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Several results in the area of complex dynamics of arrays of nonlinear dynamical systems have been obtained, including sufficient conditions for synchronization, estimates of dimensional characteristics of 2D patterns, effects of sidewall forcing on Turning patterns and bifurcation scenarios of nonautonomous chaotic circuits. A CNN universal machine cell was designed in VLSI technology. Several image enhancement, filtering and compression CNN algorithms were developed. Several mathematical problems and models were implemented on the CNN architecture, including the Navier-Stokes equations, mathematical morphological operators, cellular automata, models of population dynamics, models of pattern formation and models of optical illusions.

Cellular Nonlinear Networks (CNNs) are large arrays of nonlinear circuits coupled to their immediate neighbors. During the past three years, while partially funded by this grant, graduate student Kenneth R. Crounse, working with the principle investigator and their associates, have made many advances in understanding the dynamics of such arrays, especially their spatial pattern forming properties and the generation of spatial disorder. Pattern formation in CNNs was found to be amenable to analysis by the Turing instability and synergetics paradigms. Both of these methods are widely used to explain phenomena in physics and biology, some of which have been demonstrated on the CNN (e.g., angelfish stripes). In addition, interpreting the CNN behavior in terms of the synergetics paradigm was shown to be useful for the design of some CNN image processing templates (e.g., fingerprint enhancement). We have also developed a general method for the implementation of general Cellular Automata on the CNN Universal Machine. Cellular automata can be used as models for many complex physical systems. In particular, we have investigated methods for producing disorder through reversible gas-like automata. Some applications being explored are random number generation and cryptography

Talk by David Freedman, Professor, Department of Neurobiology, The University of Chicago.  Given at the ICBS Colloquium: Friday, Nov. 8, 2019 at UC Berkeley. Abstract Humans and other advanced animals have a remarkable ability to interpret incoming sensory stimuli and plan task-appropriate behavioral responses. This talk will present parallel experimental and computational approaches aimed at understanding how visual feature encoding in upstream sensory cortical areas is transformed across the cortical hierarchy into more flexible task-related encoding in the parietal and prefrontal cortices. The experimental studies utilize multielectrode recording approaches to monitor activity of neuronal populations, as well as reversible cortical inactivation approaches, during performance of visual decision making tasks. In parallel, our computational work employs machine learning approaches to train recurrent artificial neural networks to perform the same tasks as in the experimental studies, allowing a deep investigation of putative neural circuit mechanisms used by both artificial and biological networks to solve cognitively demanding behavioral tasks.

Bell System Technical Journal, 58: 3. March 1979 pp 729-769. Equivalent Circuits for the Analysis and Synthesis of Switched Capacitor Networks. (Laker, K.R.)

Bell System Technical Journal, 58: 3. March 1979 pp 729-769. Equivalent Circuits for the Analysis and Synthesis of Switched Capacitor Networks. (Laker, K.R.)

Bell System Technical Journal, 58: 3. March 1979 pp 729-769. Equivalent Circuits for the Analysis and Synthesis of Switched Capacitor Networks. (Laker, K.R.)

Cellular Nonlinear Networks (CNNs) are large arrays of nonlinear circuits coupled to their immediate neighbors. During this funding period we have made many advances in understanding the pattern-forming dynamics of such circuits and their relationship to problems in physics and biology, we have explicated the image processing capabilities of such CNNs, including spatial filtering and multiscale analysis, and finally we have obtained rigorous mathematical results concerning the dynamic behavior of simple CNN arrays. Large arrays of compete cells have elsewhere been shown to demonstrate interesting pattern forming behaviors such as the reaction-diffusion systems of Turing, the propagation of autowaves, and the Ising spin system. We have shown that the simple first-order CNN is capable of exhibiting the essential features found in these systems. And, due to the continuous-time nonlinear dynamics and general neighborhood weights the patterns formed by the CNN proved to he a study in their own right. The linear spatial convolution operation is essential in all manner of nonlinear and linear image processing algorithms. Under this funding, we demonstrated an approach by which any arbitrary FIR filter could be implemented in a robust and straightforward manner via a CNN Universal Machine (CNNUM) algorithm - by using only a standard 3 x 3 B-template. In addition, a general canonical form was proposed for such CNN linear convolutions, which also takes into account the use of an A-template and previous approaches to convolution. Finally, we initiated an investigation into a rigorous analysis of the CNN dynamics as a function of the template parameters. The first theorems have been obtained for the two-cell CNN case. We expect generalizations of such results to verify the proper behavior of many CNN image processing templates.

