Network Contraction Research Articles

Tensor networks for p-spin models

We introduce a tensor network algorithm for the solution of p-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system exactly and is thus lossless, yet leads to qualitative changes in runtime scaling in different regimes of the model. First, we find that bond compression emulates the so-called leaf-removal algorithm, solving the problem efficiently in the “easy” phase. Past a dynamical phase transition, we observe superpolynomial runtimes, reflecting the appearance of a core component. We then develop a graphical method to study the scaling of contraction for a minimal ensemble of core-only instances. We find subexponential scaling, improving on the exponential scaling that occurs without compression. Our results suggest that our tensor network algorithm subsumes the classical leaf removal algorithm and simplifies redundancies in the p-spin model through lossless compression, all without explicit knowledge of the problem’s structure.

Probabilistic inference in the era of tensor networks and differential programming

Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in probabilistic graphical models (PGMs) still lack corresponding TN-based adaptations. In this paper, we advance the connection between PGMs and TNs by formulating and implementing tensor-based solutions for the following inference tasks: (A) computing the partition function, (B) computing the marginal probability of sets of variables in the model, (C) determining the most likely assignment to a set of variables, (D) the same as (C) but after having marginalized a different set of variables, and (E) generating samples from a learned probability distribution using a generalized method. Our study is motivated by recent technical advances in the fields of quantum circuit simulation, quantum many-body physics, and statistical physics. Through an experimental evaluation, we demonstrate that the integration of these quantum technologies with a series of algorithms introduced in this study significantly improves the performance efficiency of existing methods for solving probabilistic inference tasks. Published by the American Physical Society 2024

No Association Between Medicare Advantage Providers' Network Restrictiveness and Star Rating Between 2013 and 2017: An Observational Study.

Medicare beneficiaries are increasingly enrolling in Medicare Advantage (MA), which employs a wide range of practices around restriction of the networks of providers that beneficiaries visit. Though Medicare beneficiaries highly value provider choice, it is unknown whether the MA contract quality metrics which beneficiaries use to inform their contract selection capture the restrictiveness of contracts' provider networks. We evaluated whether there are meaningful associations between provider network restrictiveness (across primary care, psychiatry, and endocrinology providers) and contracts' overall star quality rating, as well as between network restrictiveness and contracts' performance on access to care measures from the Consumer Assessment of Healthcare Providers and Systems (CAHPS) survey. Medicare Advantage contracts with health maintenance organization (HMO), local preferred provider organization (PPO), and point of service (POS) plans with available data. A cross-sectional analysis using multivariable linear regressions to assess the relationship between provider network restrictiveness and contract quality scores in 2013 through 2017. Statistical significance in the relationship between network restrictiveness and contract performance on quality measures. Across all study years, we included 562 unique contracts and 2801 contract-years. We find no evidence of consistent relationships between MA physician network restrictiveness and contract star rating. For primary care, psychiatry, and endocrinology, respectively, a 10 percentage point increase in restrictiveness was associated with a 0.02 (95% confidence interval [CI] -0.01 to 0.04), 0.0008 (95% CI, -0.01 to 0.02), and -0.01 (95% CI, -0.01 to 0.001) difference in star rating (p-value > 0.05 for all). Similarly, we find no evidence of consistent relationships between network restrictiveness and access to care measures. Our findings suggest that existing MA contract quality measures are not useful for indicating differences in network restrictiveness. Given the importance of provider choice to beneficiaries, more specific metrics may be needed to facilitate informed decisions about MA coverage.

Dynamic Recyclable High-Performance Epoxy Resins via Triazolinedione-Indole Click Reaction and Cation-π Interaction Synergistic Crosslinking.

