### NP-Completeness of deciding the feasibility of Linear Equations over binary- variables with coefficients and constants that are 0, 1, or -1

2 comments Posted by Dagwood EngelbergChermakani, Deepak Ponvel

*Abstract*

Pertaining to: Computation, Computational Complexity, Mathematics, NP

### Investigations of Quantum Cellular Automata in a Two Dimensional Lattice

0 comments Posted by Dagwood EngelbergYiyang Gong

Abstract

Quantum Cellular Automata (QCA) is a feasible method of manipulating a system of qubits carrying quantum information, as the same operations are applied to the entire system. With the proper initial conditions and boundaries for a two dimensional lattice, the state of one qubit can be transported to another qubit on the lattice using QCA. Such a phenomenon represents the possibility of a communication channel between different positions on the lattice. Simulations of the two-dimensional lattice using the stabilizer formalism with proper initial and boundary conditions are demonstrated. Furthermore, various errors on the gates of the system are simulated, and error probabilities on the ﬁnal results are reported. Finally, encoding schemes using qubit arrays are also investigated.

Pertaining to: Boundary Conditions, Computation, Initial Conditions, Systems

Pertaining to: Artificial Intelligence, Computation, Systems

Böckenhauer, Jens

Abstract

Based on the treatment of the chiral Ising model by Mack and Schomerus, we present examples of localized endomorphisms. It is shown that they lead to the same superselection sectors as the global ones in the sense that unitary equivalence holds. Araki's formalism of the selfdual CAR algebra is used for the proof. We prove local normality and extend representations and localized endomorphisms to a global algebra of observables which is generated by local von Neumann algebras on the punctured circle. In this framework, we manifestly prove fusion rules and derive statistics operators.

Pertaining to: Non-Euclidean Geometry, State Transitions

### On Stability of Switched Linear Hyperbolic Conservation Laws with Reflecting Boundaries

0 comments Posted by Dagwood EngelbergAmin, Saurabh; Hante, Falk M.; and Bayen, Alexandre M.

Abstract

We consider stability of an infinite dimensional switching system, posed as a system of linear hyperbolic partial differential equations (PDEs) with reflecting boundaries, where the system parameters and the boundary conditions switch in time. Asymptotic stability of the solution for arbitrary switching is proved under commutativity of the advective velocity matrices and a joint spectral radius condition involving the boundary data.

Pertaining to: Boundary Conditions, Dimensions, PDE, Systems

Pozhela, Yu K; Starikov, E V; and Shiktorov, P N.

Abstract

The frequency dependence of the longitudinal differential mobility of hot electrons is calculated using velocity averaging over the before- and after- scattering ensembles by the single-particle Monte Carlo simulation of the steady state. A dynamic negative differential mobility (NOM), due to the transit-time resonance of hot electrons in the momentum space under the predominant role of spontaneous emission of optical phonons at low lattice temperature, is observed in n-lnP. The frequency- and field-behaviour of the NOM and the noise characteristics, as well as the possibilities to use the effect for amplification and generation of the millimetre-wave radiation, are investigated. The techniques for the experimental investigation of the transit-time resonance are discussed. The noise temperature measurements are shown to be the most suitable tool for this. The transit-time resonance characteristics in n-lnP are compared with the experimentally realized and theoretically calculated parameters of the cyclotron resonance NEMAG in p-Ge. The conditions for the generation and amdification are found to be better in the former case than in the latter one.

### Mutual Decentralized Synchronization for Intervehicle Communications

0 comments Posted by Dagwood EngelbergSourour, Essam and Nakagawa, Masao

Abstract

Data exchange among vehicles can improve road safety and capacity. Most of the proposed intervehicle data communication systems require intervehicle synchronization. Synchronization must be done in a decentralized manner. In this paper, we propose a new mutual decentralized synchronization system. Using a devoted carrier frequency, each vehicle transmits a continuous periodic train of pulses. The aim of the synchronization system is to make these periodic pulses synchronous to indicate the start of data slots in slotted ALOHA types of media access protocol. Each vehicle measures the power of pulses of other vehicles as well as the time difference between other pulses and its own pulse. Using this information, each vehicle shifts its own pulse transmission time toward a weighted average of other pulse transmission times. Eventually, all periodic pulse trains are synchronized. The system performance is evaluated in nonfading and fading channels.

Pertaining to: Synchronization, Vehicles