Fixed-point Model Research Articles

Quantum current and holographic categorical symmetry

We establish the formulation for quantum current. Given a symmetry group G, let \mathcal{C}𝒞:=Rep G be its representation category. Physically, symmetry charges are objects of \mathcal{C}𝒞 and symmetric operators are morphisms in \mathcal{C}𝒞. The addition of charges is given by the tensor product of representations. For any symmetric operator O crossing two subsystems, the exact symmetry charge transported by O can be extracted. The quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. A quantum current exactly corresponds to an object in the Drinfeld center Z_1(\mathcal{C})Z1(𝒞). The condition for quantum currents to be is also specified, which corresponds to condensation of anyons in one higher dimension. To express the local conservation, the internal hom must be used to compute the charge difference, and the framework of enriched category is inevitable. To illustrate these ideas, we develop a rigorous scheme of renormalization in one-dimensional lattice systems and analyse the fixed-point models. It is proved that in the fixed-point models, superconducting quantum currents form a Lagrangian algebra in Z_1(\mathcal{C})Z1(𝒞) and the boundary-bulk correspondence is verified in the enriched setting. Overall, the quantum current provides a natural physical interpretation to the holographic categorical symmetry.

Bulk-to-boundary anyon fusion from microscopic models

Topological quantum error correction based on the manipulation of the anyonic defects constitutes one of the most promising frameworks towards realizing fault-tolerant quantum devices. Hence, it is crucial to understand how these defects interact with external defects such as boundaries or domain walls. Motivated by this line of thought, in this work, we study the fusion events between anyons in the bulk and at the boundary in fixed-point models of 2 + 1-dimensional non-chiral topological order defined by arbitrary fusion categories. Our construction uses generalized tube algebra techniques to construct a bi-representation of bulk and boundary defects. We explicitly derive a formula to calculate the fusion multiplicities of a bulk-to-boundary fusion event for twisted quantum double models and calculate some exemplary fusion events for Abelian models and the (twisted) quantum double model of S3, the simplest non-Abelian group-theoretical model. Moreover, we use the folding trick to study the anyonic behavior at non-trivial domain walls between twisted S3 and twisted Z2 as well as Z3 models. A recurring theme in our construction is an isomorphism relating twisted cohomology groups to untwisted ones. The results of this work can directly be applied to study logical operators in two-dimensional topological error correcting codes with boundaries described by a twisted gauge theory of a finite group.

Performance Analysis and Energy Efficiency of MU- (OFDMA & MIMO) Based Hybrid MAC Protocol of IEEE 802.11ax WLANs

Future wireless networks are characterized by densely populated stations (STAs) with limited battery capacity. These networks demand high aggregate throughput, increased energy efficiency, and high Random Access (RA) capability, i.e., the system's ability to allow new STAs to join the network quickly. WiFi-6 (also known as IEEE 802.11 ax) is the new generation WLAN standard proposed to meet these diverse system requirements. In this paper, we analyze the effect of Multi-User Multi-Input Multi-Output (MU-MIMO) & MU-Orthogonal Frequency Division Multiple Access (MU-OFDMA)-based Hybrid Access (HA) mechanism of WiFi-6 systems. We propose a fixed Point model for analyzing this HA mechanism. By solving the system model, we investigate the impact on critical system metrics such as throughput, energy efficiency, Random Access capability, and delay due to a variation in (i) the number of resource units (RUs), (ii) the channel sounding interval, and (iii) the Target Wake-Up time interval. We have studied the effect of the non-saturated traffic model driven by the Poisson and Pareto arrival processes. Further, we have modeled the buffer status-based dynamic scheduling of RUs for the MU-OFDMA-based HA mechanism. We have also analyzed the novel Multi-Traffic Identifier-based frame aggregation feature. Further, we have analyzed the hand-off mechanism for a multi-BSS (Basic Service Set) scenario using the Stochastic geometry-based mathematical tool. We have used Matlab-based simulations for our study and found that the simulation results closely match the analytical results. Our study sheds light on the trade-off that exists between different performance metrics of the 802.11ax HA mechanism.

