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On the hidden layer-to-layer topology of the representations of reality realised within neural networks
Get PDFPurpose: Consider an information processing algorithm that is designed to process an input data object onto an output data object via a number of successive internal {\it layers} and mappings between them. The possible activation state within each layer can be represented as a cube within Euclidean space of a high dimension (e.g. equal to the number of artificial neurons at that level). Multiple instances of such input objects produce a point cloud within each layer’s cube: this is the “representation of the reality” at that layer, as sampled by the set of input objects.
Design/methodology/approach: Most neural networks reduce the dimension of each layer’s cube from layer to successive layer. This gives the false impression of refining the inner representations of reality, distilling it down to fewer dimensions from which to discriminate or to infer outcomes (whatever is the aim). However, the representation of reality realised within each layer’s cube is a manifold, a curved subset embedded within it and of much lower dimension. Investigations show that such manifolds may not always be reducing in their local dimension. Instead, the manifold may become folded over and over, filling up further dimensions and creating non-realistic (unforeseeable) proximities.
Findings: We discuss some of the likely consequences of these relatively unforeseen characteristics and, in particular, the possible vulnerability of such algorithms to non-realistic perturbations. We consider a possible response to this issue.
Practical implications: New forms of calibration are necessary, using geometric/topological loss functions, as opposed to simple (variation-limiting) regularisation terms.
Originality/value: We apply persistent homology methods to understand how the images of the point cloud (representing the sampled reality) change as they pass from layer to layer
Accuracy and stability of CUR decompositions with oversampling
Get PDFThis work investigates the accuracy and numerical stability of CUR decompositions with oversampling. The CUR decomposition approximates a matrix using a subset of columns and rows of the matrix. When the number of columns and rows is the same, the CUR decomposition can become unstable and less accurate due to the presence of the matrix inverse in the core matrix. Nevertheless, we demonstrate that the CUR decomposition can be implemented in a numerically stable manner and illustrate that oversampling, which increases the number of either columns or rows in the CUR decomposition, can enhance its accuracy and stability. Additionally, this work devises an algorithm for oversampling motivated by the theory of the CUR decomposition and the cosine-sine decomposition, whose competitiveness is illustrated through experiments
Omnisubjectivity and some of its implications
Get PDFIn this paper, I elaborate a broadly Zagzebskian case for divine omnisubjectivity understood along the lines of her Empathy Model, defend it against an objection, and consider some implications of it
The Jadidology wars. A plea for peace from a neutral bystander
Get PDFA review article on recent controversies surrounding the Muslim reformers or 'Jadids' in late Tsarist Central Asia
Shortest paths without a map, but with an entropic regularizer
Get PDFIn a 1989 paper titled “shortest paths without a map”, Papadimitriou and Yannakakis introduced an online model of searching in a weighted layered graph for a target node, while attempting to minimize the total length of the path traversed by the searcher. This problem, later called layered graph traversal, is parametrized by the maximum cardinality of a layer of the input graph. It is an online setting for dynamic programming, and it is known to be a rather general and fundamental model of online computing, which includes as special cases other acclaimed models. The deterministic competitive ratio for this problem was soon discovered to be exponential in , and it is now nearly resolved: it lies between Ω(2 ) and (2 ). Regarding the randomized competitive ratio, in 1993 Ramesh proved, surprisingly, that this ratio has to be at least Ω( 2 /log1+ ) (for any constant > 0). In the same paper, Ramesh also gave an ( 13)-competitive randomized online algorithm. Between 1993 and the results obtained in this paper, no progress has been reported on the randomized competitive ratio of layered graph traversal. In this work we show how to apply the mirror descent framework on a carefully selected evolving metric space, and obtain an ( 2 )-competitive randomized online algorithm. This matches asymptotically an improvement of the aforementioned lower bound [8], which we announced (among other results) after the initial publication of the results here
Towards a consensus for dyslexia practice: findings of a Delphi study on assessment and identification
Get PDFThis paper discusses the findings of a Delphi study in which dyslexia experts, including academics, specialist teachers, educational psychologists, and individuals with dyslexia, were asked for their agreement with a set of key statements about defining and identifying dyslexia: why it should be assessed, and how and when this assessment should be conducted. Two rounds of survey responses provided a vehicle for moving towards consensus on how to assess for dyslexia. Forty-two consensus statements were ultimately accepted.
