We )nd that adding certain amounts of inhibitory inputs to a neuron improves its capability of accurately decoding the input information. The optimal ratio r of inhibitory to excitatory inputs for decoding the input information from an observation of the e,erent interspike intervals is calculated. Surprisingly, the Fisher information could be zero for certain values of the ratio, seemingly impl...

We prove the following result: Theorem. Every algebraic distributive lattice D with at most א1 compact elements is isomorphic to the ideal lattice of a von Neumann regular ring R. (By earlier results of the author, the א1 bound is optimal.) Therefore, D is also isomorphic to the congruence lattice of a sectionally complemented modular lattice L, namely, the principal right ideal lattice of R. F...

We construct an Identity-Based Key Encapsulation Mechanism (IBKEM) in a generic “leveled” multilinear map setting and prove its security under multilinear decisional Diffie-Hellmanin assumption in the selective-ID model. Then, we make our IB-KEM translated to the GGH framework, which defined an “approximate” version of a multilinear group family from ideal lattices, and modify our proof of secu...

We study well-rounded lattices which come from ideals in quadratic number fields, generalizing some recent results of the first author with K. Petersen [8]. In particular, we give a characterization of ideal well-rounded lattices in the plane and show that a positive proportion of real and imaginary quadratic number fields contains ideals giving rise to well-rounded lattices.

The aim of this study is to provide a generalization prime vague Γ-ideals in Γ-rings by introducing non-symmetric 2-absorbing weakly complete commutative Γ-rings. A novel algebraic structure primary Γ-ideal Γ-ring presented ideal theory. approach K-vague are examined and the relation between level subset given. image inverse studied 1-1 inclusion-preserving correspondence theorem quotient R ind...

A C *-algebra A is called an ideal C * -algebra (or equally a dual algebra) if it is an ideal in its bidual A**. M.C.F. Berglund proved that subalgebras and quotients of ideal C*-algebras are also ideal C*-algebras, that a commutative C *-algebra A is an ideal C *-algebra if and only if it is isomorphicto C (Q) for some discrete space ?. We investigate ideal J*-algebras and show that the a...

Residuation is a fundamental concept of ordered structures and categories. In this survey we consider the consequences of adding a residuated monoid operation to lattices. The resulting residuated lattices have been studied in several branches of mathematics, including the areas of lattice-ordered groups, ideal lattices of rings, linear logic and multi-valued logic. Our exposition aims to cover...

In the last few years, cryptographic multilinear maps have proved their tremendous potential as building blocks for new constructions, in particular the first viable approach to general program obfuscation. After the first candidate construction by Garg, Gentry and Halevi (GGH) based on ideal lattices, a second construction over the integers was described by Coron, Lepoint and Tibouchi (CLT). H...