Topological Constraints Research Articles

Differentiable Constraints’ Encoding for Gradient-Based Analog Integrated Circuit Placement Optimization

Analog IC design is characterized by non-systematic re-design iterations, often requiring partial or complete layout re-design. The layout task usually starts with device placement, where the several performance figures and constraints to be met escalate its complexity immensely, and, due to the inherent tradeoffs, an “optimal” floorplan solution does not usually exist. Deep learning models are now establishing for the automation of the placement task of analog integrated circuit layout design, promising to bypass the limitations of existing approaches based on: time-consuming optimization processes with several constraints; or placement retargeting from legacy designs/templates, which rely heavily on legacy layout data. However, as the complexity of analog design cases tackled by these methodologies increases, a broader set of topological constraints must be supported to cover the different layout styles and circuit classes. Here, model-independent differentiable encodings for regularity, boundary, proximity, and symmetry island constraints are formulated for the first time in the literature, and an unsupervised loss function is used for the artificial neural network model to learn how to generate placements that follow them. The use of a deep learning model makes push-button speed placement generation possible, additionally, as only sizing data are required for its training, it discards the need to acquire legacy layouts containing insights into this vast set of, often neglected, constraints. The model is ultimately used to produce floorplans from scratch at push-button speed for real state-of-the-art analog structures, including technology nodes not used for training. A case-study comparison with a floorplan design made by a human-expert presents improvements in the fulfillment of every constraint, reaching an overall improvement of around 70%, demonstrating the approach’s value in placement design.

Coarse-Grained Molecular Dynamics Simulation of Polycarbonate Deformation: Dependence of Mechanical Performance by the Effect of Spatial Distribution and Topological Constraints.

Polycarbonate is an engineering plastic used in a wide range of applications due to its excellent mechanical properties, which are closely related to its molecular structure. We performed coarse-grained molecular dynamics (CGMD) calculations to investigate the effects of topological constraints and spatial distribution on the mechanical performance of a certain range of molecular weights. The topological constraints and spatial distribution are quantified as the number of entanglements per molecule (Ne) and the radius of gyration (Rg), respectively. We successfully modeled molecular structures with a systematic variation of Ne and Rg by controlling two simulation parameters: the temperature profile and Kuhn segment length, respectively. We investigated the effect of Ne and Rg on stress-strain curves in uniaxial tension with fixed transverse strain. The result shows that the structure with a higher radius of gyration or number of entanglements has a higher maximum stress (σm), which is mainly due to a firmly formed entanglement network. Such a configuration minimizes the critical strain (εc). The constitutive relationships between the mechanical properties (σm and εc) and the initial molecular structure parameters (Ne and Rg) are suggested.

Free Vibration Characteristics of Bidirectional Graded Porous Plates with Elastic Foundations Using 2D-DQM

This manuscript develops for the first time a mathematical formulation of the dynamical behavior of bi-directional functionally graded porous plates (BDFGPP) resting on a Winkler–Pasternak foundation using unified higher-order plate theories (UHOPT). The kinematic displacement fields are exploited to fulfill the null shear strain/stress at the bottom and top surfaces of the plate without needing a shear factor correction. The bi-directional gradation of materials is proposed in the axial (x-axis) and transverse (z-axis) directions according to the power-law distribution function. The cosine function is employed to define the distribution of porosity through the transverse z-direction. Equations of motion in terms of displacements and associated boundary conditions are derived in detail using Hamilton’s principle. The two-dimensional differential integral quadrature method (2D-DIQM) is employed to transform partial differential equations of motion into a system of algebraic equations. Parametric analysis is performed to illustrate the effect of kinematic shear relations, gradation indices, porosity type, elastic foundations, geometrical dimensions, and boundary conditions (BCs) on natural frequencies and mode shapes of BDFGPP. The effect of the porosity coefficient on the natural frequency is dependent on the porosity type. The natural frequency is dependent on the coupling of gradation indices, boundary conditions, and shear distribution functions. The proposed model can be used in designing BDFGPP used in nuclear, marine, aerospace, and civil structures based on their topology and natural frequency constraints.

