Modular Inclusions Research Articles

Comments on the double cone wormhole

In this paper we revisit the double cone wormhole introduced by Saad, Shenker and Stanford (SSS), which was shown to reproduce the ramp in the spectral form factor. As a first approximation we can say that this solution computes Tr[e−iKT], a trace of the “evolution” operator that generates Schwarzschild time translations on the two sided wormhole geometry. This point of view leads to a simple way to compute the normalization factor of the wormhole. When we have bulk matter fields, SSS suggested using a modified evolution \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{K}$$\\end{document} which involves a slightly complex geometry, so that we are really computing \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{Tr}}\\left[{e}^{-i\\widetilde{K}T}\\right]$$\\end{document}. We argue that, for general black holes, the spectrum of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{K}$$\\end{document} is given by quasinormal mode frequencies. We explain that this reproduces various features that were previously predicted from the spectral form factor on hydrodynamics grounds. We also give a general algebraic construction of the modified boost in terms of operators constructed from half sided modular inclusions. For the special case of JT gravity, we work out the backreaction of matter on the geometry of the double cone and find that it deforms the geometry in an undesirable direction. We finally give some comments on the possible physical interpretation of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{K}$$\\end{document}.

Engineered Microenvironmental Cues from Fiber-Reinforced Hydrogel Composites Drive Tenogenesis and Aligned Collagen Deposition.

Effective tendon regeneration following injury is contingent on appropriate differentiation of recruited cells and deposition of mature, aligned, collagenous extracellular matrix that can withstand the extreme mechanical demands placed on the tissue. As such, myriad biomaterial approaches have been explored to provide biochemical and physical cues that encourage tenogenesis and template aligned matrix deposition in lieu of dysfunctional scar tissue formation. Fiber-reinforced hydrogels present an ideal biomaterial system toward this end given their transdermal injectability, tunable stiffness over a range amenable to tenogenic differentiation of progenitors, and capacity for modular inclusion of biochemical cues. Here, tunable and modular, fiber-reinforced, synthetic hydrogels are employed to elucidate salient microenvironmental determinants of tenogenesis and aligned collagen deposition by tendon progenitor cells. Transforming growth factor β3 drives a cell fate switch toward pro-regenerative or pro-fibrotic phenotypes, which can be biased toward the former by culture in softer microenvironments or inhibition of the RhoA/ROCK activity. Furthermore, studies demonstrate that topographical anisotropy in fiber-reinforced hydrogels critically mediates the alignment of de novo collagen fibrils, reflecting native tendon architecture. These findings inform the design of cell-free, injectable, synthetic hydrogels for tendon tissue regeneration and, likely, that of a range of load-bearing connective tissues.

Simulating collectivity in dense baryon matter with multiple fluids

A novel three-fluid dynamical model for simulations of heavy-ion collisions at RHIC Beam Energy Scan programme, called MUFFIN, has been developed. The novelty consists of modular inclusion of the Equation of State, use of hyperbolic coordinates that allow to simulate higher collision energies, and fluctuating initial conditions. The model reproduces rapidity and pt spectra of collisions from √SNN = 7.7 to 62.4 GeV. Ideal fluid is assumed, and the elliptic flow is over-predicted, particularly at lower collision energies.

Modular Structure and Inclusions of Twisted Araki-Woods Algebras

In the general setting of twisted second quantization (including Bose/Fermi second quantization, S-symmetric Fock spaces, and full Fock spaces from free probability as special cases), von Neumann algebras on twisted Fock spaces are analyzed. These twisted Araki-Woods algebras mathcal {L}_{T}(H) depend on the twist operator T and a standard subspace H in the one-particle space. Under a compatibility assumption on T and H, it is proven that the Fock vacuum is cyclic and separating for mathcal {L}_{T}(H) if and only if T satisfies a standard subspace version of crossing symmetry and the Yang-Baxter equation (braid equation). In this case, the Tomita-Takesaki modular data are explicitly determined. Inclusions mathcal {L}_{T}(K)subset mathcal {L}_{T}(H) of twisted Araki-Woods algebras are analyzed in two cases: If the inclusion is half-sided modular and the twist satisfies a norm bound, it is shown to be singular. If the inclusion of underlying standard subspaces Ksubset H satisfies an L^2-nuclearity condition, mathcal {L}_{T}(K)subset mathcal {L}_{T}(H) has type III relative commutant for suitable twists T. Applications of these results to localization of observables in algebraic quantum field theory are discussed.