Digital Implementation of Radial Basis Function Neural Networks Based on Stochastic Computing

Nowadays Internet of Things (IoT) and mobile systems use more and more Machine Learning based solutions, which implies a high computation cost with a low energy consumption. This is causing a revival of interest in unconventional hardware computing methods capable of implementing both linear and nonlinear functions with less hardware overhead than conventional fixed point and floating point alternatives. Particularly, this work proposes a novel Radial Basis Function Neural Network (RBF-NN) hardware implementation based on Stochastic Computing (SC), which applies probabilistic laws over conventional digital gates. Several complex functions design to implement RBF-NN are presented and theoretically analyzed, such as the squared Euclidean distance and the stochastic Gaussian kernel similarity function between input samples and prototypes. The efficiency and performance of the methodology is tested over well-known pattern recognition tasks, including the MNIST dataset. The results show a low-cost methodology in terms of logic resources and power, along with an inherent capability to implement complex functions in a simple way. This methodology enables the implementation of massively parallel large scale RBF-NN with relatively low hardware requirements while maintaining 96.20% accuracy, which is nearly the same for the floating point and fixed point models (96.4% and 96.25%, respectively).

Disentangling modular Walker-Wang models via fermionic invertible boundaries

Walker-Wang models are fixed-point models of topological order in $3+1$ dimensions constructed from a braided fusion category. For a modular input category $\mathcal M$, the model itself is invertible and is believed to be in a trivial topological phase, whereas its standard boundary is supposed to represent a $2+1$-dimensional chiral phase. In this work we explicitly show triviality of the model by constructing an invertible domain wall to vacuum as well as a disentangling generalized local unitary circuit in the case where $\mathcal M$ is a Drinfeld center. Moreover, we show that if we allow for fermionic (auxiliary) degrees of freedom inside the disentangling domain wall or circuit, the model becomes trivial for a larger class of modular fusion categories, namely those in the Witt classes generated by the Ising UMTC. In the appendices, we also discuss general (non-invertible) boundaries of general Walker-Wang models and describe a simple axiomatization of extended TQFT in terms of tensors.

Fully fixed-point integrated digital circuit design of discrete memristive systems

In this paper, the fully fixed-point digital integrated circuits of discrete memristive systems are designed with very low circuit area cost, where the two-stage pipeline and multi-cycle architecture is employed. Firstly, the mathematical models of the discrete memristor and a memristor chaotic map are presented and dynamics are analyzed. Secondly, data flow design is carried out and the feasibility of the fixed-point model is discussed, which provides a foundation for the further circuit design. Thirdly, different architectures are designed and we get the optimal results. As a result, gate area of the discrete memristor is 40288 μm2 and the equivalent gate counts are 4588, while gate area of the discrete memristor map is 40424 μm2 and the equivalent gate counts are 4604. Moreover, a chaotic pseudo random sequence generator is designed and the NIST test is passed. It provides the foundation for the further applications of the discrete memristor and discrete memristor chaotic systems.

Research on the Routine Mode of Educational Practice for Normal University Students

Educational practice is an important part of teacher education, and it is also an essential content of practical teaching reform for teachers’ majors in colleges and universities. In this paper, the normal practice mode of normal students is studied to provide reference for exploring more effective practice mode. First, the centralized fixed-point model. Under the unified management and arrangement of colleges and universities, normal students go to the contacted primary and secondary schools to carry out educational practice.Second, the mixed formation mode, in which normal students from different majors are organized into a team, and one or several teachers lead them to practice in primary and secondary schools.Third, the supporting education mode. The school organizes normal students to go to rural schools or weak schools to carry out educational and teaching practice activities for one semester. Fourth, the post educational practice mode. After completing professional courses and teacher education courses, normal students go to primary and secondary schools to carry out a full semester of teacher post practice training.

IVS-Caffe-Hardware-Oriented Neural Network Model Development.