Automated hippocampal unfolding for morphometry and subfield segmentation with HippUnfold.

Like neocortical structures, the archicortical hippocampus differs in its folding patterns across individuals. Here, we present an automated and robust BIDS-App, HippUnfold, for defining and indexing individual-specific hippocampal folding in MRI, analogous to popular tools used in neocortical reconstruction. Such tailoring is critical for inter-individual alignment, with topology serving as the basis for homology. This topological framework enables qualitatively new analyses of morphological and laminar structure in the hippocampus or its subfields. It is critical for refining current neuroimaging analyses at a meso- as well as micro-scale. HippUnfold uses state-of-the-art deep learning combined with previously developed topological constraints to generate uniquely folded surfaces to fit a given subject's hippocampal conformation. It is designed to work with commonly employed sub-millimetric MRI acquisitions, with possible extension to microscopic resolution. In this paper we describe the power of HippUnfold in feature extraction, and highlight its unique value compared to several extant hippocampal subfield analysis methods.

Quantum dynamics of a 4π kink in Josephson junction parallel arrays with large kinetic inductance

We present a theoretical study of the quantum dynamics of two magnetic fluxons trapped in Josephson junction parallel arrays (JJPAs) with large kinetic inductances. The Josephson phase distribution of two trapped magnetic fluxons satisfies a topological constraint, i.e., the total variation of Josephson phases along a JJPA is $4\ensuremath{\pi}$. In such JJPAs the characteristic length of the Josephson phase distribution (``the size'' of magnetic fluxon) is drastically reduced to be less than a single cell size. Two extreme dynamic patterns will be distinguished: two weakly interacting and two merged magnetic fluxons, i.e., a $4\ensuremath{\pi}$ kink. Taking into account the repulsive interaction between two magnetic fluxons located in the same or adjacent cells, we obtain the energy band spectrum ${E}_{4\ensuremath{\pi}}(p)$ for a quantum $4\ensuremath{\pi}$ kink. The coherent quantum dynamics of $4\ensuremath{\pi}$ kinks demonstrates the quantum beats with the frequency and amplitude strongly deviating from those observed for two independent magnetic fluxons. In the presence of applied dc and ac bias currents of frequency $f$ a weakly incoherent quantum dynamics of a $4\ensuremath{\pi}$ kink results in the Bloch oscillations and the seminal current steps with values ${I}_{4\ensuremath{\pi}}^{(n)}=enf$ which are two times less than those for two independent magnetic fluxons.

How enzymatic activity is involved in chromatin organization.

Spatial organization of chromatin plays a critical role in genome regulation. Previously, various types of affinity mediators and enzymes have been attributed to regulate spatial organization of chromatin from a thermodynamics perspective. However, at the mechanistic level, enzymes act in their unique ways and perturb the chromatin. Here, we construct a polymer physics model following the mechanistic scheme of Topoisomerase-II, an enzyme resolving topological constraints of chromatin, and investigate how it affects interphase chromatin organization. Our computer simulations demonstrate Topoisomerase-II's ability to phase separate chromatin into eu- and heterochromatic regions with a characteristic wall-like organization of the euchromatic regions. We realized that the ability of the euchromatic regions to cross each other due to enzymatic activity of Topoisomerase-II induces this phase separation. This realization is based on the physical fact that partial absence of self-avoiding interaction can induce phase separation of a system into its self-avoiding and non-self-avoiding parts, which we reveal using a mean-field argument. Furthermore, motivated from recent experimental observations, we extend our model to a bidisperse setting and show that the characteristic features of the enzymatic activity-driven phase separation survive there. The existence of these robust characteristic features, even under the non-localized action of the enzyme, highlights the critical role of enzymatic activity in chromatin organization.

