motor tmnsformations are performed by circuits that learn inverse differential kinematic mappings. Part three addresses fine-grained control of timing and transient forces, by treating circuit models that learn to solve inverse dynamics problems.

Modeling the Possible Influences of Eye Movements on the Refinement of Cortical Direction Selectivity

The second-order statistics of neural activity was examined in a model of the cat LGN and V1 during free-viewing of natural images. In the model, the specific patterns of thalamocortical activity required for a Bebbian maturation of direction-selective cells in VI were found during the periods of visual fixation, when small eye movements occurred, but not when natural images were examined in the absence of fixational eye movements. In addition, simulations of stroboscopic reming that replicated the abnormal pattern of eye movements observed in kittens chronically exposed to stroboscopic illumination produced results consistent with the reported loss of direction selectivity and preservation of orientation selectivity. These results suggest the involvement of the oculomotor activity of visual fixation in the maturation of cortical direction selectivity.

Vector Associative Maps: Unsupervised Real-time Error-based Learning and Control of Movement Trajectories

This article describes neural network models for adaptive control of arm movement trajectories during visually guided reaching and, more generally, a framework for unsupervised real-time error-based learning. The models clarify how a child, or untrained robot, can learn to reach for objects that it sees. Piaget has provided basic insights with his concept of a circular reaction: As an infant makes internally generated movements of its hand, the eyes automatically follow this motion. A transformation is learned between the visual representation of hand position and the motor representation of hand position. Learning of this transformation eventually enables the child to accurately reach for visually detected targets. Grossberg and Kuperstein have shown how the eye movement system can use visual error signals to correct movement parameters via cerebellar learning. Here it is shown how endogenously generated arm movements lead to adaptive tuning of arm control parameters. These movements also activate the target position representations that are used to learn the visuo-motor transformation that controls visually guided reaching. The AVITE model presented here is an adaptive neural circuit based on the Vector Integration to Endpoint (VITE) model for arm and speech trajectory generation of Bullock and Grossberg. In the VITE model, a Target Position Command (TPC) represents the location of the desired target. The Present Position Command (PPC) encodes the present hand-arm configuration. The Difference Vector (DV) population continuously.computes the difference between the PPC and the TPC. A speed-controlling GO signal multiplies DV output. The PPC integrates the (DV)·(GO) product and generates an outflow command to the arm. Integration at the PPC continues at a rate dependent on GO signal size until the DV reaches zero, at which time the PPC equals the TPC. The AVITE model explains how self-consistent TPC and PPC coordinates are autonomously generated and learned. Learning of AVITE parameters is regulated by activation of a self-regulating Endogenous Random Generator (ERG) of training vectors. Each vector is integrated at the PPC, giving rise to a movement command. The generation of each vector induces a complementary postural phase during which ERG output stops and learning occurs. Then a new vector is generated and the cycle is repeated. This cyclic, biphasic behavior is controlled by a specialized gated dipole circuit. ERG output autonomously stops in such a way that, across trials, a broad sample of workspace target positions is generated. When the ERG shuts off, a modulator gate opens, copying the PPC into the TPC. Learning of a transformation from TPC to PPC occurs using the DV as an error signal that is zeroed due to learning. This learning scheme is called a Vector Associative Map, or VAM. The VAM model is a general-purpose device for autonomous real-time error-based learning and performance of associative maps. The DV stage serves the dual function of reading out new TPCs during performance and reading in new adaptive weights during learning, without a disruption of real-time operation. YAMs thus provide an on-line unsupervised alternative to the off-line properties of supervised error-correction learning algorithms. YAMs and VAM cascades for learning motor-to-motor and spatial-to-motor maps are described. YAM models and Adaptive Resonance Theory (ART) models exhibit complementary matching, learning, and performance properties that together provide a foundation for designing a total sensory-cognitive and cognitive-motor autonomous system.

The Perception of Globally Coherent Motion

How do human observers perceive a coherent pattern of motion from a disparate set of local motion measures? Our research has examined how ambiguous motion signals along straight contours are spatially integrated to obtain a globally coherent perception of motion. Observers viewed displays containing a large number of apertures, with each aperture containing one or more contours whose orientations and velocities could be independently specified. The total pattern of the contour trajectories across the individual apertures was manipulated to produce globally coherent motions, such as rotations, expansions, or translations. For displays containing only straight contours extending to the circumferences of the apertures, observers' reports of global motion direction were biased whenever the sampling of contour orientations was asymmetric relative to the direction of motion. Performance was improved by the presence of identifiable features, such as line ends or crossings, whose trajectories could be tracked over time. The reports of our observers were consistent with a pooling process involving a vector average of measures of the component of velocity normal to contour orientation, rather than with the predictions of the intersection-of-constraints analysis in velocity space.