This article proposes a hardware-oriented neural network development tool, called Intelligent Vision System Lab (IVS)-Caffe. IVS-Caffe can simulate the hardware behavior of convolution neural network inference calculation. It can quantize weights, input, and output features of convolutional neural network (CNN) and simulate the behavior of multipliers and accumulators calculation to achieve the bit-accurate result. Furthermore, it can test the accuracy of the chosen CNN hardware accelerator. Besides, this article proposes an algorithm to solve the deviation of gradient backpropagation in the bit-accurate quantized multipliers and accumulators. This allows the training of a bit-accurate model and further increases the accuracy of the CNN model at user-designed bit width. The proposed tool takes Faster region based CNN (R-CNN) + Matthew D. Zeiler and Rob Fergus (ZF)-Net, Single Shot MultiBox Detector (SSD) + VGG, SSD + MobileNet, and Tiny you only look once (YOLO) v2 as the experimental models. These models include both one-stage object detection and two-stage object detection models, and base networks include the convolution layer, the fully connected layer, and the modern advanced layers, such as the inception module and depthwise separable convolution. In these experiments, direct quantization of layer-I/O fixed-point models to bit-accurate models will have a 2% mean average precision (mAP) drop of accuracy in the constraint that all layers' accumulators and multipliers are quantized to less or equal to 14 and 12 bit, respectively. After retraining of these quantized models with the proposed IVS-Caffe, we can achieve less than 1% mAP drop in accuracy in the constraint that all layers' accumulators and multipliers are quantized to less or equal to 14 and 11 bit, respectively. With the proposed IVS-Caffe, we can analyze the accuracy of the target model when it is running at hardware accelerators with different bit widths, which is beneficial to fine-tune the target model or customize the hardware accelerators with lower power consumption. Code is available at https://github.com/apple35932003/IVS-Caffe.

Towards topological fixed-point models beyond gappable boundaries

We consider fixed-point models for topological phases of matter formulated as discrete path integrals in the language of tensor networks. Such zero-correlation length models with an exact notion of topological invariance are known in the mathematical community as state-sum constructions or lattice topological quantum field theories. All of the established ansatzes for fixed-point models imply the existence of a gapped boundary as well as a commuting-projector Hamiltonian. Thus, they fail to capture topological phases without a gapped boundary or commuting-projector Hamiltonian, most notably chiral topological phases in $2+1$ dimensions. In this work, we present a more general fixed-point ansatz not affected by the aforementioned restrictions. Thus, our formalism opens up a possible way forward towards a microscopic fixed-point description of chiral phases and we present several strategies that may lead to concrete examples. Furthermore, we argue that our more general ansatz constitutes a universal form of topological fixed-point models, whereas established ansatzes are universal only for fixed-points of phases which admit topological boundaries.

Large-scale multimodal transportation network models and algorithms-Part I: The combined mode split and traffic assignment problem

Modelling the combined mode split and traffic assignment (CMSTA) problem is essential to capture the travelers’ behaviors and predict the flow distribution in multimodal transportation networks. In this paper, a general fixed-point model that combines the CNL-based mode split and the VI-based traffic assignment is developed to formulate the CMSTA problem in a more realistic multimodal network. The transit common line problem and asymmetric travel cost are considered. A new solution algorithm that integrated with several effective methods and strategies is proposed to solve the fixed-point model in large-scale networks. Numerical results show the effectiveness of the proposed model and algorithm.

A unified diagrammatic approach to topological fixed point models

We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories, but is formalised and unified in terms of tensor networks. In contrast to existing tensor network ansatzes for the study of ground states of topologically ordered phases, the tensor networks in our formalism represent discrete path integrals in Euclidean space-time. This language is more directly related to the Hamiltonian defining the model than other approaches, via a Trotterization of the respective imaginary time evolution. We introduce our formalism by simple examples, and demonstrate its full power by expressing known families of models in 2+1 dimensions in their most general form, namely string-net models and Kitaev quantum doubles based on weak Hopf algebras. To elucidate the versatility of our formalism, we also show how fermionic phases of matter can be described and provide a framework for topological fixed point models in 3+1 dimensions.

Hybrid Stochastic-Binary Computing for Low-Latency and High-Precision Inference of CNNs

The appealing property of low area, low power, and high bit error tolerance has made Stochastic Computing (SC) a promising alternative to conventional binary arithmetic for many computation intensive tasks, e.g., convolutional neural networks (CNNs). However, current SC-based CNN accelerators suffer from the intrinsic computation error and exponentially growing latency. In this work, we optimize both the architecture of SC multiply-and-accumulate (MAC) unit and the overall acceleration strategy of CNN accelerator to favor SC. A low-complexity bit-stream-extending method is proposed to suppress the computation error of SC and ensure the trained fix-point model can be deployed into SC-based hardware without fine-tuning. Besides, distribution-determined partition scheme is developed to design hybrid stochastic-binary computing (SBC) MAC unit which boosts the processing of bit streams at a minimum overhead. For the overall accelerator, the SBC-based MAC array is extended to reuse hardware resources and improve throughput, since the judiciously chosen loop unrolling strategy can better benefit SC operations. The proposed CNN accelerator with extended SBC-MAC array is synthesized and validated using TSMC 28nm CMOS on several representative CNNs, targeted at ImageNet dataset. Compared with precise binary implementation, our proposed design gains 44% area reduction and 50% power saving but induces only 4% additional computation latency and 0.5% accuracy degradation.