Thermosetting plastics exhibit remarkable mechanical properties and high corrosion resistance, yet the permanent covalent crosslinked network renders these materials challenging for reshaping and recycling. In this study, a high-performance polymer film (EI25-TAD5-Mg) was synthesized by combining click chemistry and cation-π interactions. The internal network of the material was selectively constructed through flexible triazolinedione (TAD) and indole via a click reaction. Cation-π interactions were established between Mg2+ and electron-rich indole units, leading to network contraction and reinforcement. Dynamic non-covalent interactions improved the covalent crosslinked network, and the reversible dissociation of cation-π interactions during loading provided effective energy dissipation. Finally, the epoxy resin exhibited excellent mechanical properties (tensile strength of 91.2 MPa) and latent dynamic behavior. Additionally, the thermal reversibility of the C-N click reaction and dynamic cation-π interaction endowed the material with processability and recyclability. This strategy holds potential value in the field of modifying covalent thermosetting materials.

Open Quantum System Dynamics from Infinite Tensor Network Contraction.

Approaching the long-time dynamics of non-Markovian open quantum systems presents a challenging task if the bath is strongly coupled. Recent proposals address this problem through a representation of the so-called process tensor in terms of a tensor network. We show that for Gaussian environments highly efficient contraction to a matrix product operator (MPO) form can be achieved with infinite MPO evolution methods, leading to significant computational speed-up over existing proposals. The result structurally resembles open system evolution with carefully designed auxiliary degrees of freedom, as in hierarchical or pseudomode methods. Here, however, these degrees of freedom are generated automatically by the MPO evolution algorithm. Moreover, the semigroup form of the resulting propagator enables us to explore steady-state physics, such as phase transitions.

Firm aggregations and firm performance: Evidence from network contracts

In Europe, the economic contraction starting in 2007–2008 has called for new economic policy tools. This paper analyses one of such policies, i.e. the network contract. Network Contracts are an innovative policy introduced in Italy with Law 9 April 2009, N. 33. This policy fosters the creation of firm aggregations with an ad hoc contract, without resorting on mergers. Network contracts are meant to increase economic efficiency for all firms involved in the contract. The paper employs a unique data base with panel data on companies’ balance sheets for the period 2007–2012 along with data on the characteristics of their network contract. The effect of signing a network contract on the economic performance of the single firms and their aggregations is econometrically analyzed. Empirical results suggest in particular that (i.) firms signing a network contract tend to outperform firms that do not, and (ii.) network contracts whose members agree to commit more effort in the contract tend to outperform network contracts with less formally stated degrees of commitment.

Firm cooperation policies: the impact of territorial spillovers

Research on program evaluation, and in particular on firm cooperation policies, has been scant on the impact of space-specific characteristics on program impacts. Few studies have analyzed how spatial features, that are sticky and non-mobile, may affect the intensity of a program’s effect on the targeted economic outcome. This paper uses a regional program (ERGON1) aimed at fostering the creation of Network Contracts to shed light on the contribution of spatial features to policy effectiveness. Network Contracts have been introduced in Italy with Law 9 April 2009, N. 33 to stimulate the formation of firm aggregations and to increase economic efficiency for network members. Empirical results, using Propensity Score Matching Estimates, suggest a positive and causative relation between membership in a Network Contract and firm productivity. Furthermore, evidence suggests that matching for urban characteristics significantly improves matching quality. Evidence is thus provided on the relevance of spatial features in shaping the returns to policies, thereby suggesting that ignoring such features may provide a biased picture of the true effect of a program.

F-actin architecture determines the conversion of chemical energy into mechanical work

Mechanical work serves as the foundation for dynamic cellular processes, ranging from cell division to migration. A fundamental driver of cellular mechanical work is the actin cytoskeleton, composed of filamentous actin (F-actin) and myosin motors, where force generation relies on adenosine triphosphate (ATP) hydrolysis. F-actin architectures, whether bundled by crosslinkers or branched via nucleators, have emerged as pivotal regulators of myosin II force generation. However, it remains unclear how distinct F-actin architectures impact the conversion of chemical energy to mechanical work. Here, we employ in vitro reconstitution of distinct F-actin architectures with purified components to investigate their influence on myosin ATP hydrolysis (consumption). We find that F-actin bundles composed of mixed polarity F-actin hinder network contraction compared to non-crosslinked network and dramatically decelerate ATP consumption rates. Conversely, linear-nucleated networks allow network contraction despite reducing ATP consumption rates. Surprisingly, branched-nucleated networks facilitate high ATP consumption without significant network contraction, suggesting that the branched network dissipates energy without performing work. This study establishes a link between F-actin architecture and myosin energy consumption, elucidating the energetic principles underlying F-actin structure formation and the performance of mechanical work.

