Kramers-Wannier Duality and Random Bond Ising Model

We present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and disordered operators defined on vertices and dual vertices respectively, thereby explicitly demonstrating the Kramers-Wannier duality. The implications of our derived formula for the random bond Ising model are further elucidated

Quantifying Long-Term Scientific Impact

The lack of predictability of citation-based measures frequently used to gauge impact, from impact factors to short-term citations, raises a fundamental question: Is there long-term predictability in citation patterns? Here, we derive a mechanistic model for the citation dynamics of individual papers, allowing us to collapse the citation histories of papers from different journals and disciplines into a single curve, indicating that all papers tend to follow the same universal temporal pattern. The observed patterns not only help us uncover basic mechanisms that govern scientific impact but also offer reliable measures of influence that may have potential policy implications

Theory of random packings

We review a recently proposed theory of random packings. We describe the volume fluctuations in jammed matter through a volume function, amenable to analytical and numerical calculations. We combine an extended statistical mechanics approach 'a la Edwards' (where the role traditionally played by the energy and temperature in thermal systems is substituted by the volume and compactivity) with a constraint on mechanical stability imposed by the isostatic condition. We show how such approaches can bring results that can be compared to experiments and allow for an exploitation of the statistical mechanics framework. The key result is the use of a relation between the local Voronoi volume of the constituent grains and the number of neighbors in contact that permits a simple combination of the two approaches to develop a theory of random packings. We predict the density of random loose packing (RLP) and random close packing (RCP) in close agreement with experiments and develop a phase diagram of jammed matter that provides a unifying view of the disordered hard sphere packing problem and further shedding light on a diverse spectrum of data, including the RLP state. Theoretical results are well reproduced by numerical simulations that confirm the essential role played by friction in determining both the RLP and RCP limits. Finally we present an extended discussion on the existence of geometrical and mechanical coordination numbers and how to measure both quantities in experiments and computer simulations.Comment: 9 pages, 5 figures. arXiv admin note: text overlap with arXiv:0808.219

Quantum Geometry of Expectation Values

We propose a novel framework for the quantum geometry of expectation values over arbitrary sets of operators and establish a link between this geometry and the eigenstates of Hamiltonian families generated by these operators. We show that the boundary of expectation value space corresponds to the ground state, which presents a natural bound that generalizes Heisenberg's uncertainty principle. To demonstrate the versatility of our framework, we present several practical applications, including providing a stronger nonlinear quantum bound that violates the Bell inequality and an explicit construction of the density functional. Our approach provides an alternative time-independent quantum formulation that transforms the linear problem in a high-dimensional Hilbert space into a nonlinear algebro-geometric problem in a low dimension, enabling us to gain new insights into quantum systems

Built-in self test of RF subsystems

textWith the rapid development of wireless and wireline communications, a variety of new standards and applications are emerging in the marketplace. In order to achieve higher levels of integration, RF circuits are frequently embedded into System on Chip (SoC) or System in Package (SiP) products. These developments, however, lead to new challenges in manufacturing test time and cost. Use of traditional RF test techniques requires expensive high frequency test instruments and long test time, which makes test one of the bottlenecks for reducing IC costs. This research is in the area of built-in self test technique for RF subsystems. In the test approach followed in this research, on-chip detectors are used to calculate circuits specifications, and data converters are used to collect the data for analysis by an on-chip processor. A novel on-chip amplitude detector has been designed and optimized for RF circuit specification test. By using on-chip detectors, both the system performance and specifications of the individual components can be accurately measured. On-chip measurement results need to be collected by Analog to Digital Converters (ADCs). A novel time domain, low power ADC has been designed for this purpose. The ADC architecture is based on a linear voltage controlled delay line. Using this structure results in a linear transfer function for the input dependent delay. The time delay difference is then compared to a reference to generate a digital code. Two prototype test chips were fabricated in commercial CMOS processes. One is for the RF transceiver front end with on-chip detectors; the other is for the test ADC. The 940MHz RF transceiver front-end was implemented with on-chip detectors in a 0.18 [micrometer] CMOS technology. The chips were mounted onto RF Printed Circuit Boards (PCBs), with tunable power supply and biasing knobs. The detector was characterized with measurements which show that the detector keeps linear performance over a wide input amplitude range of 500mV. Preliminary simulation and measurements show accurate transceiver performance prediction under process variations. A 300MS/s 6 bit ADC was designed using the novel time domain architecture in a 0.13 [micrometer] standard digital CMOS process. The simulation results show 36.6dB Signal to Noise Ratio (SNR), 34.1dB Signal to Noise and Distortion Ratio (SNDR) for 99MHz input, Differential Non-Linearity (DNL)<0.2 Least Significant Bit (LSB), and Integral Non-Linearity (INL)<0.5LSB. Overall chip power is 2.7mW with a 1.2V power supply. The built-in detector RF test was extended to a full transceiver RF front end test with a loop-back setup, so that measurements can be made to verify the benefits of the technique. The application of the approach to testing gain, linearity and noise figure was investigated. New detector types are also evaluated. In addition, the low-power delay-line based ADC was characterized and improved to facilitate gathering of data from the detector. Several improved ADC structures at the system level are also analyzed. The built-in detector based RF test technique enables the cost-efficient test for SoCs.Electrical and Computer Engineerin

