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Matthew Burke

Publications and source records attributed to Matthew Burke.

13 recordsLinked to original sources
arXiv2026

Relative dispersion and eddy diffusivity in laboratory experiments of $\beta$-plane turbulence

We present the first experimental measures of relative dispersion and turbulent diffusion in rapidly-rotating turbulence in the zonostrophic regime, i.e., in the presence of instantaneous and dominant zonal jets. Synthetic Lagrangian trajectories are computed from time-resolved experimental velocity fields, from which we measure relative (two-particle) dispersion. Time-based and separation-based statistics are calculated, including the cumulative inverse separation time (CIST), for which analytical predictions exist in the inertial ranges (direct enstrophy cascade and inverse energy cascade) and in the diffusive regime. These statistics show evidence of a transition from a Richardson regime at scales larger than the energy-injection scale, to a diffusive regime, at scales larger than the transitional scale, the scale at which turbulence becomes anisotropic due to the interaction between turbulent eddies and Rossby waves. The analytical predictions for the CIST allow us to measure the turbulent energy dissipation rate in the Richardson regime, and the turbulent diffusivity in the diffusive regime. Our measurements of diffusivity are broadly consistent with predictions from mixing-length and zonostrophic theories but suggest a shallower dependence on the energy dissipation rate.

physics.flu-dyn↗
arXiv2026

Quantum-HPC hybrid computation of biomolecular excited-state energies

We develop a workflow within the ONIOM framework and demonstrate it on the hybrid computing system consisting of the supercomputer Fugaku and the Quantinuum Reimei trapped-ion quantum computer. This hybrid platform extends the layered approach for biomolecular chemical reactions to accurately treat the active site, such as a protein, and the large and often weakly correlated molecular environment. Our result marks a significant milestone in enabling scalable and accurate simulation of complex biomolecular reactions

quant-ph↗
arXiv2021

Basil: Breaking up BFT with ACID (transactions)

This paper presents Basil, the first transactional, leaderless Byzantine Fault Tolerant key-value store. Basil leverages ACID transactions to scalably implement the abstraction of a trusted shared log in the presence of Byzantine actors. Unlike traditional BFT approaches, Basil executes non-conflicting operations in parallel and commits transactions in a single round-trip during fault-free executions. Basil improves throughput over traditional BFT systems by four to five times, and is only four times slower than TAPIR, a non-Byzantine replicated system. Basil's novel recovery mechanism further minimizes the impact of failures: with 30% Byzantine clients, throughput drops by less than 25% in the worst-case.

cs.DC↗
arXiv2021

Regular Sequential Serializability and Regular Sequential Consistency

Strictly serializable (linearizable) services appear to execute transactions (operations) sequentially, in an order consistent with real time. This restricts a transaction's (operation's) possible return values and in turn, simplifies application programming. In exchange, strictly serializable (linearizable) services perform worse than those with weaker consistency. But switching to such services can break applications. This work introduces two new consistency models to ease this trade-off: regular sequential serializability (RSS) and regular sequential consistency (RSC). They are just as strong for applications: we prove any application invariant that holds when using a strictly serializable (linearizable) service also holds when using an RSS (RSC) service. Yet they relax the constraints on services -- they allow new, better-performing designs. To demonstrate this, we design, implement, and evaluate variants of two systems, Spanner and Gryff, relaxing their consistency to RSS and RSC, respectively. The new variants achieve better read-only transaction and read tail latency than their counterparts.

cs.DB↗
arXiv2021

Tangent $\infty$-categories and Goodwillie calculus

We make precise the analogy between Goodwillie's calculus of functors in homotopy theory and the differential calculus of smooth manifolds by introducing a higher-categorical framework of which both theories are examples. That framework is an extension to infinity-categories of the tangent categories of Cockett and Cruttwell (introduced originally by Rosick\'y). The basic data of a tangent infinity-category consist of an endofunctor, that plays the role of the tangent bundle construction, together with various natural transformations that mimic structure possessed by the ordinary tangent bundles of smooth manifolds. The role of the tangent bundle functor in Goodwillie calculus is played by Lurie's tangent bundle for infinity-categories, introduced to generalize the cotangent complexes of Andr\'e, Quillen and Illusie. We show that Lurie's construction admits the additional structure maps and satisfies the conditions needed to form a tangent infinity-category which we refer to as the Goodwillie tangent structure. Cockett and Cruttwell (and others) have started to develop various aspects of differential geometry in the abstract context of tangent categories, and we begin to apply those ideas to Goodwillie calculus. For example, we show that the role of Euclidean spaces in the calculus of manifolds is played in Goodwillie calculus by the stable infinity-categories. We also show that Goodwillie's n-excisive functors are the direct analogues of n-jets of smooth maps between manifolds; to state that connection precisely, we develop a notion of tangent (infinity,2)-category and show that Goodwillie calculus is best understood in that context.

