Research
Research
Research
Research
728+ open-access research outputs.
Fluid equations are nonlinear, dissipative, and non-Hamiltonian, which makes their relation to Schr\"odinger evolution and quantum algorithms nontrivial. We derive an exact Eulerian Cole-Hopf-type ref…
Learning curves are a fundamental primitive in supervised learning, describing how an algorithm's performance improves with more data and providing a quantitative measure of its generalization ability…
We derive integrable deformations of the 2d Breitenlohner-Maison (BM) sigma model that describes the stationary, axisymmetric sector of 4d general relativity, as well as higher-rank generalisations th…
Weak constitutive fluctuations in dispersive subsurface media can induce distributed clutter that reshapes the observation structure of ground-penetrating radar (GPR). This paper analyzes this effect …
We propose a new convex programming relaxation for the weighted Nash social welfare (NSW) problem that achieves a matching $(e^{1/e}\approx 1.445)$-approximation via the rounding algorithm of Feng and…
This paper investigates the cross-frequency structure of background clutter induced by random dispersive media in single-snapshot FDA-MIMO-GPR. Representative media are modeled by the Cole--Cole formu…
Solutions to the Schr\"{o}dinger bridge problem and its generalizations yield feedback control policies for optimal density steering over a controlled diffusion. To numerically compute the same, the d…
Recent advancements in Reinforcement Learning with Verifiable Rewards (RLVR) have significantly improved Large Language Model (LLM) reasoning, yet models often struggle to explore novel trajectories b…
This paper extends path integral control (PIC) to partially observed systems by formulating the problem in Gaussian belief space. PIC relies on the diffusion being proportional to the control channel …
Anomalous relaxation with memory spectra arises in disordered solids, soft matter, biological tissues and electrochemical interfaces. Fractional-order models capture broad power-law behaviour efficien…
Controlling the evolution of a many-body stochastic system from a disordered reference state to a structured target ensemble, characterized empirically through samples, arises naturally in non-equilib…
This paper introduces a class of continuous-time, finite-player stochastic general-sum differential games that admit solutions through an exact linear PDE system. We formulate a distribution planning …
The mean-field Schr\"odinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribution from another b…
For the double of a quiver, the works of Ginzburg, Bocklandt-Le Bruyn and Schedler show that its closed paths, called the necklaces, have a natural Lie bialgebra structure. Schedler also constructed,i…
A classic data structure problem is to preprocess a string T of length $n$ so that, given a query $q$, we can quickly find all substrings of T with Hamming distance at most $k$ from the query string. …
We prove the weak relative Kawamata-Morrison movable cone conjecture for K-trivial fibrations whose very general fibre is a quotient, by a finite group of automorphisms acting freely in codimension on…
We show that the It\^o solutions of the nonlinear stochastic heat equation $$ \partial_t u^\varepsilon- \Delta u^\varepsilon =\varepsilon^{3/4} g (u^\varepsilon) \nabla \xi_\varepsilon, $$ where $ \xi…
We consider the problem of triangulating a polygon with $n$ vertices and $h$ holes, or relatedly the problem of computing the trapezoidal decomposition of a collection of $h$ disjoint simple polygonal…
State-of-the-art spoken dialogue models (D\'efossez et al. 2024; Schalkwyk et al. 2025) use neural audio codecs to "tokenize" audio signals into a lower-frequency stream of vectorial latent representa…
Accurate modeling of gas flow through porous media is critical for many technological applications, including reservoir performance prediction, carbon capture and sequestration, and fuel cells and bat…
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