Cavity method for force transmission in jammed disordered packings of hard particles

The force distribution of jammed disordered packings has always been considered a central object in the physics of granular materials. However, many of its features are poorly understood. In particular, analytic relations to other key macroscopic properties of jammed matter, such as the contact network and its coordination number, are still lacking. Here we develop a mean-field theory for this problem, based on the consideration of the contact network as a random graph where the force transmission becomes a constraint optimization problem. We can thus use the cavity method developed in the last decades within the statistical physics of spin glasses and hard computer science problems. This method allows us to compute the force distribution $\text P(f)$ for random packings of hard particles of any shape, with or without friction. We find a new signature of jamming in the small force behavior $\text P(f) \sim f^{\theta}$, whose exponent has attracted recent active interest: we find a finite value for $\text P(f=0)$, along with $\theta=0$. Furthermore, we relate the force distribution to a lower bound of the average coordination number $\, {\bar z}_{\rm c}^{\rm min}(\mu)$ of jammed packings of frictional spheres with coefficient $\mu$. This bridges the gap between the two known isostatic limits $\, {\bar z}_{\rm c}(\mu=0)=2D$ (in dimension $D$) and $\, {\bar z}_{\rm c}(\mu \to \infty)=D+1$ by extending the naive Maxwell's counting argument to frictional spheres. The theoretical framework describes different types of systems, such as non-spherical objects in arbitrary dimensions, providing a common mean-field scenario to investigate force transmission, contact networks and coordination numbers of jammed disordered packings

Modeling and Predicting Popularity Dynamics via Reinforced Poisson Processes

An ability to predict the popularity dynamics of individual items within a complex evolving system has important implications in an array of areas. Here we propose a generative probabilistic framework using a reinforced Poisson process to model explicitly the process through which individual items gain their popularity. This model distinguishes itself from existing models via its capability of modeling the arrival process of popularity and its remarkable power at predicting the popularity of individual items. It possesses the flexibility of applying Bayesian treatment to further improve the predictive power using a conjugate prior. Extensive experiments on a longitudinal citation dataset demonstrate that this model consistently outperforms existing popularity prediction methods.Comment: 8 pages, 5 figure; 3 table

From Micro to Macro: Uncovering and Predicting Information Cascading Process with Behavioral Dynamics

Cascades are ubiquitous in various network environments. How to predict these cascades is highly nontrivial in several vital applications, such as viral marketing, epidemic prevention and traffic management. Most previous works mainly focus on predicting the final cascade sizes. As cascades are typical dynamic processes, it is always interesting and important to predict the cascade size at any time, or predict the time when a cascade will reach a certain size (e.g. an threshold for outbreak). In this paper, we unify all these tasks into a fundamental problem: cascading process prediction. That is, given the early stage of a cascade, how to predict its cumulative cascade size of any later time? For such a challenging problem, how to understand the micro mechanism that drives and generates the macro phenomenons (i.e. cascading proceese) is essential. Here we introduce behavioral dynamics as the micro mechanism to describe the dynamic process of a node's neighbors get infected by a cascade after this node get infected (i.e. one-hop subcascades). Through data-driven analysis, we find out the common principles and patterns lying in behavioral dynamics and propose a novel Networked Weibull Regression model for behavioral dynamics modeling. After that we propose a novel method for predicting cascading processes by effectively aggregating behavioral dynamics, and propose a scalable solution to approximate the cascading process with a theoretical guarantee. We extensively evaluate the proposed method on a large scale social network dataset. The results demonstrate that the proposed method can significantly outperform other state-of-the-art baselines in multiple tasks including cascade size prediction, outbreak time prediction and cascading process prediction.Comment: 10 pages, 11 figure