General stochastic ridesharing user equilibrium problem with elastic demand

In this study, we propose a general stochastic ridesharing user equilibrium (SRUE) problem with elastic demand (ED) for urban transportation network analysis with ridesharing activities by extending the deterministic ridesharing user equilibrium (DRUE) problem, which is referred to as the general SRUE-ED problem. We develop a novel variational inequality (VI) model in terms of the Lagrange multipliers corresponding to the ride-matching constraints for the general SRUE-ED problem. The existence and uniqueness of the SRUE-ED solution are demonstrated under mild conditions. We proceed to put up a global convergent method to solve the developed VI model by incorporating the weighted cost averaging (WCA) method. The purpose of WCA method is to solve a parametric fixed-point model formulated for the general SRUE-ED problem without the ride-matching constraints. Finally, we use three numerical examples to provide practical insights into the operation and management of the ridesharing systems and to examine the effectiveness of the proposed model and solution method.

FPGA Implementation of Fixed-Point Model for a Single-Phase AC-DC Converter with Unity Power Factor

This paper presents a design of digital control based on a fixed-point model for an application of a single phase AC-DC boost Converter with a high power factor and low current distortion. The system uses a simple closed-loop control with a slow voltage loop (outer loop) to stabilize the output DC bus voltage at the required level and a fast current loop (inner loop) to achieve input power factor correction. The digital control uses a fixed-point structure that improves the control accuracy without increasing the number of arithmetic operations and does not require specific running conditions. The behavior of the system is fully verified by using a digital simulation under Matlab/Simulink environment and experimentally with an implementation in real-time using Xilinx ISE 14.7 software, hardware description language VHDL, Xilinx FPGA ML605 board, and EVAL-AD7656 evaluation board for high-speed analog-to-digital conversion. The obtained results show a good agreement between experiments and simulations for steady-state and transient-responses.

Fermionic Monte Carlo Study of a Realistic Model of Twisted Bilayer Graphene

The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands. An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight binding models and the long-ranged Coulomb interactions. While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit. Here we present for the first time unbiased Monte Carlo simulations of realistic models of magic angle TBG at charge-neutrality. We establish the absence of a sign problem for this model in a momentum space approach, and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion. Our results include (i) the emergence of an insulating Kramers inter-valley coherent ground state in competition with a correlated semi-metal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions which reveal a `pseudogap' regime, in which gap features are established at a higher temperature than the onset of order and (iii) predictions for electronic tunneling spectra and their evolution with temperature. Our results pave the way towards uncovering the physics of magic angle graphene through exact simulations of over a hundred electrons across a wide temperature range.

Paradoxicality in Kripke’s theory of truth

A lot has been written on solutions to the semantic paradoxes, but very little on the topic of general theories of paradoxicality. The reason for this, we believe, is that it is not easy to disentangle a solution to the paradoxes from a specific conception of what those paradoxes consist in. This paper goes some way towards remedying this situation. We first address the question of what one should expect from an account of paradoxicality. We then present one conception of paradoxicality that has been offered in the literature: the fixed-point conception. According to this conception, a statement is paradoxical if it cannot obtain a classical truth-value at any fixed-point model. In order to assess this proposal rigorously we provide a non-metalinguistic characterization of paradoxicality and we evaluate whether the resulting account satisfies a number of reasonable desiderata.

ANNet: A Lightweight Neural Network for ECG Anomaly Detection in IoT Edge Sensors.

