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A Cryptographic Proof of Regularity Lemmas
Regularity lemmas Boosting Low-complexity approximations
2016/12/8
In this work we present a unified proof for the Strong and
Weak Regularity Lemma, based on the cryptographic technique called
low-complexity approximations. In short, both problems reduce to a task
...
On the Regularity of Lossy RSA: Improved Bounds and Applications to Padding-Based Encryption
PKCS Phi-Hiding Regularity
2016/1/5
We provide new bounds on how close to regular the map x |--> x^e is on arithmetic progressions in Z_N, assuming e | Phi(N) and N is composite. We use these bounds to analyze the security of natural cr...
Existence and regularity of extremal solutions for a mean-curvature equation
Mean curvature minimal solution semi-stable solution extremal solution regularity
2015/10/15
We study a class of mean curvature equations −Mu = H +λup where M denotes the mean curvature operator and for p ≥ 1. We show that there exists an extremal parameter λ∗ such that this equat...
REGULARITY OF ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR PIECEWISE EXPANDING UNIMODAL MAPS
INVARIANT MEASURES UNIMODAL MAPS
2015/9/29
An important discovery of the 20th century mathematics is that many deterministic
systems exhibit stochastic behavior. The stochasticity is caused by exponential divergence of nearby trajectories. Th...
A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its L_infinity-norm
Matrix and singular value differentiable function frequency singular value lipschitz second derivative
2015/8/12
The ith singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one. We show that near a local maximum, however, the largest singu...
The Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity
Harnack inequality second-order parabolic equations divergence-free drifts low regularity
2015/7/14
We establish the Harnack inequality for advection-diffusion equations with divergencefree drifts of low regularity.While our previous work [IKR] considered the elliptic case, here we treat the more ch...
Capturing Gradience,Continuous Change,and Quasi-Regularity in Sound,Word,Phrase,and Meaning
Capturing Gradience Continuous Change Sound Word Phrase Meaning
2015/6/23
One vision of the nature of language holds that a language consists of a set of symbolic unit types, and a set of units of each type, together with a set of grammatical principles that constrain how t...
Did,Made,Had,Said:Capturing Quasi-Regularity in Exceptions
Did Made Had Said Quasi-Regularity
2015/6/19
The English past tense is a quasi-regular system, in that many of the irregular verbs share characteristics with regular items. Among high-frequency exceptions, in particular, several have the regular...
Low regularity solutions to a gently stochastic nonlinear wave equation in nonequilibrium statistical mechanics
System stochastic partial differential equations the nonlinear medium heat transfer and energy
2014/12/29
We consider a system of stochastic partial differential equations modeling heat conduction in a non-linear medium. We show global existence of solutions for the system in Sobolev spaces of low regular...
Regularity of Holder continuous solutions of the supercritical quasi-geostrophic equation
the 2D quasi-geostrophic equation supercritical dissipation regularity weak solutions
2014/4/4
We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical (α < 1/2) dissipation (−∆)α: If a Leray-Hopf weak solution is H¨older continuous θ...
NOTE ON GLOBAL REGULARITY FOR 2D OLDROYD-B FLUIDS WITH DIFFUSIVE STRESS
Oldroyd-B, complex uids Fokker-Planck equations blow up global existence Euler equations Navier-Stokes equations kinetic equations
2014/4/3
We prove global regularity of solutions of Oldroyd-B equations in 2 spatial dimensions with spatial di usion of the polymeric stresses.
GLOBAL REGULARITY FOR A MODIFIED CRITICAL DISSIPATIVE QUASI-GEOSTROPHIC EQUATION
GLOBAL REGULARITY A MODIFIED CRITICAL DISSIPATIVE QUASI-GEOSTROPHIC EQUATION
2014/4/3
with κ > 0, α ∈ (0,1] and θ0 ∈ L2(R2). We remark that the extra Λα−1 is introduced in order to make the scaling invariance of this system similar to the scaling invariance of the critical quasi-...
Regularity Properties of High-dimensional Covariate Matrices
high-dimensional regression instrumental variables sparse estimation compressed sensing random matrix re-stricted eigenvalue compatibility,ℓ q sensitivity computational complex-ity NP-hardness
2013/6/14
Regularity properties such as the incoherence condition, the restricted isometry property, compatibility, restricted eigenvalue and $\ell_q$ sensitivity of covariate matrices play a pivotal role in hi...
Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations
Campanato space degenerate-elliptic di erential operator degenerate di usion process Heston stochastic volatility process Holder regularity mathematical nance Schauder a priori estimate Sobolev regularity variational equation weighted Sobolev space.
2012/9/17
We establish higher-order weighted Sobolev and Holder regularity for solutions to variational equations de ned by the elliptic Heston operator, a linear second-order degenerate-elliptic operator aris...
Singular parabolic p-Laplacian systems under non-smooth external forces. Regularity up to the boundary
Initial-boundary value problems p-Laplacian parabolic singular systems regularity up to the boundary
2012/6/30
We study the regularity of the solutions to initial-boundary value problems for N-systems of the p-Laplacian type, in $n\geq 3$ space variables, with square-integrable external forces in the space-tim...