A whitehead product for track groups II

Two direct relations are exhibited between the Whitehead product for track groups studied in [4] and the generalized Whitehead product in the sense of Arkowitz. The problem of determining the order of the Whitehead square is posed and some computations given

Bivariant long exact sequences II

Given a pair of short exact sequences 1) 0 → X → Y → Z → 0, 0 → A → B → C → 0 in an abelian category A, with sufficiently many projectives and injectives, and given an additive bifunctor T we show that T applied to the pair (1) gives rise to a diagram of a type described by C. T. C. Wall that contains 15 interlocking long exact sequences involving the derived functors of T at (A, X), (A, Y), etc. and also involving the derived functors of Tp and Tq which are two functors with domain A2 that arise through the failure of T to preserve pullbacks and pushouts. In the case of Hom (respectively ø) in the category of G-modules for a group G the derived functors of Tp (respectively Tq) are expressed in terms of group cohomology (respectively homology)

The two-square lemma

A new proof is given of the connecting homomorphism

Deep learning for anisoplanatic optical turbulence mitigation in long-range imaging

We present a deep learning approach for restoring images degraded by atmospheric optical turbulence. We consider the case of terrestrial imaging over long ranges with a wide field-of-view. This produces an anisoplanatic imaging scenario where turbulence warping and blurring vary spatially across the image. The proposed turbulence mitigation (TM) method assumes that a sequence of short-exposure images is acquired. A block matching (BM) registration algorithm is applied to the observed frames for dewarping, and the resulting images are averaged. A convolutional neural network (CNN) is then employed to perform spatially adaptive restoration. We refer to the proposed TM algorithm as the block matching and CNN (BM-CNN) method. Training the CNN is accomplished using simulated data from a fast turbulence simulation tool capable of producing a large amount of degraded imagery from declared truth images rapidly. Testing is done using independent data simulated with a different well-validated numerical wave-propagation simulator. Our proposed BM-CNN TM method is evaluated in a number of experiments using quantitative metrics. The quantitative analysis is made possible by virtue of having truth imagery from the simulations. A number of restored images are provided for subjective evaluation. We demonstrate that the BM-CNN TM method outperforms the benchmark methods in the scenarios tested

Electrical coupling of neuro-ommatidial photoreceptor cells in the blowfly

A new method of microstimulation of the blowfly eye using corneal neutralization was applied to the 6 peripheral photoreceptor cells (R1-R6) connected to one neuro-ommatidium (and thus looking into the same direction), whilst the receptor potential of a dark-adapted photoreceptor cell was recorded by means of an intracellular microelectrode. Stimulation of the photoreceptor cells not impaled elicited responses in the recorded cell of about 20% of the response elicited when stimulating the recorded cell. This is probably caused by gap junctions recently found between the axon terminals of these cells. Stimulation of all 6 cells together yielded responses that were larger and longer than those obtained with stimulation of just the recorded cell, and intensity-response curves that deviated more strongly from linearity. Evidence is presented that the resistance of the axon terminal of the photoreceptor cells quickly drops in response to a light flash, depending on the light intensity. Incorporating the cable properties of the cell body and the axon, the resistance of the gap junctions, and the (adapting) terminal resistance, a theoretical model is presented that explains the measurements well. Finally, it is argued that the gap junctions between the photoreceptor cells may effectively uncouple the synaptic responses of the cells by counteracting the influence of field potentials.

A semi-classical over-barrier model for charge exchange between highly charged ions and one-optical electron atoms

Absolute total cross sections for electron capture between slow, highly charged ions and alkali targets have been recently measured. It is found that these cross sections follow a scaling law with the projectile charge which is different from the one previously proposed basing on a classical over-barrier model (OBM) and verified using rare gases and molecules as targets. In this paper we develop a "semi-classical" (i.e. including some quantal features) OBM attempting to recover experimental results. The method is then applied to ion-hydrogen collisions and compared with the result of a sophisticated quantum-mechanical calculation. In the former case the accordance is very good, while in the latter one no so satisfactory results are found. A qualitative explanation for the discrepancies is attempted.Comment: RevTeX, uses epsf; 6 pages text + 3 EPS figures Journal of Physics B (scehduled March 2000). This revision corrects fig.