Topological and Dimensional constraints based optimal placement of Layout Entities using Clustering and Genetic Algorithm

Layout planning involves the placement of layout entities, such as kitchen, living-room, office-space, in a house or building in appropriate positions conforming to topological and dimensional constraints. This paper harnesses varied approaches at different phases for optimal layout planning. These include Vaastu Shastra, an ancient Indian system of architecture that optimizes the layout design in buildings and houses. Vaastu Shastra is used to provide the topological structure of layout entities (LE) and for finding appropriate positions for them in the layout. Using the topological constraints, the entities are first divided into four groups: North-East (NE), South-East (SE), North-West (NW) and South-West (SW). Multi-Population Genetic Algorithm (MPGA) is next employed to find topological relations between layout entities. Finally, Entity Planning Genetic Algorithm (EPGA) is used to optimally place the groups in the layout incorporating these topological relations and preserving the various dimensional constraints. The dimensional constraints include the length and width of the layout entities, aspect ratios of the length and width of the layout entities, and the length and width of the layout itself. The system is implemented in AutoCAD as a tool and Auto Lisp as a programming language.

Nanobridge Stencil Enabling High Resolution Arbitrarily Shaped Metallic Thin Films on Various Substrates

AbstractStencil lithography (SL), which uses a perforated membrane as a reusable shadow mask to locally add material patterns on substrates provides a simple but versatile approach for the fabrication of functional devices on a large variety of substrate materials by physical vapor deposition (PVD). Mechanical stress induced by the accumulation of condensed material on the thin stencil membrane during the PVD step leads to stencil bending and breaking, therefore, suspended stencil membranes with arbitrary openings are, in practice, not possible. Here, a new approach to remedy this limitation is reported by introducing auxiliary bridges in stencils. These bridges prevent the suspended membrane from bending out of plane, thereby enabling aperture openings to have almost arbitrary geometry. These bridges are sufficiently narrow so that they do not entirely block the material deposition by PVD and thus create a continuous material pattern by taking advantage of the blurring effect. The successful metal deposition through the designed nanobridge stencil on a wide range of substrate materials underlines the usability and the versatility of the proposed stencil design. The work presented here provides a versatile fabrication method to produce arbitrarily shaped metal patterns that were previously impossible due to the topological constraints of nanostencils.

Concept Representation and the Geometric Model of Mind

Abstract Current cognitive architectures are either working at the abstract, symbolic level, or the low, emergent level related to neural modeling. The best way to understand phenomena is to see, or imagine them, hence the need for a geometric model of mental processes. Geometric models should be based on an intermediate level of modeling that describe mental states in terms of features relevant from the first-person perspective but also linked to neural events. Concepts should be represented as geometrical objects that have sufficiently rich structures to show their properties and their relations to other concepts. The best way to create such geometrical representations of concepts is through the approximate description of the physical states of neural networks. The evolution of brain states is then represented as a trajectory linking successful concepts, and topological constraints on the shape of such trajectory define grammar and logic.

NetMix2: A Principled Network Propagation Algorithm for Identifying Altered Subnetworks.

A standard paradigm in computational biology is to leverage interaction networks as prior knowledge in analyzing high-throughput biological data, where the data give a score for each vertex in the network. One classical approach is the identification of altered subnetworks, or subnetworks of the interaction network that have both outlier vertex scores and a defined network topology. One class of algorithms for identifying altered subnetworks search for high-scoring subnetworks in subnetwork families with simple topological constraints, such as connected subnetworks, and have sound statistical guarantees. A second class of algorithms employ network propagation-the smoothing of vertex scores over the network using a random walk or diffusion process-and utilize the global structure of the network. However, network propagation algorithms often rely on ad hoc heuristics that lack a rigorous statistical foundation. In this work, we unify the subnetwork family and network propagation approaches by deriving the propagation family, a subnetwork family that approximates the sets of vertices ranked highly by network propagation approaches. We introduce NetMix2, a principled algorithm for identifying altered subnetworks from a wide range of subnetwork families. When using the propagation family, NetMix2 combines the advantages of the subnetwork family and network propagation approaches. NetMix2 outperforms other methods, including network propagation on simulated data, pan-cancer somatic mutation data, and genome-wide association data from multiple human diseases.

