Clustering with shallow trees

We propose a new method for hierarchical clustering based on the optimisation of a cost function over trees of limited depth, and we derive a message--passing method that allows to solve it efficiently. The method and algorithm can be interpreted as a natural interpolation between two well-known approaches, namely single linkage and the recently presented Affinity Propagation. We analyze with this general scheme three biological/medical structured datasets (human population based on genetic information, proteins based on sequences and verbal autopsies) and show that the interpolation technique provides new insight.Comment: 11 pages, 7 figure

Topology-Induced Inverse Phase Transitions

Inverse phase transitions are striking phenomena in which an apparently more ordered state disorders under cooling. This behavior can naturally emerge in tricritical systems on heterogeneous networks and it is strongly enhanced by the presence of disassortative degree correlations. We show it both analytically and numerically, providing also a microscopic interpretation of inverse transitions in terms of freezing of sparse subgraphs and coupling renormalization.Comment: 4 pages, 4 figure

A comprehensive framework for training stable and passive multivariate behavioral models

We present a theoretical framework and related algorithms for the construction of behavioral models of linear or linearized devices. Unlike competing approaches, the proposed method is robust and guarantees theoretically the uniform stability and passivity of the models in a multivariate setting, where the model behavior depends not only on time or frequency but also on a number of design/stochastic parameters. Various examples demonstrate the high accuracy and reliability of proposed framework

Data-driven extraction of uniformly stable and passive parameterized macromodels

A Robust algorithm for the extraction of reduced-order behavioral models from sampled frequency responses is proposed. The system under investigation can be any Linear and Time Invariant structure, although the main emphasis is on devices that are relevant for Signal and Power Integrity and RF design, such as electrical interconnects and integrated passive components. We assume that the device under modeling is parameterized by one or more design variables, which can be related to geometry or materials. Therefore, we seek for multivariate macromodels that reproduce the dynamic behavior over a predefined frequency band, with an explicit embedded dependence of the model equations on these external parameters. Such parameterized macromodels may be used to construct component libraries and prove very useful in fast system-level numerical simulations in time or frequency domain, including optimization, what-if, and sensitivity analysis. The main novel contribution is the formulation of a finite set of convex constraints that are applied during model identification, which provide sufficient conditions for uniform model stability and passivity throughout the parameter space. Such constraints are characterized by an explicit control allowing for a trade-off between model accuracy and runtime, thanks to some special properties of Bernstein polynomials. In summary, we solve the longstanding problem of multivariate stability and passivity enforcement in data-driven model order reduction, which insofar has been tackled only via either overconservative or heuristic and possibly unreliable methods

Multivariate macromodeling with stability and passivity constraints

We present a general framework for the construction of guaranteed stable and passive multivariate macromodels from sampled frequency responses. The obtained macromodels embed in closed form the dependence on external parameters, through a data-driven approximation of input data samples based on orthogonal polynomial bases. The key novel contribution of this work is an extension to the multivariate and possibly high-dimensional case of Hamiltonian-based passivity check and enforcement algorithms, which can be applied to enforce both uniform stability and uniform passivity of the models. The modeling flow is demonstrated on a representative interconnect example

On stabilization of parameterized macromodeling

We propose an algorithm for the identification of guaranteed stable parameterized macromodels from sampled frequency responses. The proposed scheme is based on the standard Sanathanan-Koerner iteration in its parameterized form, which is regularized by adding a set of inequality constraints for enforcing the positiveness of the model denominator at suitable discrete points. We show that an ad hoc aggregation of such constraints is able to stabilize the iterative scheme by significantly improving its convergence properties, while guaranteeing uniformly stable model poles as the parameter(s) change within their design range

Phase transitions for the cavity approach to the clique problem on random graphs

We give a rigorous proof of two phase transitions for a disordered system designed to find large cliques inside Erdos random graphs. Such a system is associated with a conservative probabilistic cellular automaton inspired by the cavity method originally introduced in spin glass theory.Comment: 36 pages, 4 figure

Enabling fast power integrity transient analysis through parameterized small-signal macromodels

In this paper, we present an automated strategy for extracting behavioral small-signal macromodels of biased nonlinear circuit blocks. We discuss in detail the case study of a Low DropOut (LDO) voltage regulator, which is an essential part of the power distribution network in electronic systems. We derive a compact yet accurate surrogate model of the LDO, which enables fast transient power integrity simulations, including all parasitics due to the specific layout of the LDO realization. The model is parameterized through its DC input voltage and its output current and is thus available as a SPICE netlist. Numerical experiments show that a speedup up to 700X is achieved when replacing the extracted post-layout netlist with the surrogate model, with practically no loss in accuracy

Efficient EM-based variability analysis of passive microwave structures through parameterized reduced-order behavioral models

In this contribution we demonstrate how reduced-order behavioral models allow for extremely accurate and computationally efficient electromagnetic-based variability analysis of microwave passive structures. In particular, we report the MonteCarlo analysis of a wideband matching network at Ka-band, designed with a commercial foundry GaN-HEMT process PDK. As sources of variation we considered the thickness of the two dielectric layers available in the PDK to implement MIM capacitors of different order of magnitude, both exploited in the network. Based on a limited set of electromagnetic simulations, a parameterized behavioral model is extracted and then translated into a parameterized circuit equivalent (SPICE netlist) straightforward to be imported into RF CAD tools. The adopted model, implementing a rational approximation of the simulated S-parameters with rational dependence on the two parameters, provides excellent agreement with electromagnetic simulations, robustness against port impedance change and good extrapolation capabilities

Structured black-box parameterized macromodels of integrated passive components

A novel black-box model representation and identification process is introduced, specifically designed to extract layout-scalable behavioral macromodels of passive integrated devices from sampled frequency-domain responses. An automated choice of structured frequency-domain basis functions enables extremely accurate approximations for responses characterized by high dynamic ranges over extended frequency bands, overcoming the main limitations of standard approaches. Numerical results confirm that the proposed structured approach provides robust and reliable scalable models, with guaranteed stability and passivity over the frequency band and parameter space of interest