Myosin-induced F-actin fragmentation facilitates contraction of actin networks.

Mechanical forces play a crucial role in diverse physiological processes, such as cell migration, cytokinesis, and morphogenesis. The actin cytoskeleton generates a large fraction of the mechanical forces via molecular interactions between actin filaments (F-actins) and myosin motors. Recent studies have shown that the common tendency of actomyosin networks to contract into a smaller structure deeply involves F-actin buckling induced by motor activities, fragmentation of F-actins, and the force-dependent unbinding of cross-linkers that inter-connect F-actins. The fragmentation of F-actins was shown to originate from either buckling or tensile force from previous single-molecule experiments. While the role of buckling in network contraction has been studied extensively, to date, the role of tension-induced F-actin fragmentation in network contraction has not been investigated. In this study, we employed in vitro experiments and an agent-based computational model to illuminate when and how the tension-induced F-actin fragmentation facilitates network contraction. Our experiments demonstrated that F-actins can be fragmented due to tensile forces, immediately followed by catastrophic rupture and contraction of networks. Using the agent-based model, we showed that F-actin fragmentation by tension results in distinct rupture dynamics different from that observed in networks only with cross-linker unbinding. Moreover, we found that tension-induced F-actin fragmentation is particularly important for the contraction of networks with high connectivity. Results from our study shed light on an important regulator of the contraction of actomyosin networks which has been neglected. In addition, our results provide insights into the rupture mechanisms of polymeric network structures and bio-inspired materials.

Friction, not myosin, directs actin network contraction

Friction, not myosin, directs actin network contraction

Hyperoptimized Approximate Contraction of Tensor Networks with Arbitrary Geometry

Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a hyperoptimization over the compression and contraction strategy itself to minimize error and cost. We demonstrate that our protocol outperforms both handcrafted contraction strategies in the literature as well as recently proposed general contraction algorithms on a variety of synthetic and physical problems on regular lattices and random regular graphs. We further showcase the power of the approach by demonstrating approximate contraction of tensor networks for frustrated three-dimensional lattice partition functions, dimer counting on random regular graphs, and to access the hardness transition of random tensor network models, in graphs with many thousands of tensors. Published by the American Physical Society 2024

Verifying Quantum Advantage Experiments with Multiple Amplitude Tensor Network Contraction.

The quantum supremacy experiment, such as Google Sycamore [F. Arute et al., Nature (London) 574, 505 (2019).NATUAS0028-083610.1038/s41586-019-1666-5], poses a great challenge for classical verification due to the exponentially increasing compute cost. Using a new-generation Sunway supercomputer within 8.5 d, we provide a direct verification by computing 3×10^{6} exact amplitudes for the experimentally generated bitstrings, obtaining a cross-entropy benchmarking fidelity of 0.191% (the estimated value is 0.224%). The leap of simulation capability is built on a multiple-amplitude tensor network contraction algorithm which systematically exploits the "classical advantage" (the inherent "store-and-compute" operation mode of von Neumann machines) of current supercomputers, and a fused tensor network contraction algorithm which drastically increases the compute efficiency on heterogeneous architectures. Our method has a far-reaching impact in solving quantum many-body problems, statistical problems, as well as combinatorial optimization problems.