Comparative Performance Measures of Fuzzy ARTMAP, Learned Vector Quantization, and Back Propagation for Handwritten Character Recognition

This article compares the performance of Fuzzy ARTMAP with that of Learned Vector Quantization and Back Propagation on a handwritten character recognition task. Training with Fuzzy ARTMAP to a fixed criterion used many fewer epochs. Voting with Fuzzy ARTMAP yielded the highest recognition rates.

Power system parameters forecasting using Hilbert-Huang transform and machine learning

A novel hybrid data-driven approach is developed for forecasting power system parameters with the goal of increasing the efficiency of short-term forecasting studies for non-stationary time-series. The proposed approach is based on mode decomposition and a feature analysis of initial retrospective data using the Hilbert-Huang transform and machine learning algorithms. The random forests and gradient boosting trees learning techniques were examined. The decision tree techniques were used to rank the importance of variables employed in the forecasting models. The Mean Decrease Gini index is employed as an impurity function. The resulting hybrid forecasting models employ the radial basis function neural network and support vector regression. A part from introduction and references the paper is organized as follows. The second section presents the background and the review of several approaches for short-term forecasting of power system parameters. In the third section a hybrid machine learningbased algorithm using Hilbert-Huang transform is developed for short-term forecasting of power system parameters. Fourth section describes the decision tree learning algorithms used for the issue of variables importance. Finally in section six the experimental results in the following electric power problems are presented: active power flow forecasting, electricity price forecasting and for the wind speed and direction forecasting.

Design Optimization and Security For Communication Networks

In this work we introduce a new mathematical tool for optimization of routes, topology design, and energy efficiency in wireless sensor networks. We introduce a vector field formulation that models communication in the network, and routing is performed in the direction of this vector field at every location of the network. The magnitude of the vector field at every location represents the density of amount of data that is being transited through that location. We define the total communication cost in the network as the integral of a quadratic form of the vector field over the network area. With the above formulation, we introduce a mathematical machinery based on partial differential equations very similar to the Maxwell's equations in electrostatic theory. We show that in order to minimize the cost, the routes should be found based on the solution of these partial differential equations. In our formulation, the sensors are sources of information, and they are similar to the positive charges in electrostatics, the destinations are sinks of information and they are similar to negative charges, and the network is similar to a non-homogeneous dielectric media with variable dielectric constant (or permittivity coefficient). In one of the applications of our mathematical model based on the vector fields, we offer a scheme for energy efficient routing. Our routing scheme is based on changing the permittivity coefficient to a higher value in the places of the network where nodes have high residual energy, and setting it to a low value in the places of the network where the nodes do not have much energy left. Our simulations show that our method gives a significant increase in the network life compared to the shortest path and weighted shortest path schemes. Our initial focus is on the case where there is only one destination in the network, and later we extend our approach to the case where there are multiple destinations in the network. In the case of having multiple destinations, we need to partition the network into several areas known as regions of attraction of the destinations. Each destination is responsible for collecting all messages being generated in its region of attraction. The complexity of the optimization problem in this case is how to define regions of attraction for the destinations and how much communication load to assign to each destination to optimize the performance of the network. We use our vector field model to solve the optimization problem for this case. We define a vector field, which is conservative, and hence it can be written as the gradient of a scalar field (also known as a potential field). Then we show that in the optimal assignment of the communication load of the network to the destinations, the value of that potential field should be equal at the locations of all the destinations. Another application of our vector field model is to find the optimal locations of the destinations in the network. We show that the vector field gives the gradient of the cost function with respect to the locations of the destinations. Based on this fact, we suggest an algorithm to be applied during the design phase of a network to relocate the destinations for reducing the communication cost function. The performance of our proposed schemes is confirmed by several examples and simulation experiments. In another part of this work we focus on the notions of responsiveness and conformance of TCP traffic in communication networks. We introduce the notion of responsiveness for TCP aggregates and define it as the degree to which a TCP aggregate reduces its sending rate to the network as a response to packet drops. We define metrics that describe the responsiveness of TCP aggregates, and suggest two methods for determining the values of these quantities. The first method is based on a test in which we drop a few packets from the aggregate intentionally and measure the resulting rate decrease of that aggregate. This kind of test is not robust to multiple simultaneous tests performed at different routers. We make the test robust to multiple simultaneous tests by using ideas from the CDMA approach to multiple access channels in communication theory. Based on this approach, we introduce tests of responsiveness for aggregates, and call it CDMA based Aggregate Perturbation Method (CAPM). We use CAPM to perform congestion control. A distinguishing feature of our congestion control scheme is that it maintains a degree of fairness among different aggregates. In the next step we modify CAPM to offer methods for estimating the proportion of an aggregate of TCP traffic that does not conform to protocol specifications, and hence may belong to a DDoS attack. Our methods work by intentionally perturbing the aggregate by dropping a very small number of packets from it and observing the response of the aggregate. We offer two methods for conformance testing. In the first method, we apply the perturbation tests to SYN packets being sent at the start of the TCP 3-way handshake, and we use the fact that the rate of ACK packets being exchanged in the handshake should follow the rate of perturbations. In the second method, we apply the perturbation tests to the TCP data packets and use the fact that the rate of retransmitted data packets should follow the rate of perturbations. In both methods, we use signature based perturbations, which means packet drops are performed with a rate given by a function of time. We use analogy of our problem with multiple access communication to find signatures. Specifically, we assign orthogonal CDMA based signatures to different routers in a distributed implementation of our methods. As a result of orthogonality, the performance does not degrade because of cross interference made by simultaneously testing routers. We have shown efficacy of our methods through mathematical analysis and extensive simulation experiments.