Modular parallel transport of multiple intervals in 1+1-dimensional free fermion theory

Modular parallel transport is a generalization of Berry phases, applied to modular (entanglement) Hamiltonians. Here we initiate the study of modular parallel transport for disjoint field theory regions. We study modular parallel transport in the kinematic space of multi-interval regions in the vacuum of 1+1-dimensional free fermion theory — one of the few theories for which modular Hamiltonians on disjoint regions are known. We compute explicitly the generators of modular parallel transport, and explain why their relatively simple form follows from a half-sided modular inclusion. We also compute explicitly the curvature two-form of modular parallel transport. We contrast all calculations with the expected behavior of modular parallel transport in holographic theories, emphasizing the role of non-local terms that couple distinct intervals.

Physical and Soluble Cues Enhance Tendon Progenitor Cell Invasion into Injectable Synthetic Hydrogels.

Synthetic hydrogels represent an exciting avenue in the field of regenerative biomaterials given their injectability, orthogonally tunable mechanical properties, and potential for modular inclusion of cellular cues. Separately, recent advances in soluble factor release technology have facilitated control over the soluble milieu in cell microenvironments via tunable microparticles. A composite hydrogel incorporating both of these components can robustly mediate tendon healing following a single injection. Here, a synthetic hydrogel system with encapsulated electrospun fiber segments and a novel microgel-based soluble factor delivery system achieves precise control over topographical and soluble features of an engineered microenvironment, respectively. It isdemonstrated that three-dimensionalmigration of tendon progenitor cells can be enhanced via combined mechanical, topographical, and microparticle-delivered soluble cues in both a tendon progenitor cell spheroid model and an ex vivo murine Achilles tendon model. These results indicate that fiber reinforced hydrogels can drive the recruitment of endogenous progenitor cells relevant to the regeneration of tendon and, likely, a broad range of connective tissues.

Madelung Formalism for Electron Spill-Out in Nonlocal Nanoplasmonics.

Current multiscale plasmonic systems pose a modeling challenge. Classical macroscopic theories fail to capture quantum effects in such systems, whereas quantum electrodynamics is impractical given the total size of the experimentally relevant systems, as the number of interactions is too large to be addressed one by one. To tackle the challenge, in this paper we propose to use the Madelung form of the hydrodynamic Drude model, in which the quantum effect electron spill-out is incorporated by describing the metal–dielectric interface using a super-Gaussian function. The results for a two-dimensional nanoplasmonic wedge are correlated to those from nonlocal full-wave numerical calculations based on a linearized hydrodynamic Drude model commonly employed in the literature, showing good qualitative agreement. Additionally, a conformal transformation perspective is provided to explain qualitatively the findings. The methodology described here may be applied to understand, both numerically and theoretically, the modular inclusions of additional quantum effects, such as electron spill-out and nonlocality, that cannot be incorporated seamlessly by using other approaches.

Quantum error correction in SYK and bulk emergence

We analyze the error correcting properties of the Sachdev-Ye-Kitaev model, with errors that correspond to erasures of subsets of fermions. We study the limit where the number of fermions erased is large but small compared to the total number of fermions. We compute the price of the quantum error correcting code, defined as the number of physical qubits needed to reconstruct whether a given operator has been acted upon the thermal state or not. By thinking about reconstruction via quantum teleportation, we argue for a bound that relates the price to the ordinary operator size in systems that display so-called detailed size winding [1]. We then find that in SYK the price roughly saturates this bound. Computing the price requires computing modular flowed correlators with respect to the density matrix associated to a subset of fermions. We offer an interpretation of these correlators as probing a quantum extremal surface in the AdS dual of SYK. In the large N limit, the operator algebras associated to subsets of fermions in SYK satisfy half-sided modular inclusion, which is indicative of an emergent Type III1 von Neumann algebra. We discuss the relationship between the emergent algebra of half-sided modular inclusions and bulk symmetry generators.