Anomaly Detection of Distribution Network Based on Adversarial Dual Autoencoder

Anomaly detection on attributed graphs aims to identify individuals or groups whose patterns deviate significantly from most samples, which is very important for internet security, power system, and other applications. Especially in the power system, the energy flow pattern of the distribution network is very similar to the graph topological constraints. Taking each equipment and bus as nodes and the relevant electrical measurement data as attributes, the distribution network fault location problem is mapped to the anomaly detection task on the attributed graph. The traditional GNN-based anomaly detection algorithm for distribution networks has some problems, such as over-smoothing and inefficient embedding learning. To solve the problem of anomaly detection in the distribution network, an anomaly detection algorithm based on adversarial dual autoencoder (DGAE_GAN) is proposed, which is composed of a structural encoder and attribute encoder based on residual connection GAT. Through joint learning, the attributed graph is mapped to the low-dimensional space, and the decoders reconstruct the attributed graph. Then, a discriminator is invited to learn the sample similarity, and the game strategy can effectively alleviate the over-smoothing problem. Finally, the anomaly node detection task is realized by calculating the reconstruction errors from both the structure and attribute levels. We conducted multiple experiments on three real-world datasets, and the IEEE standard example shows that our proposed model is superior to the existing methods.

Exploiting a Deep Learning Toolbox for Human-Machine Feedback towards Analog Integrated Circuit Placement Automation

The layout design of analog integrated circuits has been defying all automation attempts, and it is still primarily a handcrafting process carried by circuit designers on traditional layout editing frameworks. This paper presents a toolbox based on deep learning techniques and a sturdy graphical user interface to assist designers during that process. The underlying mechanism of this toolbox relies on a simple pairwise device interaction circuit description, i.e., the circuits’ topological constraints, to propose valid floorplan solutions for block-level structures, including topologies and deep nanometer technology nodes not used for its training, at push-button speed. Despite its automatic functionalities, the toolbox is focused on explainable artificial intelligence, involving the designer in the synthesis flow via filtering and editing options over the candidate floorplan solutions. This constant state of human-machine feedback environment turns the designer aware of the impact of each device’s position change and inherent tradeoffs while suggesting subsequent moves, ultimately increasing the designers’ productivity in this time-consuming and iterative task. Finally, the toolbox is shown to instantly generate floorplans with similar or better constraint fulfilment than human designed solutions for state-of-the-art analog circuit blocks.

Jacobi partial waves for a set of 3D noncentral rational scatterers

The common tool of choice for basis expansions for the scattering problem with 3D quantum systems remains the spherical harmonics as eigenfunctions of the Laplace–Beltrami operator on the sphere, with approximations for deviations made around the usually dominant s-wave spherically symmetric state. However, with the growing number of technologically accessible nonspherically symmetric geometries of cold atomic and molecular systems, there is a need to explore as orthonormal bases for partial wave analysis the larger class of weighted Jacobi polynomials, subsuming the spherical harmonics. In particular, the lowest angular state for this bigger class is a toroid instead of a spherical s-orbital. This allows analytic treatment of a wider array of rational angular-dependent potentials which can describe rings and systems with topological constraints such as monopoles. Here, we present exact analytic solutions for the quantum scattering problem by partial wave analysis using the weighted Jacobi polynomials as an expanded basis. We obtain the scattering amplitude, differential and total cross-sections for exactly solvable 3D potentials included in the Smorodinsky-Winternitz noncentral systems with dynamical symmetries. Moreover, this procedure also solves the quantum scattering problem from a novel series of rational trigonometric forms of anisotropic potentials including double ring-shaped configurations.

