A topological approach to mapping space signatures by Giusti, C, Lee, D, Nanda, V, Oberhauser, H

“…A common approach for describing classes of functions and probability measures on a topological space X is to construct a suitable map Φ from X into a vector space, where linear methods can be applied to address both problems. …”

Tangent space and dimension estimation with the Wasserstein distance by Lim, U, Oberhauser, H, Nanda, V

“…Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space. We provide mathematically rigorous bounds on the number of sample points required to estimate both the dimension and the tangent spaces of that manifold with high confidence. …”

Feynman rules for QCD in space-cone gauge by Karlberg, A, Sondergaard, T

“…We present the Lagrangian and Feynman rules for QCD written in space-cone gauge and after eliminating unphysical degrees of freedom from the gluonic sector. …”

Bordism categories and orientations of gauge theory moduli spaces by Joyce, D, Upmeier, M

“…</p> <p>We prove that the orientability of moduli spaces of connections in gauge theory for <i>all</i> principal <i>G</i>-bundles <i>P</i>→<i>X</i> over compact spin <i>n</i>-manifolds <i>at once</i> is equivalent to the vanishing of a certain morphism Ω^Spin_<i>n</i>(<i>L</i><i>BG</i>)→<i>Z</i>₂ on the <i>n</i>-dimensional spin bordism group of the free loop space of the classifying space of <i>G</i>, and we give a complete list of all compact, connected Lie groups <i>G</i> for which this holds. …”

Symmetry TFTs from string theory by Apruzzi, F, Bonetti, F, Etxebarria, IG, Hosseini, SS, Schafer-Nameki, S

“…We determine the d+1 dimensional topological field theory, which encodes the higher-form symmetries and their 't Hooft anomalies for d-dimensional QFTs obtained by compactifying M-theory on a non-compact space X. The resulting theory, which we call the Symmetry TFT, or SymTFT for short, is derived by reducing the topological sector of 11d supergravity on the boundary ∂X of the space X. …”

Grid-free computation of probabilistic safety with Malliavin Calculus by Cosentino, F, Oberhauser, H, Abate, A

“…This work concerns continuous-time, continuous-space stochastic dynamical systems described by stochastic differential equations (SDE). …”

General signature kernels by Cass, T, Lyons, T, Xu, X

“…As an application we evaluate the use of different general signature kernels as the basis for non-parametric goodness-of-fit tests to Wiener measure on path space.…”

Neural rough differential equations for long time series by Morrill, J, Salvi, C, Kidger, P, Foster, J, Lyons, T

“…Existing methods for computing the forward pass of a Neural CDE involve embedding the incoming time series into path space, often via interpolation, and using evaluations of this path to drive the hidden state. …”

LaLaLoc: latent layout localisation in dynamic, unvisited environments by Howard-Jenkins, H, Ruiz-Sarmiento, J-R, Prisacariu, VA

“…LaLaLoc learns a rich embedding space shared between RGB panoramas and layouts inferred from a known floor plan that encodes the structural similarity between locations. …”

Collisionless relaxation of a Lynden-Bell plasma by Ewart, RJ, Brown, A, Adkins, T, Schekochihin, AA

“…It is suggested that collisionless dynamics may favour maximising entropy locally in phase space before converging to global maximum-entropy states. …”

A PDE approach for solving the characteristic function of the generalised signature process by Lyons, T, Ni, H, Tao, J

“…The signature of a path, as a fundamental object in Rough path theory, serves as a generating function for non-communicative monomials on path space. It transforms the path into a grouplike element in the tensor algebra space, summarising the path faithfully up to a generalised form of re-parameterisation (a negligible equivalence class in this context). …”

‘Resolve me of all ambiguities’: a review of Thomas McGlothlin’s Resurrection as Salvation by Strawbridge, J

“…It is a rapidly expanding network of scholars who are interested in not merely reviewing one another&#x2019;s work, but engaging it with substance. It is a discursive space where mutual inquiry and collaboration are encouraged and nourished.…”

Stable liftings of polynomial traces on tetrahedra by Parker, C, Suli, E

“…The operator is stable as a mapping from the trace space of Ws,p(K) to Ws,p(K) for all p∈(1,∞) and s∈(k+1/p,∞). …”

Approximating continuous convolutions for deep network compression by Costain, TW, Prisacariu, V

“…Reframing conventional discrete convolution as continuous convolution of parametrised functions over space, we use functional approximations to capture the essential structures of CNN filters with fewer parameters than conventional operations. …”

On RKHS choices for assessing graph generators via kernel Stein statistics by Weckbecker, M, Xu, W, Reinert, G

“…Score-based kernelised Stein discrepancy (KSD) tests have emerged as a powerful tool for the goodness of fit tests, especially in high dimensions; however, the test performance may depend on the choice of kernels in an underlying reproducing kernel Hilbert space (RKHS). Here we assess the effect of RKHS choice for KSD tests of random networks models, developed for exponential random graph models (ERGMs) in Xu and Reinert (2021)and for synthetic graph generators in Xu and Reinert (2022). …”

Markov chain approximations to stochastic differential equations by recombination on lattice trees by Cosentino, F, Oberhauser, H, Abate, A

“…We revisit the classical problem of approximating a stochastic differential equation by a discrete-time and discrete-space Markov chain. Our construction iterates Caratheodory's theorem over time to match the moments of the increments locally. …”

Symmetry breaking and consistent truncations from m5-branes wrapping a disc by Bomans, P, Couzens, C, Lee, Y, Ning, S

“…The presence of such scalar fields breaks one of the U(1) isometries of the internal space, explicitly realising the breaking by the Stuckelberg mechanism observed previously. …”

Modelling chemical processes in explicit solvents with machine learning potentials by Zhang, H, Juraskova, V, Duarte, F

“…Our approach combines active learning with descriptor-based selectors and automation, enabling the construction of data-efficient training sets that span the relevant chemical and conformational space. We demonstrate the versatility of this strategy by applying it to investigate a Diels-Alder reaction in water and methanol. …”

GroSS: Group-Size Series decomposition for grouped architecture search by Howard-Jenkins, H, Li, Y, Prisacariu, VA

“…In doing so, GroSS is able to train an entire grouped convolution architecture search-space concurrently. We demonstrate this through architecture searches with performance objectives on multiple datasets and networks. …”

Finding non-uniform quantization schemes using multi-task Gaussian processes by Gennari do Nascimento, M, Costain, TW, Prisacariu, VA

“…We perform the search assuming a Multi-Task Gaussian Processes prior, which splits the problem to multiple tasks, each corresponding to different number of training epochs, and explore the space by sampling those configurations that yield maximum information. …”