In(ρ) = 1 N log det (ΣnΣ ∗ n + ρIN ) , (ρ > 0) where Σn = n−1/2D 1/2 n XnD̃ 1/2 n + An, as the dimensions of the matrices go to infinity at the same pace. Matrices Xn and An are respectively random and deterministic N ×n matrices; matrices Dn and D̃n are deterministic and diagonal, with respective dimensions N×N and n×n; matrixXn = (Xij) has centered, independent and identically distributed entri...

Gukov, Martinec, Moore and Strominger found that the D1-D5-D5′ system with the D5-D5′ angle at 45 degrees admits a deformation ρ preserving supersymmetry. Under this deformation, the D5-branes and D5’-branes reconnect along a single special Lagrangian manifold. We construct the near-horizon limit of this brane setup (for which no supergravity solution is currently known), imposing the requisite...

We present a new locality sensitive hashing (LSH) algorithm for c-approximate nearest neighbor search in lp with 1 < p < 2. For a database of n points in lp, we achieve O(dn ) query time and O(dn + n) space, where ρ ≤ O((ln c)/c). This improves upon the previous best upper bound ρ ≤ 1/c by Datar et al. (SOCG 2004), and is close to the lower bound ρ ≥ 1/c by O’Donnell, Wu and Zhou (ITCS 2011). T...

Algebraic Manipulation Detection (AMD) Codes detect adversarial noise that is added to a coded message which is stored in a storage that is opaque to the adversary. We study AMD codes when the storage can leak up to ρ log |G| bits of information about the stored codeword, where G is the group that contains the codeword and ρ is a constant. We propose ρ-AMD codes that provide protection in this ...

We propose a new first-order augmented Lagrangian algorithm ALCC for solving convex conic programs of the form min { ρ(x) + γ(x) : Ax− b ∈ K, x ∈ χ } , where ρ : Rn → R ∪ {+∞}, γ : Rn → R are closed, convex functions, and γ has a Lipschitz continuous gradient, A ∈ Rm×n, K ⊂ Rm is a closed convex cone, and χ ⊂ dom(ρ) is a “simple” convex compact set such that optimization problems of the form mi...

An instance of a constraint satisfaction problem (CSP) is variable k-consistent if any subinstance with at most k variables has a solution. For a fixed constraint language L, ρk(L) is the largest ratio such that any variable k-consistent instance has a solution that satisfies at least a fraction of ρk(L) of the constraints. We provide an expression for the limit ρ(L) := limk→∞ ρk(L), and show t...

Based on reasonable assumptions and mathematical approximations a one dimensional, analytical model for solar quiescent prominences is constructed, which is in both magnetohydrostatic and thermal equilibrium. Thermal equilibrium here is a balance among thermal conduction, radiation and wave heating. The wave heating (H) is assumed to be equal to a constant (EH ) times the product of pressure (p...

in the δ2 metric with constant probability for at least some graphons. In particular, our bound rules out any nontrivial estimation (that is, with δ2 error substantially less than ρ) when k ≥ n√ρ. Combined with previous upper and lower bounds, our results characterize, up to logarithmic terms, the accuracy of graphon estimation in the δ2 metric. A similar lower bound to ours was obtained indepe...

We consider the coulomb gas model on the upper half plane with different boundary conditions, namely Drichlet, Neuman and mixed. We related this model to SLE(κ, ρ) theories. We derive a set of conditions connecting the total charge of the coulomb gas, the boundary charges, the parameters κ and ρ. Also we study a free fermion theory in presence of a boundary and show with the same methods that i...