Solution-processed thin-films of semiconducting carbon nanotubes as the channel material for flexible electronics simultaneously offers high performance, low cost and ambient stability, which significantly outruns the organic semiconductor materials. In this work, we report the use of semiconductor-enriched carbon nanotubes for high-performance integrated circuits on mechanically flexible substrates for digital, analog and radio frequency applications. The as-obtained thin-film transistors (TFTs) exhibit highly uniform device performance with on-current and transconductance up to 15 microA/micron and 4 mircoS/micron. By performing capacitance-voltage measurements, the gate capacitance of the nanotube TFT is precisely extracted and the corresponding peak effective device mobility is evaluated to be around 50 sq cm/V/s. Using such devices, digital logic gates including inverters, NAND, and NOR gates with superior bending stability have been demonstrated. Moreover radio frequency measurements show that cutoff frequency of 170 MHz can be achieved in devices with a relatively long channel length of 4 microns, which is sufficient for certain wireless communication applications. This proof-of-concept demonstration indicates that our platform can serve as a foundation for scalable, low-cost, high-performance flexible electronics.

To each Boolean function F from {0,1}^n to itself and each point x in {0,1}^n, we associate the signed directed graph G_F(x) of order n that contains a positive (resp. negative) arc from j to i if the partial derivative of f_i with respect of x_j is positive (resp. negative) at point x. We then focus on the following open problem: Is the absence of a negative circuit in G_F(x) for all x in {0,1}^n a sufficient condition for F to have at least one fixed point? As main result, we settle this problem under the additional condition that, for all x in {0,1}^n, the out-degree of each vertex of G_F(x) is at most one.

The growth in number and nature of dynamical attractors in Kauffman NK network models are still not well understood properties of these important random boolean networks. Structural circuits in the underpinning graph give insights into the number and length distribution of attractors in the NK model. We use a fast direct circuit enumeration algorithm to study the NK model and determine the growth behaviour of structural circuits. This leads to an explanation and lower bound on the growth properties and the number of attractor loops and a possible K-relationship for circuit number growth with network size N. We also introduce a mixed-K model that allows us to explore between pairs of integer K values in Kauffman-like systems. We find that the circuits' behaviour is a useful metric in identifying phase transitional behaviour around the critical connectivity in that model too. We identify an intermediate phase transition in circuit growth behaviour at K_S approximately 1.5, that is distinct from both the percolation transition at K_P = 1 and the Kauffman transition at K_C = 2. We relate this transition to mutual node reachability within the giant component of nodes.

The Kitaev honeycomb model is a paradigm of exactly-solvable models, showing non-trivial physical properties such as topological quantum order, abelian and non-abelian anyons, and chirality. Its solution is one of the most beautiful examples of the interplay of different mathematical techniques in condensed matter physics. In this paper, we show how to derive a tensor network (TN) description of the eigenstates of this spin-1/2 model in the thermodynamic limit, and in particular for its ground state. In our setting, eigenstates are naturally encoded by an exact 3d TN structure made of fermionic unitary operators, corresponding to the unitary quantum circuit building up the many-body quantum state. In our derivation we review how the different "solution ingredients" of the Kitaev honeycomb model can be accounted for in the TN language, namely: Jordan-Wigner transformation, braidings of Majorana modes, fermionic Fourier transformation, and Bogoliubov transformation. The TN built in this way allows for a clear understanding of several properties of the model. In particular, we show how the fidelity diagram is straightforward both at zero temperature and at finite temperature in the vortex-free sector. We also show how the properties of two-point correlation functions follow easily. Finally, we also discuss the pros and cons of contracting of our 3d TN down to a 2d Projected Entangled Pair State (PEPS) with finite bond dimension. The results in this paper can be extended to generalizations of the Kitaev model, e.g., to other lattices, spins, and dimensions.

