Let S(N) ≡ PG(1, 2)×PG(1, 2)×· · ·×PG(1, 2) be a Segre variety that is N -fold direct product of projective lines of size three. Given two geometric hyperplanes H ′ and H ′′ of S(N), let us call the triple {H , H , H ∆H } the Veldkamp line of S(N). We shall demonstrate, for the sequence 2 ≤ N ≤ 4, that the properties of geometric hyperplanes of S(N) are fully encoded in the properties of Veldka...

Given an o-minimal expansion M of a real closed field R which is not polynomially bounded. Let P∞ denote the definable indefinitely Peano differentiable functions. If we further assume that M admits P∞ cell decomposition, each definable closed set A ⊂ Rn is the zero-set of a P∞ function f : Rn → R. This implies P∞ approximation of definable continuous functions and gluing of P∞ functions define...

In this paper, we present a set of sequence pairs which produce zero correlation windows not only in the middle part of the sum of aperiodic correlation functions, but also in the two terminal parts. We name it “Ear Windows.” In approximately synchronous CDMA communication system, this set of sequences is able to completely remove the inter-symbol interference (ISI) and multi-user interference ...

We propose a non-interactive zero knowledge pairwise multiset sum equality test (PMSET) argument in the common reference string (CRS) model that allows a prover to show that the given committed multisets Aj for j ∈ {1, 2, 3, 4} satisfy A1 ] A2 = A3 ] A4, i.e., every element is contained in A1 and A2 exactly as many times as in A3 and A4. As a corollary to the PMSET argument, we present argument...

We introduce 0 | • (“zero hand-grenade”) as a sharp for an inner model with a proper class of strong cardinals. We prove the existence of the core model K in the theory “ZFC + 0 | • doesn’t exist.” Combined with work of Woodin, Steel, and earlier work of the author, this provides the last step for determining the exact consistency strength of the assumption in the statement of the 12th Delfino ...

Knowledge of human presence and interaction in a vehicle is of growing interest to vehicle manufacturers for design and safety purposes. We present a framework to perform the tasks of occupant detection and occupant classification for automatic child locks and airbag suppression. It operates for all passenger seats, using a single overhead camera. A transfer learning technique is introduced to ...

SUMMARY An efficient computational Zero-Knowledge Proof of Knowledge whose security relies on the NP-completeness of the Independent Set Problem is presented here. The proposed algorithm is constructed from a bit commitment scheme based on the hardness of the Discrete Logarithm Problem, which guarantees the fulfillment of soundness, completeness and computational zero-knowledge properties, and ...

The zero set of a linear recurrence is {m | xm = 0}, where xm is the m-th term. For a linear recurrence over the complex numbers C it is classical that xm = P1(m) · α1 + · · ·+ Pd(m) ·αd where P1(m), . . . , Pd(m) are polynomials in m, and α1, . . . , αd are the distinct zeros of the recurrence’s characteristic polynomial. We show that if the zero set of a linear recurrence over C is infinite, ...

Let A be a zero-sum free subset of Zn with |A| = k. We compute for k ≤ 7 the least possible size of the set of all subset-sums of A.

Let A be a zero-sum free subset of Zn with |A| = k. We compute for k ≤ 7 the least possible size of the set of all subset-sums of A.