Computation and Formal Verification of Neural Network Contraction Metrics

Computation and Formal Verification of Neural Network Contraction Metrics

A comprehensive theoretical framework for sustainable network contracts: Contracting dimensions and Contract classification

Disruptions in the supply chains/networks result in both performance failures and a poor return on investment (ROI) of network assets. We propose that addressing this situation requires the governance of exchange relationships through contracts guided by sustainability principles. Specifically, we refer to these contracts in the supply and distribution context as “sustainable network contracts”, and the overall framework as the “sustainable contracting framework (SCF)/theory”. Despite the critical role of sustainable network contracts for all key stakeholders in the network, we identify a gap in the existing literature regarding the theory of sustainable network contracts. We bridge this gap by extending the extant dimensions of contracts, as described in Transaction Cost Economics and Relational Exchange Theory, to include sustainability dimensions - constituting the ‘what’ of theory building. To inform sustainable contracts, we propose and employ three factors: costs, benefits, and risks (CBR). We present the ‘how’ of the theory building, outlined in a five-step approach along with an analytical tool, to demonstrate the practical application of our framework. Additionally, we provide a rationale for adopting sustainable network contracts (the ‘why’ of the theory building). Our research methodology involves collecting interview-based data from senior executives (CXOs) (secondary and primary), collecting primary and secondary cost data (objective), integrating behavioral elements (subjective), and employing constrained optimization techniques to determine quantity allocation under various contract policies. Further, we map the proposed eight distinct contract types onto the CBR-space, thereby highlight the relevance of the contract types to real-world practices. This mapping considers network externalities, risks, and allows for a coordinated sustainable approach to contracting from the buyer's (retailer's) perspective. For managers, our framework would serve as an important tool that would inform the contract evaluation process, facilitate local versus global decision-making, safeguard network investments, and help align the interests of buyers and suppliers in each contracting cycle.

Sampling diverse near-optimal solutions via algorithmic quantum annealing.

Sampling a diverse set of high-quality solutions for hard optimization problems is of great practical relevance in many scientific disciplines and applications, such as artificial intelligence and operations research. One of the main open problems is the lack of ergodicity, or mode collapse, for typical stochastic solvers based on Monte Carlo techniques leading to poor generalization or lack of robustness to uncertainties. Currently, there is no universal metric to quantify such performance deficiencies across various solvers. Here, we introduce a new diversity measure for quantifying the number of independent approximate solutions for NP-hard optimization problems. Among others, it allows benchmarking solver performance by a required time-to-diversity (TTD), a generalization of often used time-to-solution (TTS). We illustrate this metric by comparing the sampling power of various quantum annealing strategies. In particular, we show that the inhomogeneous quantum annealing schedules can redistribute and suppress the emergence of topological defects by controlling space-time separated critical fronts, leading to an advantage over standard quantum annealing schedules with respect to both TTS and TTD for finding rare solutions. Using path-integral Monte Carlo simulations for up to 1600 qubits, we demonstrate that nonequilibrium driving of quantum fluctuations, guided by efficient approximate tensor network contractions, can significantly reduce the fraction of hard instances for random frustrated 2D spin glasses with local fields. Specifically, we observe that by creating a class of algorithmic quantum phase transitions, the diversity of solutions can be enhanced by up to 40% with the fraction of hard-to-sample instances reducing by more than 25%.

Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments

Today’s experimental noisy quantum processors can compete with and surpass all known algorithms on state-of-the-art supercomputers for the computational benchmark task of Random Circuit Sampling (Boixo et al., 2018, Arute et al., 2019, Wu et al., 2021, Zhu et al., 2022, Morvan et al., 2023). Additionally, a circuit-based quantum simulation of quantum information scrambling (Mi et al., 2021), which measures a local observable, has already outperformed standard full wave function simulation algorithms, e.g., exact Schrodinger evolution and Matrix Product States (MPS). However, this experiment has not yet surpassed tensor network contraction for computing the value of the observable. Based on those studies, we provide a unified framework that utilizes the underlying effective circuit volume to explain the tradeoff between the experimentally achievable signal-to-noise ratio for a specific observable, and the corresponding computational cost. We apply this framework to recent quantum processor experiments of Random Circuit Sampling (Morvan et al., 2023), quantum information scrambling (Mi et al., 2021), and a Floquet circuit unitary (Kim et al., 2023). This allows us to reproduce the results of Ref. (Kim et al., 2023) in less than one second per data point using one GPU.