Findings suggested that assessment practice should take account of risks to the accurate identification of dyslexia. An assessment model, with guidelines for assessors, is presented, based on the Delphi’s findings. This hypothesis-testing model requires assessors to investigate and weigh up the factors most likely to result in an accurate assessment before reaching conclusions, assigning terminology, and making recommendations for intervention and management
The evolution of signalling and monitoring in plant-fungal networks
Get PDFExperiments have shown that when one plant is attacked by a pathogen or herbivore, this can lead to other plants connected to the same mycorrhizal network up-regulating their defense mechanisms. It has been hypothesized that this represents signaling, with attacked plants producing a signal to warn other plants of impending harm. We examined the evolutionary plausibility of this and other hypotheses theoretically. We found that the evolution of plant signaling about an attack requires restrictive conditions, and so will rarely be evolutionarily stable. The problem is that signaling about an attack provides a benefit to competing neighbors, even if they are kin, and so reduces the relative fitness of signaling plants. Indeed, selection is often more likely to push plant behavior in the opposite direction—with plants signaling dishonestly about an attack that has not occurred, or suppressing a cue that they have been attacked. Instead, we show that there are two viable alternatives that could explain the empirical data: 1) the process of being attacked leads to a cue (information about the attack) which is too costly for the attacked plant to fully suppress; 2) mycorrhizal fungi monitor their host plants, detect when they are attacked, and then the fungi signal this information to warn other plants in their network. Our results suggest the empirical work that would be required to distinguish between these possibilities
Two paradoxes in women’s wellbeing
Get PDFWe review the literature on the gender gap in well-being, identifying two key paradoxes. First, although women today report higher levels of life satisfaction and overall happiness than men, they experience worse outcomes in mental health and negative affect. Second, despite substantial advances in women’s social and economic status over the past 50 years, their well-being relative to men has declined. We explore the evidence supporting these paradoxes, considering potential explanations related to differential expectations, biology, and scale use. Using global data from 2006 to 2023 and long-term data from Europe and the US since the 1970s, we provide empirical illustrations. These findings reveal a diverse and seemingly inconsistent pattern of gender well-being gaps between countries, suggesting that the first paradox is not universally applicable. However, there is clear global evidence of a relative decline in women’s well-being, particularly in terms of negative affect
Modelling laser-induced vapour bubbles for lithotripsy treatment of kidney stones
Get PDFLaser lithotripsy, a common treatment for kidney stones, involves passing a flexible scope containing a laser fibre into the kidney via the bladder and ureter. Within the kidney, laser pulses are fired at the stone to break it into pieces small enough to flush out. During the procedure, laser energy is also transferred to the surrounding liquid, resulting in localised boiling and the production of vapour bubbles. While bubbles can have undesirable effects – for example, causing retropulsion of the stone – they can also be utilised to make stone ablation more efficient. The aim of this work is to contribute to improving the speed and ease of laser lithotripsy kidney stone treatment via mathematical modelling, focusing on the vapour bubbles that form during the treatment.
The size, shape and duration of a laser-induced bubble is dependent on the total energy of the laser pulse and the way in which this energy is temporally distributed. The time dependent power profile of the pulse is referred to as ‘pulse shape’ and can be manipulated to produce bubbles with desirable properties. Using two different modelling approaches, we predict properties of the bubble as a function of the pulse shape, as well as understanding the physics driving bubble expansion. Previous models of laser-induced bubbles assume the energy transfer from the laser to the fluid to be instantaneous, which is not a good approximation for the ∼ 100 μs pulses employed in lithotripsy. To reflect the effect that the laser parameters have on the bubble size, shape and duration, we model the laser as a time and space dependent source of energy in the liquid-vapour fluid system.
Our first model considers the simplified case of a single, spherical vapour bubble in liquid, with phase change at the bubble wall. With this model, we build upon an existing method of coupling the Rayleigh-Plesset equation to an energy equation in the surrounding liquid and an energy flux balance at the bubble wall. Mathematical analysis of the governing equations reveals the physical effects occurring at three stages of bubble expansion and the time-scales at which these stages occur. We then examine the effect on the bubble of varying pulse power, pulse duration, and total pulse energy.
A second modelling approach tackles the challenging problem of breaking spherical symmetry in bubble modelling by utilising the ‘volume of fluid’ method on an axisymmetric domain. With localised phase change due to laser heating, we are able to reflect the elongated shapes that occur during laser lithotripsy and study how the proportions of the bubble — length and width — as well as its size and duration are affected by the properties of the pulse. Axisymmetry gives the flexibility to introduce solid boundaries near the bubble and measure the effect this has on both the bubble and the boundary.
Through numerical and analytical methods alongside experimental work we develop an understanding of the physical factors driving bubble expansion and provide a framework to guide the future development and clinical usage of lasers
Examining two of the ingredients of cognitive therapy for adolescent social anxiety disorder: back-translation from a treatment trial
Get PDFBackground
Cognitive Therapy for Social Anxiety Disorder (CT-SAD) based on the Clark & Wells model is a complex intervention comprised of a series of therapeutic elements. Two of the key ingredients are the self-focused attention and safety behaviour experiment and video feedback. The present study examined the effects of these two therapeutic procedures in adolescents with SAD, as well as common themes of the young people's social fears and negative self-images.
Method
35 participants with a diagnosis of SAD completed internet-delivered CT-SAD as part of a randomised controlled trial. We conducted a series of paired samples t-tests to evaluate the effects of the self-focused attention and safety behaviour experiment and video feedback. We applied Latent Dirichlet Allocation to identify latent topics based on participants' description of their social fears and negative self-images that were elicited during the course of these therapy procedures.
Results
Participants reported lower anxiety and more positive self-appraisals when focusing externally and dropping safety behaviours, compared to when focusing internally and using safety behaviours (ps < 0.0025). After they watched the videos compared to before, they reported more positive appraisals of their appearance and performance (ps < 0.0025). The differences in these outcomes were significantly larger when they focused internally and used safety behaviours, compared to focusing externally and dropping safety behaviours (ps < 0.0025). Topic modelling identified six social fear topics and five negative self-image topics.
Conclusions
Self-focused attention, safety behaviours, and negative self-imagery are modifiable with the ‘self-focused attention and safety behaviour experiment’ and ‘video feedback’ as part of internet delivered CT-SAD