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Transcending shift-invariance in the paraxial regime via end-to-end inverse design of freeform nanophotonics
Published 2023“…<jats:p>Traditional optical elements and conventional metasurfaces obey shift-invariance in the paraxial regime. For imaging systems obeying paraxial shift-invariance, a small shift in input angle causes a corresponding shift in the sensor image. …”
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Seeded graph matching via large neighborhood statistics
Published 2021“…Moreover, we show the number of seeds needed for perfect recovery in polynomial-time can be as low as (Formula presented.) in the sparse graph regime (with the average degree smaller than (Formula presented.)) and (Formula presented.) in the dense graph regime, for a small positive constant (Formula presented.). …”
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Explicit Construction of RIP Matrices Is Ramsey‐Hard
Published 2021“…The notable exception is the work by Bourgain et al. constructing an n × p RIP matrix with sparsity s = Θ(n1/2 + ϵ), but in the regime n = Ω(p1 − δ). In this short note we resolve this open question by showing that an explicit construction of a matrix satisfying the RIP in the regime n = O(log2p) and s = Θ(n1/2) implies an explicit construction of a three-colored Ramsey graph on p nodes with clique sizes bounded by O(log2p) — a question in the field of extremal combinatorics that has been open for decades. © 2019 Wiley Periodicals, Inc.…”
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Almost sure well-posedness for the periodic 3D quintic nonlinear Schrödinger equation below the energy space
Published 2018“…We prove an almost sure local well-posedness result for the periodic 3D quintic nonlinear Schrödinger equation in the supercritical regime, that is, below the critical space H ¹ (T³). …”
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Critical Percolation on Scale-Free Random Graphs: New Universality Class for the Configuration Model
Published 2021“…In this paper, we initiate the study of critical random graphs in the infinite second-moment regime by identifying the critical window for the configuration model. …”
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Water entry of small hydrophobic spheres
Published 2010“…Theoretical predictions compare favourably with our experimental observations in the low Bond number regime, and also yield new insight into the high Bond number regime considered by previous investigators. …”
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Breaking of 1RSB in Random Regular MAX-NAE-SAT
Published 2021“…In the unsatisfiable regime, it is natural to consider the problem of max-satisfiability: violating the least number of constraints. …”
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Seeded Graph Matching via Large Neighborhood Statistics
Published 2021“…Finally, for each i, π∗(i) is revealed independently with probability α as seeds. In the sparse graph regime where np ≤ n for any < 1/6, we give a polynomial-time algorithm which perfectly recovers π∗, provided that nps2 − log n → +∞ and α ≥ n−1+3. …”
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A stochastic telegraph equation from the six-vertex model
Published 2021“…We show that such fields arise naturally as asymptotic fluctuations of the height function in a certain limit regime of the stochastic six-vertex model in a quadrant. …”
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Liouville Quantum Gravity with Matter Central Charge in (1, 25): A Probabilistic Approach
Published 2022“…Physics considerations suggest that LQG should also make sense in the regime when $${\mathbf {c}}_{\mathrm M} > 1$$ c M > 1 . …”
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Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime
Published 2019“…As an application, we are able to quantitatively control the energy flux along the horizon and null infinity and establish integrated local energy decay for solutions to the wave equation in any bounded-frequency regime. Keywords: Black Hole, Wave Equation, Half Plane, Quasinormal Mode, Mode Stability…”
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Limits of determinantal processes near a tacnode
Published 2018“…The main result of the paper is a derivation of the local correlation kernel around the tacnode in the transition regime ε ↓ 0. We also prove that the local process interpolates between the Pearcey process and the GUE minor process.…”
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The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system
Published 2013“…In addition, we show that on any Lorentzian manifold, the MBI system is hyperbolic in the interior of the field-strength regime in which its Lagrangian is real-valued.…”
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Bouncing droplet dynamics above the Faraday threshold
Published 2019“…A number of new dynamical regimes are reported, including meandering, zig-zagging, erratic bouncing, coalescing, and trapped regimes. …”
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Hydrodynamic spin states
Published 2020“…We use an integro-differential trajectory equation for the droplet's horizontal motion to specify the parameter regimes for which the innermost spin state can be stabilized. …”
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The number of solutions for random regular NAE-SAT
Published 2022“…Here we revisit one of these models, random regular k-nae-sat: knowing the satisfiability threshold, it is natural to study, in the satisfiable regime, the number of solutions in a typical instance. …”
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Eventual linear convergence of the Douglas-Rachford iteration for basis pursuit
Published 2017“…We make no attempt at characterizing the transient regime preceding the onset of linear convergence.…”
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