Entropic Mixing of Ring/Linear Polymer Blends.

The topological constraints of nonconcatenated ring polymers force them to form compact loopy globular conformations with much lower entropy than unconstrained ideal rings. The closed-loop structure of ring polymers also enables them to be threaded by linear polymers in ring/linear blends, resulting in less compact ring conformations with higher entropy. This conformational entropy increase promotes mixing rings with linear polymers. Here, using molecular dynamics simulations for bead-spring chains, ring/linear blends are shown to be significantly more miscible than linear/linear blends and that there is an entropic mixing, negative χ, for ring/linear blends compared to linear/linear and ring/ring blends. In analogy with small angle neutron scattering, the static structure function S(q) is measured, and the resulting data are fit to the random phase approximation model to determine χ. In the limit that the two components are the same, χ = 0 for the linear/linear and ring/ring blends as expected, while χ < 0 for the ring/linear blends. With increasing chain stiffness, χ for the ring/linear blends becomes more negative, varying reciprocally with the number of monomers between entanglements. Ring/linear blends are also shown to be more miscible than either ring/ring or linear/linear blends and stay in single phase for a wider range of increasing repulsion between the two components.

Chain Confinement and Anomalous Diffusion in the Cross over Regime between Rouse and Reptation.

By neutron spin echo (NSE) and pulsed field gradient (PFG) NMR, we study the dynamics of a polyethylene-oxide melt (PEO) with a molecular weight in the transition regime between Rouse and reptation dynamics. We analyze the data with a Rouse mode analysis allowing for reduced long wavelength Rouse modes amplitudes. For short times, subdiffusive center-of-mass mean square displacement ⟨rcom2(t)⟩ was allowed. This approach captures the NSE data well and provides accurate information on the topological constraints in a chain length regime, where the tube model is inapplicable. As predicted by reptation for the polymer ⟨rcom2(t)⟩, we experimentally found the subdiffusive regime with an exponent close to , which, however, crosses over to Fickian diffusion not at the Rouse time, but at a later time, when the ⟨rcom2(t)⟩ has covered a distance related to the tube diameter.

Connectivity and collision constrained opportunistic routing for emergency communication using UAV

Emergency communication is essential for search and rescue operations in the aftermath of natural disasters. Unmanned Aerial Vehicle (UAV)-assisted networking is emerging as a promising method for establishing emergency communication. UAVs can intelligently self-adjust their positions, communicate while moving at high speeds, and effectively capture and relay disaster site information to a Terrestrial Base Station (TBS). However, data forwarding from the UAVs to TBS is challenging because of the former’s dynamic network topology, high mobility and resource constraints. Designing efficient routing protocols is crucial in the context of these challenges. To the best of our knowledge, none of the previous works have integratively addressed the post-disaster routing concerns like coverage requirements, inter-UAV collision avoidance and reliable multi-hop routing in the absence of trajectory planning. This paper proposes a novel Multi-hop Opportunistic 3D Routing (MO3DR) algorithm for post-disaster data dissemination. The MO3DR algorithm employs coverage and inter-UAV collision constraints for selecting the next forwarding node to maximize the expected progress of data towards the TBS. Simulations validate the numerical results from closed-form analytical models. Results reveal that operating UAVs within the threshold inter-UAV distance meets the coverage and collision constraints while maximizing the expected progress of data towards the TBS.