All higher order central nervous systems exhibit spontaneous neural activity, though the purpose and mechanistic origin of such activity remains poorly understood. We explore the ignition and spread of collective spontaneous electrophysiological burst activity in networks of cultured cortical neurons growing on microelectrode arrays using information theory and first-spike-in-burst analysis methods. We show the presence of burst leader neurons, which form a mono-synaptically connected primary circuit, and initiate a majority of network bursts. Leader/follower firing delay times form temporally stable positively skewed distributions. Blocking inhibitory synapses usually results in shorter delay times with reduced variance. These distributions are generalized characterizations of internal network dynamics and provide estimates of pair-wise synaptic distances. We show that mutual information between neural nodes is a function of distance, which is maintained under disinhibition. The resulting analysis produces specific quantitative constraints and insights into the activation patterns of collective neuronal activity in self-organized cortical networks, which may prove useful for models emulating spontaneously active systems.

All higher order central nervous systems exhibit spontaneous neural activity, though the purpose and mechanistic origin of such activity remains poorly understood. We explore the ignition and spread of collective spontaneous electrophysiological burst activity in networks of cultured cortical neurons growing on microelectrode arrays using information theory and first-spike-in-burst analysis methods. We show the presence of burst leader neurons, which form a mono-synaptically connected primary circuit, and initiate a majority of network bursts. Leader/follower firing delay times form temporally stable positively skewed distributions. Blocking inhibitory synapses usually results in shorter delay times with reduced variance. These distributions are generalized characterizations of internal network dynamics and provide estimates of pair-wise synaptic distances. We show that mutual information between neural nodes is a function of distance, which is maintained under disinhibition. The resulting analysis produces specific quantitative constraints and insights into the activation patterns of collective neuronal activity in self-organized cortical networks, which may prove useful for models emulating spontaneously active systems.

Advances in research have been made in the following areas: (1) The detailed test and characterization of the first ever ARAM in the CNN Chip Set Architecture; (2) The constructive use of the local activity principle in designing Cellular Nonlinear Networks with complex behavior; (3) Analogic CNN subroutine design for various practical applications, including coding, and optical flow estimation; and (4) Advances in testing qualitative properties of CNN, including stability test of non-symmetric feedback CNN.

An electronic network /circuit consists of components like resistors, diodes, capacitors, transistors and ICs, arranged such that the network contains maximum number of components using minimum space. When translated into geometry, this results in an arrangement of lines and points called CONFIGURATION. Thus, the geometrical configuration finds its natural application to circuit theory through network topology[1][network topology is the geometrical relationship between the electrical components that are to be equipped in the network]. Moreover configurations may be used to represent electrical components equipped in the network. For instance, an n 1 configuration, is a resistor (or capacitor, inductor, diode or a battery (source) ) when n = 2, a transistor when n = 3 and an IC when n > 3. In this paper, we demonstrate as to how a certain configuration results in a working model called “Boot strapped emitter follower as Colpitt’s oscillator”. In this paper, we also recall the definitions of “perspective from a point (PFP) and perspective from a line(PFL)” and define these concepts in terms of physical facts “Projection, reflection and refraction” and translate these to circuits. In this paper, we also demonstrate as to how perspective from a point results in a series circuit and perspective from a line results in a parallel circuit. 

An electronic network /circuit consists of components like resistors, diodes, capacitors, transistors and ICs, arranged such that the network contains maximum number of components using minimum space. When translated into geometry, this results in an arrangement of lines and points called CONFIGURATION. Thus, the geometrical configuration finds its natural application to circuit theory through network topology[1][network topology is the geometrical relationship between the electrical components that are to be equipped in the network]. Moreover configurations may be used to represent electrical components equipped in the network. For instance, an n 1 configuration, is a resistor (or capacitor, inductor, diode or a battery (source) ) when n = 2, a transistor when n = 3 and an IC when n > 3. In this paper, we demonstrate as to how a certain configuration results in a working model called “Boot strapped emitter follower as Colpitt’s oscillator”. In this paper, we also recall the definitions of “perspective from a point (PFP) and perspective from a line(PFL)” and define these concepts in terms of physical facts “Projection, reflection and refraction” and translate these to circuits. In this paper, we also demonstrate as to how perspective from a point results in a series circuit and perspective from a line results in a parallel circuit. 