Deformations of Half-Sided Modular Inclusions and Non-local Chiral Field Theories

We construct explicit examples of half-sided modular inclusions mathcal {N}subset mathcal {M} of von Neumann algebras with trivial relative commutants. After stating a general criterion for triviality of the relative commutant in terms of an algebra localized at infinity, we consider a second quantization inclusion mathcal {N}subset mathcal {M} with large relative commutant and construct a one-parameter family mathcal {N}_kappa subset mathcal {M}_kappa , kappa ge 0, of half-sided inclusions such that mathcal {N}_0=mathcal {N}, mathcal {M}_0=mathcal {M} and mathcal {N}_kappa 'cap mathcal {M}_kappa =mathbb {C}1 for kappa >0. The technique we use is an explicit deformation procedure (warped convolution), and we explain the relation of this result to the construction of chiral conformal quantum field theories on the real line and on the circle.

Relative Entropy of Coherent States on General CCR Algebras

For a subalgebra of a generic CCR algebra, we consider the relative entropy between a general (not necessarily pure) quasifree state and a coherent excitationthereof. We give a unified formula for this entropy in terms of single-particle modular data. Further, we investigate changes of the relative entropy along subalgebras arising from an increasing family of symplectic subspaces; here convexity of the entropy (as usually considered for the Quantum Null Energy Condition) is replaced with lower estimates for the second derivative, composed of “bulk terms” and “boundary terms”. Our main assumption is that the subspaces are in differential modular position, a regularity condition that generalizes the usual notion of half-sided modular inclusions. We illustrate our results in relevant examples, including thermal states for the conformal U(1)-current.

Relative entropy and curved spacetimes

Given any half-sided modular inclusion of standard subspaces, we show that the entropy function associated with the decreasing one-parameter family of translated standard subspaces is convex for any given (not necessarily smooth) vector in the underlying Hilbert space. In second quantisation, this infers the convexity of the vacuum relative entropy with respect to the translation parameter of the modular tunnel of von Neumann algebras. This result allows us to study the QNEC inequality for coherent states in a free Quantum Field Theory on a stationary curved spacetime, given a KMS state. To this end, we define wedge regions and appropriate (deformed) subregions. Examples are given by the Schwarzschild spacetime and null translated subregions with respect to the time translation Killing flow. More generally, we define wedge and strip regions on a globally hyperbolic spacetime, so to have non trivial modular inclusions of von Neumann algebras, and make our analysis in this context.

What can cluster analysis offer in investing? - Measuring structural changes in the investment universe

The return on assets of the investment universe tends to form a cluster structure. This study quantifies this strength of the clustering tendency as a single econometric measure, referred to as modularity. Through an empirical study of the US equity market, we demonstrate that the strength of the clustering tendency changes over time with market fluctuations. That is, normal markets tend to have a clear cluster structure (high modularity), while stressed markets tend to have a blurry cluster structure (low modularity). Modularity assesses the quality of an investment opportunity set in terms of potential diversification benefits. Modularity is an important pricing variable in the cross-sectional returns of US stocks. From 1992 to 2015, the average return of the stocks with the lowest sensitivity to modularity (low modularity beta) exceeds that of the stocks with the highest sensitivity (high modularity beta) by approximately 10.49% annually, adjusted for the Fama-French five-factor exposures. The inclusion of modularity as an asset pricing factor, therefore, expands the investment opportunity set for factor-based investors.

