The quantum logic gates used in the design of a computer should be both universal, meaning arbitrary computations can performed, and fault-tolerant, keep errors from cascading out control. A number no-go theorems constrain ways which set fault-tolerant universal. These are very restrictive, conventional wisdom holds that universal gate cannot implemented natively, requiring us to use costly dis...

A theorem of Mina evaluates the determinant of a matrix with entries D(f(x)). We note the important special case where the matrix entries are evaluated at x = 0 and give a simple proof of it, as well as some special additivity properties that hold in this case, but not in general. Some applications are given also. We then give a short proof of the general case. October 25, 1998 An old theorem o...

This thesis has two flavors: 1. A universal theory of universal multi-user communication with fidelity criteria: We prove the optimality of digital communication for universal multi-user communication with fidelity criteria, both in the point-to-point setting and in the multi-user setting. In other words, we prove a universal source-channel separation theorem for rate-distortion, both in the po...

We revisit the status of asymptotic symmetries in higher even dimensions and propose a definition superrotation charge beyond linearized gravity. prove that there is well-defined spacetime action on space asymptotically flat geometries. Additionally, we demonstrate Ward identity associated with charges follows from subleading soft graviton theorem, which universal constraint (in $d>4$) along...

We prove that the variety of nuclear implicative semilattices is locally finite, thus generalizing Diego’s Theorem. The key ingredients our proof include coloring technique and construction universal models from modal logic. For this we develop duality theory for finite semilattices, Köhler duality. main result remains true bounded give an alternative Theorem, provide explicit description free ...

In this paper, a robust bounded control law for a class of uncertain nonlinear systems is proposed. The proposed bounded controller guarantees asymptotic stability, asymptotic tracking and asymptotic disturbance rejection of systems in strict feedback form with the sum of unmatched uncertainties and the unbounded exogenous disturbance. A feedback law emerged from Artstein's Theorem and Sontag's...

Economists have heralded the formulation of the expected utility theorem as a universal method of choice under uncertainty. In their seminal paper, Stigler and Becker (Stigler & Becker, 1977) declared that “human behavior can be explained by a generalized calculus of utility-maximizing behavior” (p.76). The universality of the rational choice theory has been widely criticized by psychologists, ...

From a suitable large cardinal hypothesis, we provide a model with a supercompact cardinal in which universal indestructibility holds: every supercompact and partially supercompact cardinal κ is fully indestructible by <κ-directed closed forcing. Such a state of affairs is impossible with two supercompact cardinals or even with a cardinal which is supercompact beyond a measurable cardinal. Lave...

Let X be a compact metric space and let α be a homeomorphism on X. Related to a theorem of Pimsner, we show that C(X) ⋊α Z can be embedded into a unital simple AF-algebra if and only if there is a strictly positive α-invariant Borel probability measure. Suppose that Λ is a Z action on X. If C(X)⋊Λ Z can be embedded into a unital simple AF-algebra, then there must exist a strictly positive Λ-inv...