Spatial vision in the purple sea urchin Strongylocentrotus purpuratus (Echinoidea).

Recent evidence that echinoids of the genus Echinometra have moderate visual acuity that appears to be mediated by their spines screening off-axis light suggests that the urchin Strongylocentrotus purpuratus, with its higher spine density, may have even more acute spatial vision. We analyzed the movements of 39 specimens of S. purpuratus after they were placed in the center of a featureless tank containing a round, black target that had an angular diameter of 6.5 deg. or 10 deg. (solid angles of 0.01 sr and 0.024 sr, respectively). An average orientation vector for each urchin was determined by testing the animal four times, with the target placed successively at bearings of 0 deg., 90 deg., 180 deg. and 270 deg. (relative to magnetic east). The urchins showed no significant unimodal or axial orientation relative to any non-target feature of the environment or relative to the changing position of the 6.5 deg. target. However, the urchins were strongly axially oriented relative to the changing position of the 10 deg. target (mean axis from -1 to 179 deg.; 95% confidence interval +/- 12 deg.; P<0.001, Moore's non-parametric Hotelling's test), with 10 of the 20 urchins tested against that target choosing an average bearing within 10 deg. of either the target center or its opposite direction (two would be expected by chance). In addition, the average length of the 20 target-normalized bearings for the 10 deg. target (each the vector sum of the bearings for the four trials) were far higher than would be expected by chance (P<10(-10); Monte Carlo simulation), showing that each urchin, whether it moved towards or away from the target, did so with high consistency. These results strongly suggest that S. purpuratus detected the 10 deg. target, responding either by approaching it or fleeing it. Given that the urchins did not appear to respond to the 6.5 deg. target, it is likely that the 10 deg. target was close to the minimum detectable size for this species. Interestingly, measurements of the spine density of the regions of the test that faced horizontally predicted a similar visual resolution (8.3+/-0.5 deg. for the interambulacrum and 11+/-0.54 deg. for the ambulacrum). The function of this relatively low, but functional, acuity - on par with that of the chambered Nautilus and the horseshoe crab - is unclear but, given the bimodal response, is likely to be related to both shelter seeking and predator avoidance.

An alphavirus vector overcomes the presence of neutralizing antibodies and elevated numbers of Tregs to induce immune responses in humans with advanced cancer.

