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We prove a one-to-one correspondence between the operadic ideals of the operad uAss and T-ideals. As a consequence, we show that uAss is noetherian and that every proper operadic ideal of uAss is generated by a single element. 

We study several classes of operadic ideals of the unital associative algebra operad uAss. As an application, we classify quotient operads of uAss of GK-dimension no more than 6. This corresponds to a classification of all T-ideals of codimension growth no more than 5 (or equivalently, varieties of grade no more than 5). 

Quantum Infrared Hyperspectral Imaging for Cardiac Pathologies Using Undetected Photons Adriana C. Salazar Coariti*,1, Yameng Zhang1, Peter Moroshkin1, Jimmy Xu1 1School of Engineering, Brown University, 182 Hope Street, Providence, RI 02912, USA *adriana_carola_salazar@brown.edu Abstract: We used hyperspectral quantum imaging with undetected photons (QIUP) to analyze cardiovascular pathology. Multiwavelength probing enabled quantitative detection of fibrosis and biochemical remodeling, demonstrating QIUP’s potential for label-free diagnostics in cardiac tissue. 1. Introduction Cardiovascular diseases (CVDs) remain the leading cause of mortality worldwide. Excess adiposity around the heart constitutes a major risk factor, resulting in structural and functional cardiac remodeling which raises the likelihood of heart failure. Fibrosis is a central pathological feature of many CVDs, characterized by the progressive replacement of healthy myocardium with stiff, collagen-rich extracellular matrix. This excessive scar formation disrupts tissue architecture, impairs contractility, and ultimately contributes to organ dysfunction and failure. While histology is the gold standard to investigate morphological changes in CVD, it provides structural detail but is not able to quantify biochemical markers of fibrosis, collagen crosslinking, lipid infiltration and extracellular matrix remodeling. Label-free vibrational techniques facilitate direct measurement of early tissue modeling, distinguish mature vs immature collagen, map lipid content around cardiomyocytes and detect subtle changes in water content. Classical Short-Wave Infrared (SWIR) and Mid-Infrared (MIR) imaging provide rich biochemical specificity but face fundamental limitations. These techniques suffer from low spatial resolution, limited depth discrimination in 3D samples, strong water absorption, thermal-background noise, low photon flux, high detector noise and the requirement for cryogenic MIR detectors [1]. Quantum Imaging with Undetected Photons (QIUP) overcomes these constraints by probing the sample with MIR photons generated via spontaneous parametric down-conversion (SPDC) while detecting only the correlated and entangled visible-NIR photons[2]. These visible-NIR photons can be detected using high-sensitivity low-cost silicon-based cameras, more importantly without cryogenic cooling. It enables label-free imaging across multiple wavelengths. Here, we take a step further and use quantum holography with undetected photons to measure the absorbance and refractive index of the tissues containing fibrotic tissue from chronic rheumatic valvular disease (CRVD) and healthy cardiac samples. Our method [3] follows the classical Carre technique that uses a series of interferograms taken when the interferometer arm length is changed in steps of λ /4. Combining the data of four interferograms allows us to recover the change of the contrast and the shift of the interference pattern induced by the object. Here, we investigate hyperspectral QIUP in 1.5–2.1 µm wavelength range to distinguish between multiple cardiac pathologies based on their MIR absorption and phase characteristics. This spectral window includes adipose tissue overtone bands (1.720 and 1.760 µm), water–collagen transition features (1.85–1.95 µm), and collagen combination/maturity bands (2.04 and 2.17 µm)[4]. We apply this approach to a heterogeneous dataset of pathological human cardiac tissue cores to explore its potential for label-free characterization of fibrosis and extracellular‑matrix remodeling. 2. Results and discussion The experimental setup is shown in Figure 1. A continuous-wave 532 nm pump laser is directed onto the first dichroic mirror (DM1), which reflects the pump into a Beta Barium Borate (BBO) crystal operated under type-I phase matching. SPDC in the BBO generates an entangled signal-idler photon pair (pair 1). The pump, signal, and idler beams are then reflected by mirrors M1 and M2 back into the crystal, where the pump produces a second down-converted pair (pair 2). The system is aligned such that the photon pairs from the two passes are spatially and spectrally indistinguishable, thereby producing the interference pattern with the sample inserted in the idler beam in front of M1. DM1 transmits only the signal photons which then are spectrally filtered using 710 nm and 720 nm interference bandpass filters before being imaged on a CMOS detector. We image a cardiac disease and normal tissue array (US Biomax BC30013) that contained 1.5 mm diameter circular cores of 5 µm thick sections, including CRVD, hypertrophic myocardium, embolic lesions and healthy tissue. Figure 2 shows representative raw images of (a) healthy cardiac cores and (b) CRVD cores. The pump λ is incrementally tuned across the 1.5–2.1 µm band. Absorption spectra were extracted from absolute transmission profile, while phase maps quantify tissue density variations associated with collagen crosslinking and structural remodeling. Our preliminary results indicate increased mature collagen content in CRVD samples, consistent with the fibrotic pathology of the disease. This, to our knowledge, represents the first demonstration of label-free infrared imaging of cardiac pathological features by quantum hyperspectral imaging without cooling in the 1.5–2.1 µm band. These findings demonstrate how hyperspectral QIUP can identify cardiac pathology through a combination of MIR absorption signatures and high-resolution phase contrast while relying solely on visible-band detection. The ability to characterize biochemical markers relevant to CVDs including lipid content, fibrosis, collagen maturity, and crosslinking highlights QIUP as a promising label-free platform for future cardiovascular diagnostics. This work is supported by ARO W911NF2410138, AOARD FA2386-24-1-4068, NSF 2231901. Reference: 1. D. Zhang, C. Li, C. Zhang, M. N. Slipchenko, G. Eakins, and J.-X. Cheng, "Depth-resolved mid-infrared photothermal imaging of living cells and organisms with submicrometer spatial resolution," Sci. Adv. 2, e1600521 (2016). 2. G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, "Quantum imaging with undetected photons," Nature 512, 409–412 (2014). 3. Y. Zhang, W. Liu, P. Moroshikin, and J. Xu, "Multiwavelength Quantum Holography with Noninteracting Photons," in CLEO 2025 (Optica Publishing Group, 2025), p. AA104_4. 4. S. A. Filatova, I. A. Shcherbakov, and V. B. Tsvetkov, "Optical properties of animal tissues in the wavelength range from 350 to 2600 nm," J. Biomed. Opt. 22, 35009 (2017). 

