An Ising machine having a network of resistively coupled circuit nodes where at least one node comprises a capacitor whose voltage between its terminals represents a state variable of the node and the voltage is resistively coupled to at least one other node in the network and a two-terminal active electronics element connected in parallel with the capacitor supplying energy to the node, and the element having an odd-symmetric current-voltage characteristic exhibiting a negative current gradient for voltages across its terminals that are below a predetermined threshold value in magnitude, and a positive gradient otherwise and zero current for three voltage instances: zero volts, +V.sub.1 volts, and −V.sub.1 volts, where V.sub.1 is a constant greater than the predetermined threshold.

Self-organizing logic gates formed from a combination of memristor devices and dynamic correction modules configured to provide a stable operation upon application of a signal to any terminal. A SOLG of the invention can accept signals from any terminal and does not require an absence of signals at any other terminal. Terminal signals can superpose and the gate finds equilibrium, if an equilibrium exists.

A vehicle control apparatus includes: a plurality of operation devices, a plurality of reaction applying devices, a plurality of driving devices, and control device. The control device is capable of controlling the plurality of reaction applying devices and the plurality of driving devices. When the occupant operates preceding operation devices and subsequently operates subsequent operation devices different from the preceding operation devices, the control device causes a reactive perception quantity that is perceived by the occupant when the occupant starts operating the subsequent operation devices to substantially match a reactive perception quantity that is perceived by the occupant when the occupant finishes operating the preceding operation devices.

A vehicle control apparatus includes: a plurality of operation devices, a plurality of reaction applying devices, a plurality of driving devices, and control device. The control device is capable of controlling the plurality of reaction applying devices and the plurality of driving devices. When the occupant operates preceding operation devices and subsequently operates subsequent operation devices different from the preceding operation devices, the control device causes a reactive perception quantity that is perceived by the occupant when the occupant starts operating the subsequent operation devices to substantially match a reactive perception quantity that is perceived by the occupant when the occupant finishes operating the preceding operation devices.

An example apparatus includes a crossbar array of signal lines and control lines. The example apparatus also includes an input controller in circuit with the control lines. The input control is to select one of the control lines. The example apparatus also includes first resistive elements connected between corresponding ones of the control lines and corresponding ones of the signal lines. The first resistive elements have first conductances set to operate as a matrix of probabilities that define a fixed transition kernel of a Markov Chain. The example apparatus also includes second resistive elements in circuit with the signal lines. The second resistive elements have second conductances set to select one of the signal lines exclusive of others of the signal lines based on a subset of the probabilities in the matrix of the probabilities.

An analog circuit for solving optimization algorithms comprises three voltage controlled current sources and three capacitors, operatively coupled in parallel to the three voltage controlled current sources, respectively. The circuit further comprises a first inductor, operatively coupled in series between a first pair of the capacitors and the voltage controller current sources and a second pair of the capacitors and the voltage controller current sources. The circuit further comprises a second inductor, operatively coupled in series between the second pair of the capacitors and the voltage controller current sources and a third pair of the capacitors and the voltage controller current sources.

An analog circuit for solving optimization algorithms comprises three voltage controlled current sources and three capacitors, operatively coupled in parallel to the three voltage controlled current sources, respectively. The circuit further comprises a first inductor, operatively coupled in series between a first pair of the capacitors and the voltage controller current sources and a second pair of the capacitors and the voltage controller current sources. The circuit further comprises a second inductor, operatively coupled in series between the second pair of the capacitors and the voltage controller current sources and a third pair of the capacitors and the voltage controller current sources.

An analog circuit for solving optimization algorithms comprises three voltage controlled current sources and three capacitors, operatively coupled in parallel to the three voltage controlled current sources, respectively. The circuit further comprises a first inductor, operatively coupled in series between a first pair of the capacitors and the voltage controller current sources and a second pair of the capacitors and the voltage controller current sources. The circuit further comprises a second inductor, operatively coupled in series between the second pair of the capacitors and the voltage controller current sources and a third pair of the capacitors and the voltage controller current sources.

An analog circuit for solving optimization algorithms comprises three voltage controlled current sources and three capacitors, operatively coupled in parallel to the three voltage controlled current sources, respectively. The circuit further comprises a first inductor, operatively coupled in series between a first pair of the capacitors and the voltage controller current sources and a second pair of the capacitors and the voltage controller current sources. The circuit further comprises a second inductor, operatively coupled in series between the second pair of the capacitors and the voltage controller current sources and a third pair of the capacitors and the voltage controller current sources.

A non-Boolean analog system includes a first Mott memristor having a first value of a characteristic, and a second Mott memristor having a second value of the characteristic different than the first value. The system includes a resistance in series with the first and second Mott memristors to form a network having a capacitance and that is operable as a relaxation oscillator. Responsive to electrical excitation, a temperature of the network operating an environment including ambient thermal noise settles at an equilibrium corresponding to a global minimum that is a maximally optimal global solution to a global optimization problem to which the network corresponds.