Friction patterns guide actin network contraction

The shape of cells is the outcome of the balance of inner forces produced by the actomyosin network and the resistive forces produced by cell adhesion to their environment. The specific contributions of contractile, anchoring and friction forces to network deformation rate and orientation are difficult to disentangle in living cells where they influence each other. Here, we reconstituted contractile actomyosin networks in vitro to study specifically the role of the friction forces between the network and its anchoring substrate. To modulate the magnitude and spatial distribution of friction forces, we used glass or lipids surface micropatterning to control the initial shape of the network. We adapted the concentration of Nucleating Promoting Factor on each surface to induce the assembly of actin networks of similar densities and compare the deformation of the network toward the centroid of the pattern shape upon myosin-induced contraction. We found that actin network deformation was faster and more coordinated on lipid bilayers than on glass, showing the resistance of friction to network contraction. To further study the role of the spatial distribution of these friction forces, we designed heterogeneous micropatterns made of glass and lipids. The deformation upon contraction was no longer symmetric but biased toward the region of higher friction. Furthermore, we showed that the pattern of friction could robustly drive network contraction and dominate the contribution of asymmetric distributions of myosins. Therefore, we demonstrate that during contraction, both the active and resistive forces are essential to direct the actin network deformation.

4d Bioprinting via Molecular Network Contraction for Membranous Tissue Fabrication.

Generation of thin membranous tissues (TMT), such as the cornea, epidermis, and periosteum, presents a difficult fabrication challenge in tissue engineering (TE). TMTs consist of several cell layers that are less than 100μm in thickness per layer. While traditional methods provide the necessary resolution for TMT fabrication, they require significant handling and incorporation of several layers is limited. Extrusion bioprinting offers precise control over deposition of different biomaterials and cell populations within the same construct but lacks the resolution to generate biomimetic TMTs. W e have developed, for the first time, a 4D bioprinting strategy that allows for the generation of cell-laden TMTs. Anionic gelatin methacrylate (GelMA) hydrogels are treated with cationic poly-L-lysine (PLL), which induces charge attraction, microscale network collapse, and macroscale hydrogel shrinking. The impact of shrinking on hydrogel properties, print resolution, and cell viability are presented. Additionally, o ur work suggests that a novel mechanism is occurring, where PLL exhibits a contractile force on GelMA and PLL molecular weight drives GelMA shrinking capabilities. Finally, w e show that this phenomenon can occur while maintaining an encapsulated cell population. These findings address a critical barrier in TE by generating macroscale tissue structures with their microscale TMT counterparts in the same print. This article is protected by copyright. All rights reserved.

Resource Complementarity, Market Overlap and Market Performance in the Italian Network Contracts

Resource Complementarity, Market Overlap and Market Performance in the Italian Network Contracts

Integrating spatially-and temporally-heterogeneous data on river network dynamics using graph theory

The study of non-perennial streams requires extensive experimental data on the temporal evolution of surface flow presence across different nodes of channel networks. However, the consistency and homogeneity of available datasets is threatened by the empirical burden required to map stream network expansions and contractions. Here, we developed a data-driven, graph-theory framework aimed at representing the hierarchical structuring of channel network dynamics (i.e., the order of node activation/deactivation during network expansion/retraction) through a directed acyclic graph. The method enables the estimation of the configuration of the active portion of the network based on a limited number of observed nodes, and can be utilized to combine datasets with different temporal resolutions and spatial coverage. A proof-of-concept application to a seasonally-dry catchment in central Italy demonstrated the ability of the approach to reduce the empirical effort required for monitoring network dynamics and efficiently extrapolate experimental observations in space and time.