In this paper, we propose a lightweight neural network for real-time electrocardiogram (ECG) anomaly detection and system level power reduction of wearable Internet of Things (IoT) Edge sensors. The proposed network utilizes a novel hybrid architecture consisting of Long Short Term Memory (LSTM) cells and Multi-Layer Perceptrons (MLP). The LSTM block takes a sequence of coefficients representing the morphology of ECG beats while the MLP input layer is fed with features derived from instantaneous heart rate. Simultaneous training of the blocks pushes the overall network to learn distinct features complementing each other for making decisions. The network was evaluated in terms of accuracy, computational complexity, and power consumption using data from the MIT-BIH arrhythmia database. To address the class imbalance in the dataset, we augmented the dataset using SMOTE algorithm for network training. The network achieved an average classification accuracy of 97% across several records in the database. Further, the network was mapped to a fixed point model, retrained in a bit accurate fixed-point environment to compensate for the quantization error, and ported to an ARM Cortex M4 based embedded platform. In laboratory testing, the overall system was successfully demonstrated, and a significant saving of ≅ 50% power was achieved by gating the wireless transmission using the classifier. Wireless transmission was enabled only to transmit the beats deemed anomalous by the classifier. The proposed technique compares favourably with current methods in terms of computational complexity and has the advantage of stand-alone operation in the edge node, without the need for always-on wireless connectivity making it ideal for IoT wearable devices.

Fixed-point models for paradoxical predicates

This paper introduces a new kind of fixed-point semantics, filling a gap within approaches to Liar-like paradoxes involving fixed-point models à la Kripke (1975). The four-valued models presented below, (i) unlike the three-valued, consistent fixed-point models defined in Kripke (1975), are able to differentiate between paradoxical and pathological-but-unparadoxical sentences, and (ii) unlike the four-valued, paraconsistent fixed-point models first studied in Visser (1984) and Woodruff (1984), preserve consistency and groundedness of truth. Keywords: Semantic Paradoxes · Fixed-point semantics · Many-valued logic · Kripke’s theory oftruth

Multi-vehicle assignment with elastic vehicle choice behaviour: Fixed-point, deterministic process and stochastic process models

New types of vehicles, such as electricity-powered and/or autonomous cars or buses, are under rapid development, but the time needed to turn the existing stock of traditional vehicles, such as privately-owned human-driven fossil fuelled passenger cars, will likely last several years during which mixed traffic is expected. Moreover, the likely effects of the introduction of such vehicles may not be necessarily positive. Thus, a careful analysis of their various impacts through well designed tools is needed. Main tools for transportation systems analysis are based on methods for travel demand assignment to a transportation network, commonly used to support transportation project assessment and evaluation.The original contribution of this paper is twofold. First, a modelling approach to multi vehicle type assignment is proposed, in this approach the user choice proportions among vehicle types available to users are the results of an explicit choice behaviour model instead of input data as in all existing papers on multi-vehicle assignment. This approach is applied for analysing assignment to transportation networks including Fixed-Point models for equilibrium assignment and Deterministic and Stochastic Process models for day-to-to dynamic assignment.Second, statistical methods are introduced to study the bifurcation of SP models, in order to account for the stochasticity of such models. In particular, the Hartigan’s Dip statistic, which measure the degree of unimodality of a distribution, showed to be the most effective one in identifying bifurcation in SP models.Fixed-point stability and bifurcation analysis are carried out too, and some simple numerical examples are also discussed.Reported results show that innovative vehicles with less impact on congestion than traditional ones may not have a positive effect on equilibrium stability since negative effect of reducing route choice dispersion may be compensate the positive effects on congestion.

A Neuromorphic Proto-Object Based Dynamic Visual Saliency Model With a Hybrid FPGA Implementation.

Computing and attending to salient regions of a visual scene is an innate and necessary preprocessing step for both biological and engineered systems performing high-level visual tasks including object detection, tracking, and classification. Computational bandwidth and speed are improved by preferentially devoting computational resources to salient regions of the visual field. The human brain computes saliency effortlessly, but modeling this task in engineered systems is challenging. We first present a neuromorphic dynamic saliency model, which is bottom-up, feed-forward, and based on the notion of proto-objects with neurophysiological spatio-temporal features requiring no training. Our neuromorphic model outperforms state-of-the-art dynamic visual saliency models in predicting human eye fixations (i.e., ground truth saliency). Secondly, we present a hybrid FPGA implementation of the model for real-time applications, capable of processing 112×84 resolution frames at 18.71 Hz running at a 100 MHz clock rate - a 23.77× speedup from the software implementation. Additionally, our fixed-point model of the FPGA implementation yields comparable results to the software implementation.