math.CT↗
arXiv2019

Involution algebroids: a generalisation of Lie algebroids for tangent categories

We define involution algebroids which generalise Lie algebroids to the abstract setting of tangent categories. As a part of this generalisation the Jacobi identity which appears in classical Lie theory is replaced by an identity similar to the Yang-Baxter equation. Every classical Lie algebroid has the structure of an involution algebroid and every involution algebroid in a tangent category admits a Lie bracket on the sections of its underlying bundle. As an illustrative application we take the first steps in developing the homotopy theory of involution algebroids.

math.CT↗
arXiv2018

Obladi: Oblivious Serializable Transactions in the Cloud

This paper presents the design and implementation of Obladi, the first system to provide ACID transactions while also hiding access patterns. Obladi uses as its building block oblivious RAM, but turns the demands of supporting transactions into a performance opportunity. By executing transactions within epochs and delaying commit decisions until an epoch ends, Obladi reduces the amortized bandwidth costs of oblivious storage and increases overall system throughput. These performance gains, combined with new oblivious mechanisms for concurrency control and recovery, allow Obladi to execute OLTP workloads with reasonable throughput: it comes within 5x to 12x of a non-oblivious baseline on the TPC-C, SmallBank, and FreeHealth applications. Latency overheads, however, are higher (70x on TPC-C).

cs.DC↗
arXiv2017

The Algebroid of a Groupoid in a Tangent Category

We generalise the construction of the Lie algebroid of a Lie groupoid so that it can be carried out in any tangent category. First we reconstruct the bijection between left invariant vector fields and source constant tangent vectors based at an identity element for a groupoid in a category equipped with an endofunctor that has a retraction onto the identity functor. Second we use the full structure of a tangent category to construct the algebroid of a groupoid. Finally we show how the classical result concerning the splitting of the tangent bundle of a Lie group can be carried out for any pregroupoid.

math.CT↗
arXiv2017

Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry

We extend some fundamental definitions and constructions in the established generalisation of Lie theory involving Lie groupoids by reformulating them in terms of groupoids internal to a well-adapted model of synthetic differential geometry. In particular we define internal counterparts of the definitions of source path and source simply connected groupoid and the integration of $A$-paths. The main results of this paper show that if a classical Hausdorff Lie groupoid satisfies one of the classical connectedness conditions it also satisfies its internal counterpart.

math.CT↗
arXiv2016

A Synthetic Version of Lie's Second Theorem

We formulate and prove a twofold generalisation of Lie's second theorem that integrates homomorphisms between formal group laws to homomorphisms between Lie groups. Firstly we generalise classical Lie theory by replacing groups with categories. Secondly we include categories whose underlying spaces are not smooth manifolds. The main intended application is when we replace the category of smooth manifolds with a well-adapted model of synthetic differential geometry. In addition we provide an axiomatic system that specifies the abstract structures that are required to prove Lie's second theorem. As a part of this abstract structure we define the notion of enriched mono-coreflective subcategory which makes precise the notion of a subcategory of local models.

math.CT↗
arXiv2014

Solvable Leibniz algebras with triangular nilradical

A classification exists for Lie algebras whose nilradical is the triangular Lie algebra $T(n)$. We extend this result to a classification of all solvable Leibniz algebras with nilradical $T(n)$. As an example we show the complete classification of all Leibniz algebras whose nilradical is $T(4)$.

math.RA↗
arXiv2013

Convex and subharmonic functions on graphs

We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of convexity on graphs and show that more structure is needed to establish the desired result. To that end, we consider a notion of convexity defined on lattice-like graphs generated by normed abelian groups. For this class of graphs, we are able to prove that all convex functions are subharmonic.

math.CO↗