Super-resolution in the presence of atmospheric optical turbulence

The design of imaging systems involves navigating a complex trade space. As a result, many imaging systems employ focal plane arrays with a detector pitch that is insufficient to meet the Nyquist sampling criterion under diffraction-limited imaging conditions. This undersampling may result in aliasing artifacts and prevent the imaging system from achieving the full resolution afforded by the optics. Another potential source of image degradation, especially for long-range imaging, is atmospheric optical turbulence. Optical turbulence gives rise to spatially and temporally varying image blur and warping from fluctuations in the index of refraction along with optical path. Under heavy turbulence, the blurring from the turbulence acts as an anti-aliasing filter, and undersampling does not generally occur. However, under light to moderate turbulence, many imaging systems will exhibit both aliasing artifacts and turbulence degradation. Few papers in the literature have analyzed or addressed both of these degradations together. In this paper, we provide a novel analysis of undersampling in the presence of optical turbulence. Specifically, we provide an optical transfer function analysis that illustrates regimes where aliasing and turbulence are both present, and where they are not. We also propose and evaluate a super-resolution (SR) method for combating aliasing that offers robustness to optical turbulence. The method has a tuning parameter that allows it to transition from traditional diffraction-limited SR, to pure turbulence mitigation with no SR. The proposed method is based on Fusion of Interpolated Frames (FIF) SR, recently proposed by two of the current authors. We quantitatively evaluate the SR method with varying levels of optical turbulence using simulated sequences. We also presented results using real infrared imagery

Outdoor Mental Health Interventions and Outdoor Therapy: A statement of good practice

Health, well-being and self-development has been a cornerstone of the impact and value of outdoor learning practices for many decades. Over recent years, we have seen an exponential growth in therapeutic outdoor initiatives and programmes being developed and utilised for mental health and well-being benefits. Traditional terms such as adventure therapy, wilderness therapy, nature therapy and outdoor counselling, have more recently been joined with a plethora of wider terms, such as eco-therapy, forest bathing, and a Natural Health Service, to name a few. All of these terms are taking claim to some kind of health benefit (physical or psychological) for getting outdoors. This Institute for Outdoor Learning (IOL) statement purposefully sets out a view on competence when combining mental health and well-being interventions with outdoor learning: o The primary goal was to develop a model that could support organisations and individuals who provide and utilise services for mental health and well-being in an outdoor setting. The statement has been strongly informed by mapping current practice in the UK. o It has been created to ensure that those engaging outdoor learning services to improve mental health and well-being can do so with confidence and trust in what they are offered

Fusion of interpolated frames superresolution in the presence of atmospheric optical turbulence

An extension of the fusion of interpolated frames superresolution (FIF SR) method to perform SR in the presence of atmospheric optical turbulence is presented. The goal of such processing is to improve the performance of imaging systems impacted by turbulence. We provide an optical transfer function analysis that illustrates regimes where significant degradation from both aliasing and turbulence may be present in imaging systems. This analysis demonstrates the potential need for simultaneous SR and turbulence mitigation (TM). While the FIF SR method was not originally proposed to address this joint restoration problem, we believe it is well suited for this task. We propose a variation of the FIF SR method that has a fusion parameter that allows it to transition from traditional diffraction-limited SR to pure TM with no SR as well as a continuum in between. This fusion parameter balances subpixel resolution, needed for SR, with the amount of temporal averaging, needed for TM and noise reduction. In addition, we develop a model of the interpolation blurring that results from the fusion process, as a function of this tuning parameter. The blurring model is then incorporated into the overall degradation model that is addressed in the restoration step of the FIF SR method. This innovation benefits the FIF SR method in all applications. We present a number of experimental results to demonstrate the efficacy of the FIF SR method in different levels of turbulence. Simulated imagery with known ground truth is used for a detailed quantitative analysis. Three real infrared image sequences are also used. Two of these include bar targets that allow for a quantitative resolution enhancement assessment