Recovering the QNEC from the ANEC

We study the relative entropy in QFT comparing the vacuum state to a special family of purifications determined by an input state and constructed using relative modular flow. We use this to prove a conjecture by Wall that relates the shape derivative of relative entropy to a variational expression over the averaged null energy (ANE) of possible purifications. This variational expression can be used to easily prove the quantum null energy condition (QNEC). We formulate Wall’s conjecture as a theorem pertaining to operator algebras satisfying the properties of a half-sided modular inclusion, with the additional assumption that the input state has finite averaged null energy. We also give a new derivation of the strong superadditivity property of relative entropy in this context. We speculate about possible connections to the recent methods used to strengthen monotonicity of relative entropy with recovery maps.

A general proof of the quantum null energy condition

We prove a conjectured lower bound on 〈T__(x)〉ψ in any state ψ of a CFT on Minkowski space, dubbed the Quantum Null Energy Condition (QNEC). The bound is given by the second order shape deformation, in the null direction, of the geometric entanglement entropy of an entangling cut passing through x. Our proof involves a combination of the two independent methods that were used recently to prove the weaker Averaged Null Energy Condition (ANEC). In particular the properties of modular Hamiltonians under shape deformations for the state ψ play an important role, as do causality considerations. We study the two point function of a “probe” operator mathcal{O} in the state ψ and use a lightcone limit to evaluate this correlator. Instead of causality in time we consider causality on modular time for the modular evolved probe operators, which we constrain using Tomita-Takesaki theory as well as certain generalizations pertaining to the theory of modular inclusions. The QNEC follows from very similar considerations to the derivation of the chaos bound and the causality sum rule. We use a kind of defect Operator Product Expansion to apply the replica trick to these modular flow computations, and the displacement operator plays an important role. We argue that the proof extends to more general relativistic QFT with an interacting UV fixed point and also prove a higher spin version of the QNEC. Our approach was inspired by the AdS/CFT proof of the QNEC which follows from properties of the Ryu-Takayanagi (RT) surface near the boundary of AdS, combined with the requirement of entanglement wedge nesting. Our methods were, as such, designed as a precise probe of the RT surface close to the boundary of a putative gravitational/stringy dual of any QFT with an interacting UV fixed point.

Probabilistic associative learning suffices for learning the temporal structure of multiple sequences.

From memorizing a musical tune to navigating a well known route, many of our underlying behaviors have a strong temporal component. While the mechanisms behind the sequential nature of the underlying brain activity are likely multifarious and multi-scale, in this work we attempt to characterize to what degree some of this properties can be explained as a consequence of simple associative learning. To this end, we employ a parsimonious firing-rate attractor network equipped with the Hebbian-like Bayesian Confidence Propagating Neural Network (BCPNN) learning rule relying on synaptic traces with asymmetric temporal characteristics. The proposed network model is able to encode and reproduce temporal aspects of the input, and offers internal control of the recall dynamics by gain modulation. We provide an analytical characterisation of the relationship between the structure of the weight matrix, the dynamical network parameters and the temporal aspects of sequence recall. We also present a computational study of the performance of the system under the effects of noise for an extensive region of the parameter space. Finally, we show how the inclusion of modularity in our network structure facilitates the learning and recall of multiple overlapping sequences even in a noisy regime.

Free products in AQFT

We apply the free product construction to various local algebras in algebraic quantum field theory. If we take the free product of infinitely many identical half-sided modular inclusions with ergodic canonical endomorphism, we obtain a half-sided modular inclusion with ergodic canonical endomorphism and trivial relative commutant. On the other hand, if we take Mobius covariant nets with trace class property, we are able to construct an inclusion of free product von Neumann algebras with large relative commutant, by considering either a finite family of identical inclusions or an infinite family of inequivalent inclusions. In two dimensional spacetime, we construct Borchers triples with trivial relative commutant by taking free products of infinitely many, identical Borchers triples. Free products of finitely many Borchers triples are possibly associated with Haag-Kastler net having S-matrix which is nontrivial and non asymptotically complete, yet the nontriviality of double cone algebras remains open.

Comments on black hole interiors and modular inclusions

We show how the traversable wormhole induced by a double-trace deformation of the thermofield double state can be understood as a modular inclusion of the algebras of exterior operators. The effect of this deformation is the creation of a new region of spacetime deep in the bulk, corresponding to a non-trivial center between the left and right algebras. This set-up provides a precise framework for investigating how black hole interiors are encoded in the CFT. In particular, we use modular theory to demonstrate that state dependence is an inevitable feature of any attempt to represent operators behind the horizon. Building on this geometrical structure, we propose that modular inclusions may provide a more precise means of investigating the nascent relationship between entanglement and geometry in the context of the emergent spacetime paradigm.

A multiply-partitioned methodology for fully-coupled computational wind-structure interaction simulation considering the inclusion of arbitrary added mass dampers

Recent advances of the numerical wind tunnel result in a flexible methodological framework, which enables the fully-coupled simulation of wind-structure interactions considering the arbitrary and modular inclusion of additional devices into the system – such as added mass dampers – for the mitigation of vibrations caused by the wind flow. This feature could be seen as an add-on to what can be done with experimental methods and enables further possibilities when the predictive character of such simulations is used for structural design or even for the development and optimization of the additional devices themselves. The procedure promotes an approach fully-solved in time domain using a multiply-partitioned concept to be able to deal with the respective components in an efficient way. It is crucial to adopt a coupled approach and analysis in time as the involved systems can heavily influence each other. The systematic preparation of each module accompanied by coupled simulations is presented, which aims to ensure and enhance the quality of the overall solution strategy. The effectiveness and industrial relevance of the concept is presented on a tall building undergoing dynamic excitation due to vortex shedding with an integrated vibration mitigation device.

Antiunitary representations and modular theory

Antiunitary representations of Lie groups take values in the group of unitary and antiunitary operators on a Hilbert space H. In quantum physics, antiunitary operators implement time inversion or a PCT symmetry, and in the modular theory of operator algebras they arise as modular conjugations from cyclic separating vectors of von Neumann algebras. We survey some of the key concepts at the borderline between the theory of local observables (Quantum Field Theory (QFT) in the sense of Araki--Haag--Kastler) and modular theory of operator algebras from the perspective of antiunitary group representations. Here a central point is to encode modular objects in standard subspaces V in H which in turn are in one-to-one correspondence with antiunitary representations of the multiplicative group R^x. Half-sided modular inclusions and modular intersections of standard subspaces correspond to antiunitary representations of Aff(R), and these provide the basic building blocks for a general theory started in the 90s with the ground breaking work of Borchers and Wiesbrock and developed in various directions in the QFT context. The emphasis of these notes lies on the translation between configurations of standard subspaces as they arise in the context of modular localization developed by Brunetti, Guido and Longo, and the more classical context of von Neumann algebras with cyclic separating vectors. Our main point is that configurations of standard subspaces can be studied from the perspective of antiunitary Lie group representations and the geometry of the corresponding spaces, which are often fiber bundles over ordered symmetric spaces. We expect this perspective to provide new and systematic insight into the much richer configurations of nets of local observables in QFT.

Network modularity reveals critical scales for connectivity in ecology and evolution

For nearly a century, biologists have emphasized the profound importance of spatial scale for ecology, evolution and conservation. Nonetheless, objectively identifying critical scales has proven incredibly challenging. Here we extend new techniques from physics and social sciences that estimate modularity on networks to identify critical scales for movement and gene flow in animals. Using four species that vary widely in dispersal ability and include both mark-recapture and population genetic data, we identify significant modularity in three species, two of which cannot be explained by geographic distance alone. Importantly, the inclusion of modularity in connectivity and population viability assessments alters conclusions regarding patch importance to connectivity and suggests higher metapopulation viability than when ignoring this hidden spatial scale. We argue that network modularity reveals critical meso-scales that are probably common in populations, providing a powerful means of identifying fundamental scales for biology and for conservation strategies aimed at recovering imperilled species.