Therapeutic anticancer vaccines are designed to boost patients' immune responses to tumors. One approach is to use a viral vector to deliver antigen to in situ DCs, which then activate tumor-specific T cell and antibody responses. However, vector-specific neutralizing antibodies and suppressive cell populations such as Tregs remain great challenges to the efficacy of this approach. We report here that an alphavirus vector, packaged in virus-like replicon particles (VRP) and capable of efficiently infecting DCs, could be repeatedly administered to patients with metastatic cancer expressing the tumor antigen carcinoembryonic antigen (CEA) and that it overcame high titers of neutralizing antibodies and elevated Treg levels to induce clinically relevant CEA-specific T cell and antibody responses. The CEA-specific antibodies mediated antibody-dependent cellular cytotoxicity against tumor cells from human colorectal cancer metastases. In addition, patients with CEA-specific T cell responses exhibited longer overall survival. These data suggest that VRP-based vectors can overcome the presence of neutralizing antibodies to break tolerance to self antigen and may be clinically useful for immunotherapy in the setting of tumor-induced immunosuppression.

Integrated vector management for malaria control in Uganda: knowledge, perceptions and policy development.

BACKGROUND: Integrated vector management (IVM) is increasingly being recommended as an option for sustainable malaria control. However, many malaria-endemic countries lack a policy framework to guide and promote the approach. The objective of the study was to assess knowledge and perceptions in relation to current malaria vector control policy and IVM in Uganda, and to make recommendations for consideration during future development of a specific IVM policy. METHODS: The study used a structured questionnaire to interview 34 individuals working at technical or policy-making levels in health, environment, agriculture and fisheries sectors. Specific questions on IVM focused on the following key elements of the approach: integration of chemical and non-chemical interventions of vector control; evidence-based decision making; inter-sectoral collaboration; capacity building; legislation; advocacy and community mobilization. RESULTS: All participants were familiar with the term IVM and knew various conventional malaria vector control (MVC) methods. Only 75% thought that Uganda had a MVC policy. Eighty percent (80%) felt there was inter-sectoral collaboration towards IVM, but that it was poor due to financial constraints, difficulties in involving all possible sectors and political differences. The health, environment and agricultural sectors were cited as key areas requiring cooperation in order for IVM to succeed. Sixty-seven percent (67%) of participants responded that communities were actively being involved in MVC, while 48% felt that the use of research results for evidence-based decision making was inadequate or poor. A majority of the participants felt that malaria research in Uganda was rarely used to facilitate policy changes. Suggestions by participants for formulation of specific and effective IVM policy included: revising the MVC policy and IVM-related policies in other sectors into a single, unified IVM policy and, using legislation to enforce IVM in development projects. CONCLUSION: Integrated management of malaria vectors in Uganda remains an underdeveloped component of malaria control policy. Cooperation between the health and other sectors needs strengthening and funding for MVC increased in order to develop and effectively implement an appropriate IVM policy. Continuous engagement of communities by government as well as monitoring and evaluation of vector control programmes will be crucial for sustaining IVM in the country.

Assessment of toxicity and biodistribution of recombinant AAV8 vector-mediated immunomodulatory gene therapy in mice with Pompe disease.

A preclinical safety study was conducted to evaluate the short- and long-term toxicity of a recombinant adeno-associated virus serotype 8 (AAV2/8) vector that has been developed as an immune-modulatory adjunctive therapy to recombinant human acid α-glucosidase (rhGAA, Myozyme) enzyme replacement treatment (ERT) for patients with Pompe disease (AAV2/8-LSPhGAApA). The AAV2/8-LSPhGAApA vector at 1.6 × 10(13) vector particles/kg, after intravenous injection, did not cause significant short- or long-term toxicity. Recruitment of CD4(+) (but not CD8(+)) lymphocytes to the liver was elevated in the vector-dosed male animals at study day (SD) 15, and in group 8 animals at SD 113, in comparison to their respective control animals. Administration of the vector, either prior to or after the one ERT injection, uniformly prevented the hypersensitivity induced by subsequent ERT in males, but not always in female animals. The vector genome was sustained in all tissues through 16-week postdosing, except for in blood with a similar tissue tropism between males and females. Administration of the vector alone, or combined with the ERT, was effective in producing significantly increased GAA activity and consequently decreased glycogen accumulation in multiple tissues, and the urine biomarker, Glc4, was significantly reduced. The efficacy of the vector (or with ERT) was better in males than in females, as demonstrated both by the number of tissues showing significantly effective responses and the extent of response in a given tissue. Given the lack of toxicity for AAV2/8LSPhGAApA, further consideration of clinical translation is warranted in Pompe disease.