Integrated nonholonomic multi-robot consensus tracking formation using neural-network-optimized distributed model predictive control strategy

For constructing a distributed consensus formation scheme for the two-wheel mobile robots with directed communication topology and nonholonomic constraints, in this work, an integrated leader–follower consensus formation framework using neural-network-optimized distributed model predictive control (NNODMPC) strategy is presented. The proposed leader–follower formation framework can be regarded as integrating a consensus trajectories planning subsystem (CTPS) and a consensus tracking subsystem. The CTPS can plan the consensus trajectories for the mobile robots through a leader–follower structure, and in the consensus tracking subsystem, the robots are guided to the consensus. To simultaneously control these two subsystems, the NNODMPC based protocol is applied. The errors and constraints of the integrated system can be incorporated and formulated into a constrained quadratic programming (QP) problem whose optimal solution can be obtained by a primal–dual neural networks (PDNN) QP optimizer. Stability analysis illustrates the convergence of the proposed DMPC-based consensus formation system. The novelties of this work are rooted in the construction of a generalized consensus formation scheme for the practical wheeled robots with nonholonomic constraints, the formulation of an MPC-based distributed consensus controller and the consideration of system constraints. The experimental results on the mobile robots are conducted to verify the effectiveness of the proposed strategy.

Untangling the roles of TOP2A and TOP2B in transcription and cancer.

Type II topoisomerases (TOP2) are conserved regulators of chromatin topology that catalyze reversible DNA double-strand breaks (DSBs) and are essential for maintaining genomic integrity in diverse dynamic processes such as transcription, replication, and cell division. While controlled TOP2-mediated DSBs are an elegant solution to topological constraints of DNA, DSBs also contribute to the emergence of chromosomal translocations and mutations that drive cancer. The central importance of TOP2 enzymes as frontline chemotherapeutic targets is well known; however, their precise biological functions and impact in cancer development are still poorly understood. In this review, we provide an updated overview of TOP2A and TOP2B in the regulation of chromatin topology and transcription, and discuss the recent discoveries linking TOP2 activities with cancer pathogenesis.

Topological aspects in nonlinear optical frequency conversion

Nonlinear optical frequency conversion, observed more than half a century ago, is a corner stone in modern applications of nonlinear and quantum optics. It is well known that frequency conversion processes are constrained by conservation laws, such as momentum conservation that requires phase matching conditions for efficient conversion. However, conservation laws alone could not fully capture the features of nonlinear frequency conversion. Here it is shown that topology can provide additional constraints in nonlinear multi-frequency conversion processes. Unlike conservation laws, a topological constraint concerns with the conserved properties under continuous deformation, and can be regarded as a new indispensable degree of freedom to describe multi-frequency processes. We illustrate such a paradigm by considering sum frequency generation under a multi-frequency pump wave, showing that, akin topological phases in topological insulators, topological phase transitions can be observed in the frequency conversion process both at classical and quantum level.

Enhanced Multiview Fuzzy Clustering Using Double Visible-Hidden View Cooperation and Network LASSO Constraint

Multiview clustering is an important topic in multiview learning, where the cooperation of different views is used to improve clustering performance. Although multiview clustering has made considerable progress, most existing methods only utilize the information of the original visible views, or only consider some hidden space information shared by different views. Two of the challenges are: 1) insufficient exploitation of cooperative learning between visible and hidden information despite some preliminary attempts, and 2) inadequate consideration of topological information for improving multiview clustering. To meet the challenges, we propose the cooperation enhanced multiview fuzzy clustering method (CE-MVFC) in this article. First, we characterize multiview data with two hidden views, which are obtained by adaptive multiview non-negative matrix factorization (NMF) and fuzzy partition information of each sample in different clusters. Then, we integrated the hidden views and the original visible views to realize visible-hidden cooperation learning. Furthermore, we establish a similarity matrix for each visible view and the hidden view obtained through NMF to describe the data topology in these views. Based on the spatial topological relationship of the samples and the representation of hidden view obtained by fuzzy partition, the network least absolute shrinkage and selection operator is constructed to constrain multiview learning. Finally, we develop the multiview clustering method by exploiting the visible-hidden information cooperation and the spatial topological information constraints. Experiments on benchmark multiview datasets are conducted to demonstrate the highly competitive performance of the proposed CE-MVFC against the state-of-the-art methods.