On Representations of Conformal Field Theories and the Construction of Orbifolds

We consider representations of meromorphic bosonic chiral conformal field theories, and demonstrate that such a representation is completely specified by a state within the theory. The necessary and sufficient conditions upon this state are derived, and, because of their form, we show that we may extend the representation to a representation of a suitable larger conformal field theory. In particular, we apply this procedure to the lattice (FKS) conformal field theories, and deduce that Dong's proof of the uniqueness of the twisted representation for the reflection-twisted projection of the Leech lattice conformal field theory generalises to an arbitrary even (self-dual) lattice. As a consequence, we see that the reflection-twisted lattice theories of Dolan et al are truly self-dual, extending the analogies with the theories of lattices and codes which were being pursued. Some comments are also made on the general concept of the definition of an orbifold of a conformal field theory in relation to this point of view.Comment: 11 pages, LaTeX. Updated references and added preprint n

Asymmetry in functional connectivity of the human habenula revealed by high-resolution cardiac-gated resting state imaging

The habenula is a hub for cognitive and emotional signals that are relayed to the aminergic centers in the midbrain and, thus, plays an important role in goal-oriented behaviors. Although it is well described in rodents and non-human primates, the habenula functional network remains relatively uncharacterized in humans, partly because of the methodological challenges associated with the functional magnetic resonance imaging of small structures in the brain. Using high-resolution cardiac-gated resting state imaging in healthy humans and precisely identifying each participants' habenula, we show that the habenula is functionally coupled with the insula, parahippocampus, thalamus, periaqueductal grey, pons, striatum and substantia nigra/ventral tegmental area complex. Furthermore, by separately examining and comparing the functional maps from the left and right habenula, we provide the first evidence of an asymmetry in the functional connectivity of the habenula in humans. Hum Brain Mapp 37:2602-2615, 2016. © 2016 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc

Demyelination and axonal preservation in a transgenic mouse model of Pelizaeus-Merzbacher disease

It is widely thought that demyelination contributes to the degeneration of axons and, in combination with acute inflammatory injury, is responsible for progressive axonal loss and persistent clinical disability in inflammatory demyelinating disease. In this study we sought to characterize the relationship between demyelination, inflammation and axonal transport changes using a Plp1-transgenic mouse model of Pelizaeus-Merzbacher disease. In the optic pathway of this non-immune mediated model of demyelination, myelin loss progresses from the optic nerve head towards the brain, over a period of months. Axonal transport is functionally perturbed at sites associated with local inflammation and 'damaged' myelin. Surprisingly, where demyelination is complete, naked axons appear well preserved despite a significant reduction of axonal transport. Our results suggest that neuroinflammation and/or oligodendrocyte dysfunction are more deleterious for axonal health than demyelination per se, at least in the short ter

Conformal Field Theories, Representations and Lattice Constructions

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and $Z_2$-twisted theories, $H(\Lambda)$ and $\tilde H(\Lambda)$ respectively, which may be constructed from a suitable even Euclidean lattice $\Lambda$. Similarly, one may construct lattices $\Lambda_C$ and $\tilde\Lambda_C$ by analogous constructions from a doubly-even binary code $C$. In the case when $C$ is self-dual, the corresponding lattices are also. Similarly, $H(\Lambda)$ and $\tilde H(\Lambda)$ are self-dual if and only if $\Lambda$ is. We show that $H(\Lambda_C)$ has a natural ``triality'' structure, which induces an isomorphism $H(\tilde\Lambda_C)\equiv\tilde H(\Lambda_C)$ and also a triality structure on $\tilde H(\tilde\Lambda_C)$. For $C$ the Golay code, $\tilde\Lambda_C$ is the Leech lattice, and the triality on $\tilde H(\tilde\Lambda_C)$ is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories $H(\Lambda)$ and $\tilde H(\Lambda)$ with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.Comment: 65 page

It's Simplex! Disaggregating Measures to Improve Certified Robustness

Certified robustness circumvents the fragility of defences against adversarial attacks, by endowing model predictions with guarantees of class invariance for attacks up to a calculated size. While there is value in these certifications, the techniques through which we assess their performance do not present a proper accounting of their strengths and weaknesses, as their analysis has eschewed consideration of performance over individual samples in favour of aggregated measures. By considering the potential output space of certified models, this work presents two distinct approaches to improve the analysis of certification mechanisms, that allow for both dataset-independent and dataset-dependent measures of certification performance. Embracing such a perspective uncovers new certification approaches, which have the potential to more than double the achievable radius of certification, relative to current state-of-the-art. Empirical evaluation verifies that our new approach can certify $9\%$ more samples at noise scale $\sigma = 1$, with greater relative improvements observed as the difficulty of the predictive task increases.Comment: IEEE S&P 2024, IEEE Security & Privacy 2024, 14 page

Enhancing the Antidote: Improved Pointwise Certifications against Poisoning Attacks

Poisoning attacks can disproportionately influence model behaviour by making small changes to the training corpus. While defences against specific poisoning attacks do exist, they in general do not provide any guarantees, leaving them potentially countered by novel attacks. In contrast, by examining worst-case behaviours Certified Defences make it possible to provide guarantees of the robustness of a sample against adversarial attacks modifying a finite number of training samples, known as pointwise certification. We achieve this by exploiting both Differential Privacy and the Sampled Gaussian Mechanism to ensure the invariance of prediction for each testing instance against finite numbers of poisoned examples. In doing so, our model provides guarantees of adversarial robustness that are more than twice as large as those provided by prior certifications

Exploiting Certified Defences to Attack Randomised Smoothing

In guaranteeing that no adversarial examples exist within a bounded region, certification mechanisms play an important role in neural network robustness. Concerningly, this work demonstrates that the certification mechanisms themselves introduce a new, heretofore undiscovered attack surface, that can be exploited by attackers to construct smaller adversarial perturbations. While these attacks exist outside the certification region in no way invalidate certifications, minimising a perturbation's norm significantly increases the level of difficulty associated with attack detection. In comparison to baseline attacks, our new framework yields smaller perturbations more than twice as frequently as any other approach, resulting in an up to $34 \%$ reduction in the median perturbation norm. That this approach also requires $90 \%$ less computational time than approaches like PGD. That these reductions are possible suggests that exploiting this new attack vector would allow attackers to more frequently construct hard to detect adversarial attacks, by exploiting the very systems designed to defend deployed models.Comment: 15 pages, 7 figure

Categories of First-Order Quantifiers

One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial languages generated by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k \u3e 0 is treated as a two-argument functorfunction defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility