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The prime geodesic theorem for PSL₂(ℤ[i]) and spectral exponential sums
No full textThis work addresses the prime geodesic theorem for the Picard manifold M = PSL₂(ℤ[i])∖h³, which asks for the asymptotic evaluation of a counting function for the closed geodesics on M. Let E_(Γ)(X) be the error term in the prime geodesic theorem. We establish that E_(Γ)(X) = O_(ϵ)(X^(3/2+ϵ)) on average as well as many pointwise bounds. The second moment bound parallels an analogous result for Γ = PSL₂(ℤ) due to Balog et al. and our innovation features the delicate analysis of sums of Kloosterman sums with an explicit manipulation of oscillatory integrals. The proof of the pointwise bounds requires Weyl-strength subconvexity for quadratic Dirichlet L-functions over ℚ(i). Moreover, an asymptotic formula for a spectral exponential sum in the spectral aspect for a cofinite Kleinian group Γ is given. Our numerical experiments visualise in particular that E_(Γ)(X) obeys a conjectural bound of size O_(ϵ)(X^(1+ϵ)
Conservative finite volume scheme for first-order viscous relativistic hydrodynamics
No full textWe present the first conservative finite volume numerical scheme for the causal, stable relativistic Navier-Stokes equations developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK). BDNK theory has arisen very recently as a promising means of incorporating entropy-generating effects (viscosity, heat conduction) into relativistic fluid models, appearing as a possible alternative to the so-called Müller-Israel-Stewart (MIS) theory successfully used to model quark-gluon plasma. The major difference between the two lies in the structure of the system of partial differential equations (PDEs): BDNK theory only has a set of conservation laws, whereas MIS also includes a set of evolution equations for its dissipative degrees of freedom. The simpler structure of the BDNK PDEs in this respect allows for rigorous proofs of stability, causality, and hyperbolicity in full generality which have as yet been impossible for MIS. To capitalize on these advantages, we present the first fully conservative multidimensional fluid solver for the BDNK equations suitable for physical applications. The scheme includes a flux-conservative discretization, nonoscillatory reconstruction, and a central-upwind numerical flux and is designed to smoothly transition to a high-resolution shock-capturing perfect fluid solver in the inviscid limit. We assess the robustness of our new method in a series of flat-spacetime tests for a conformal fluid and provide a detailed comparison with previous approaches of Pandya and Pretorius [Phys. Rev. D 104, 023015 (2021)]
Deterministic Generation of Multidimensional Photonic Cluster States with a Single Quantum Emitter
No full textMultidimensional photonic graph states, such as cluster states, have prospective applications in quantum metrology, secure quantum communication, and measurement-based quantum computation. However, to date, generation of multidimensional cluster states of photonic qubits has relied on probabilistic methods that limit the scalability of typical generation schemes in optical systems. Here we present an experimental implementation in the microwave domain of a resource-efficient scheme for the deterministic generation of 2D photonic cluster states. By utilizing a coupled resonator array as a slow-light waveguide, a single flux-tunable transmon qubit as a quantum emitter, and a second auxiliary transmon as a switchable mirror, we achieve rapid, shaped emission of entangled photon wavepackets, and selective time-delayed feedback of photon wavepackets to the emitter qubit. We leverage these capabilities to generate a 2D cluster state of four photons with 70\% fidelity, as verified by tomographic reconstruction of the quantum state. We discuss how our scheme could be straightforwardly extended to the generation of even larger cluster states, of even higher dimension, thereby expanding the scope and practical utility of such states for quantum information processing tasks
Sequencing and chromosome-scale assembly of the giant Pleurodeles waltl genome
No full textThe Iberian ribbed newt (Pleurodeles waltl) constitutes a central model for probing the basis of regeneration. Here, we present the sequencing and chromosome-scale assembly of the 20.3Gb P.waltl genome, which exhibits the highest level of contiguity and completeness among giant genomes. We uncover that DNA transposable elements are the major contributors to its expansion, with hAT transposons comprising a large portion of repeats. Several hATs are actively transcribed and differentially expressed during adult P. waltl limb regeneration, along with domesticated hAT transposons of the ZBED transcription factor family. Despite its size, syntenic relationships are conserved across the genome. As an example we show the high degree of conservation of the regeneration-associated Tig1 locus with several neighbouring genes. Together, the P. waltl genome provides a fundamental resource for the study of regenerative, developmental and evolutionary principles
Quantifying orthogonal barcodes for sequence census assays
No full textBarcode-based sequence census assays utilize custom or random oligonucloetide sequences to label various biological features, such as cell-surface proteins or CRISPR perturbations. These assays all rely on barcode quantification, a task that is complicated by barcode design and technical noise. We introduce a modular approach to quantifying barcodes that achieves speed and memory improvements over existing tools. We also introduce a set of quality control metrics, and accompanying tool, for validating barcode designs
Control of spatio-temporal patterning via cell density in a multicellular synthetic gene circuit
No full textA major goal in synthetic development is to design and construct gene regulatory circuits that control the patterning and morphogenesis of synthetic multicellular structures. In natural development, an interplay between mechanical and chemical communication shapes the dynamics of gene regulatory circuits that underlie patterning and morphogenesis. However, for synthetic gene circuits, how the non-genetic properties of the growth environment impact circuit behavior remains poorly understood. Here, we describe an occurrence of mechano-chemical coupling in synthetic contact-dependent synNotch patterning circuits demonstrating that cell density modulates the transduction of signal between a sender and receiver cell. By exploiting density-dependent signaling, we construct multicellular signal propagation circuits with synNotch and control the patterning outcome both temporally and spatially via cell density gradients established in vitro via plating or small-molecule mediated modulation of proliferation. Our work demonstrates that synthetic gene circuits can be critically impacted by their context, providing an alternate means for programming multi-cellular circuit patterning outcomes
Photoacoustic imaging reveals transient decrease of oxygenation in murine blood due to monoclonal IgG4 antibody
No full textOver 100 monoclonal antibodies have been approved by the FDA for clinical use; however, a paucity of knowledge exists regarding the injection site behavior of these formulated therapeutics, i.e., the effect of antibody and formulation on the tissue around the injection site and vice versa. In this report, we injected a near-infrared dye-labeled IgG4 isotope control antibody into the subcutaneous space in mouse ears to analyze the injection site dynamics, including quantifying molecular movement. Surprisingly, we discovered that the antibody reduces the local blood oxygen saturation levels in mice after prolonged anesthesia without affecting the total hemoglobin content and oxygen extraction fraction. The local oxygen saturation results open a new pathway to study the functional effects of monoclonal antibodies
Unsupervised Restoration of a Complex Learned Behavior After Large-Scale Neuronal Perturbation
No full textReliable execution of behaviors requires that brain circuits correct for variations in neuronal dynamics. Genetic perturbation of the majority of excitatory neurons in a brain region involved in song production in adult songbirds with stereotypical songs triggered severe degradation of their songs. The song fully recovered within two weeks, and substantial improvement occurred even when animals were prevented from singing during the recovery period, indicating that offline mechanisms enable recovery in an unsupervised manner. Song restoration was accompanied by increased excitatory synaptic inputs to unmanipulated neurons in the same region. A model inspired by the behavioral and electrophysiological findings suggests that a combination of unsupervised single-cell and population-level homeostatic plasticity rules can support the observed functional restoration after large-scale disruption of networks implementing sequential dynamics. In the model the sequence is restored through a parallel homeostatic process, rather than regrown serially, and predicts that sequences should recover in a saltatory fashion. Correspondingly, we observed such recovery in the songs of manipulated animals, with syllables that rapidly alternate between abnormal and normal durations from rendition to rendition until eventually they permanently settled into their original length. These observations indicate the existence of cellular and systems-level restorative mechanisms that ensure behavioral resilience
A model-free Data-Driven paradigm for in situ patient-specific prediction of human brain response to ultrasound stimulation
No full textWe present a class of model-free Data-Driven solvers that effectively enable the utilization of in situ and in vivo imaging data directly in full-scale calculations of the mechanical response of the human brain to ultrasound stimulation, entirely bypassing the need for analytical modeling or regression of the data. We demonstrate the approach, including its ability to make detailed spatially-resolved patient-specific predictions of wave patterns, using public-domain MRI images, MRE data and commercially available solid-mechanics software
Reversing the enantioselectivity of enzymatic carbene N–H insertion through mechanism-guided protein engineering
No full textIn this work, we report a computationally driven approach to access enantiodivergent enzymatic carbene N–H bond insertions catalyzed by P411 enzyme variants. Computational modeling was employed to guide engineering efforts to control the accessible conformations of a key lactone-carbene (LAC) intermediate in the enzyme active site by installing a new H-bond anchoring point. By combining MD simulations and protein engineering, a reversed (R-selective) P411 enzyme variant, L5_FL-B3, was obtained in a single round of semi-rational directed evolution. L5_FL-B3 accepts a broad scope of amine substrates with excellent yields (up to >99%), high efficiency (up to 12,300 TTN) and good enantiocontrol (up to 7:93 er), which complements the previously engineered S-selective P411-L7_LF variant