The algorithm for quadratic global optimization performed by a cellular neural network (CNN) with a slowly varying slope of the output characteristic is analyzed. It is shown that the only CNN which finds the global minimum of a quadratic function for any values of the input parameters is the network composed by only two cells. If the dimension is higher than two, even the CNN described by the simplest one-dimensional space-invariant template A=A(exp 1), A (exp 0), A (exp 1), fails to find the global minimum in a subset of the parameter space. Extensive simulations show that the CNN described by the above three-element template works correctly within several parameter ranges; however, if the parameters are chosen according to a random algorithm, the error rate increases with the number of cells.

Index

Index

During the period July 1997 - June 1998 work has continued according to the proposed plan. Advances in research have been made in the following areas: (1) The design and implementation of the first-ever ARAM in the CNN Chip Set Architecture was successfully competed, and the samples were successfully tested; (2) A major theoretical breakthrough has been achieved: it was shown that the genesis of complexity lies in the local activity of the cells and local interactions of the Cellular Nonlinear Networks; (3) Several CNN templates and subroutine designs, including mathematical morphology, have been developed and used in various applications; and (4) Advances in application of CNN have been made in the area of condition-based maintenance and image fusion.

The investigation of new memory schemes, neural networks, computer systems and many other improved electronic devices is very important for future generations of electronic circuits and for their widespread application in all the areas of industry. Relatedly, the analysis of new efficient and advanced electronic elements and circuits is an essential field of highly developed electrical and electronic engineering. The resistance-switching phenomenon, observed in many amorphous oxides, has been investigated since 1970 and is promising for inclusion in technologies for constructing new electronic memories. It has been established that such oxide materials have the ability to change their conductance in accordance to the applied voltage and memorizing their state for a long time interval. Similar behavior was predicted for the memristor element by Leon Chua in 1971. The memristor was proposed in accordance with symmetry considerations and the relationships between the four basic electric quantities—electric current i, voltage v, charge q and flux linkage Ψ. The memristor is a passive one-port element, together with the capacitor, inductor and resistor. The Williams Hewlett Packard (HP) research group has made a link between resistive switching devices and the memristor proposed by Chua. In addition, a number of scientific papers related to memristors and memristor devices have been issued and several models for them have been proposed. The memristor is a highly nonlinear component. It relates the electric charge q and the flux linkage Ψ, expressed as a time integral of the voltage v. It has the important capability of remembering the electric charge passing through its cross-section, and its respective resistance, when the electrical signals are switched off. Due to its nano-scale dimensions, non-volatility and memorizing properties, the memristor is a sound potential candidate for applications in high-density computer memories, artificial neural networks, and many other electronic devices.

The investigation of new memory schemes, neural networks, computer systems and many other improved electronic devices is very important for future generations of electronic circuits and for their widespread application in all the areas of industry. Relatedly, the analysis of new efficient and advanced electronic elements and circuits is an essential field of highly developed electrical and electronic engineering. The resistance-switching phenomenon, observed in many amorphous oxides, has been investigated since 1970 and is promising for inclusion in technologies for constructing new electronic memories. It has been established that such oxide materials have the ability to change their conductance in accordance to the applied voltage and memorizing their state for a long time interval. Similar behavior was predicted for the memristor element by Leon Chua in 1971. The memristor was proposed in accordance with symmetry considerations and the relationships between the four basic electric quantities—electric current i, voltage v, charge q and flux linkage Ψ. The memristor is a passive one-port element, together with the capacitor, inductor and resistor. The Williams Hewlett Packard (HP) research group has made a link between resistive switching devices and the memristor proposed by Chua. In addition, a number of scientific papers related to memristors and memristor devices have been issued and several models for them have been proposed. The memristor is a highly nonlinear component. It relates the electric charge q and the flux linkage Ψ, expressed as a time integral of the voltage v. It has the important capability of remembering the electric charge passing through its cross-section, and its respective resistance, when the electrical signals are switched off. Due to its nano-scale dimensions, non-volatility and memorizing properties, the memristor is a sound potential candidate for applications in high-density computer memories, artificial neural networks, and many other electronic devices.