Single-shot Multiwavelength Quantum Holography in Off-axis Fourier Domain Yameng Zhang†, Wenyu Liu, Ning Zhang, Peter Moroshkin, Jimmy Xu School of Engineering, Brown University, 182 Hope Street, Providence, RI 02912, USA yameng zhang@brown.edu Abstract: We report on a single-shot quantum multiwavelength holography with undetected photons and reconstruction of non-phase-wrapped 3D images from single-acquisition phase and transmission profiles, and along with a deep learning algorithm for enhanced spatial resolution. 1. Introduction Digital holography has found applications in numerous fields such as biology, security, and manufacturing. However, conventional implementations are predominantly restricted to the visible spectral range due to the high cost and low sensitivity of infrared cameras. The use of visible light itself can be problematic—short penetration depth, great scattering loss or disruption of delicate biological processes. Quantum multi-wavelength holography overcomes such limitations by delivering infrared undetected photons (QHUP) to the imaging target [1], and exploiting interference between entangled photon pairs with induced coherence [2]. In this scheme, one photon of each pair probes the sample, while its entangled partner—which does not interact with the object—forms the image on the detector. This decoupling of the sensing and detection wavelengths enables simultaneous measurement of phase and transmission in the infrared (IR) regime. However, this scheme also has its own fundamental limitations. First, phase and transmission reconstruction typically requires multiple phase-shifted interferograms, which increases measurement time, introduces phase errors, and adds experimental complexity, making real-time imaging impractical. Second, the retrieved phase is wrapped between [0, 2π). The absolute axial optical path difference (OPD) cannot be retrieved for samples whose axial profile exceeds the probing wavelength. Third, the spatial resolution of QHUP is in principle superior to but in practice has yet to match that of classical imaging methods. These constraints are particularly problematic for imaging biological structures such as cancer cell where real-time, high-resolution 3D image is essential. We report on single-shot, multiwavelength quantum holography technique with undetected photons that has the potential to overcome these limitations. It is based an off-axis approach that enables simultaneous acquisition of phase and transmission profiles from a single image. Using multiple wavelengths enables non phase wrapped reconstruction of 3D samples. Furthermore, we couple the quantum imaging with a deep learning algorithm that enhances the final image resolution. Together, this development represents a major advancement towards real-time, high-resolution, 3D, noninvasive infrared imaging of biological cells. 2. Results As shown in Fig. 1a, the Beta Barium Borate (BBO) crystal cut for Type-I SPDC is pumped by a 532 nm continuous wave laser. The signal and idler photons produced by the SPDC are in the visible and infrared spectrum, respectively. In the interferometer, the pump and signal are sent into one arm, whereas the idler is sent into another where it probes the object. All three are reflected back to the BBO. The pump then generates a second pair of SPDC photons. Coherence is induced on the overlapping signal photons because the idler photons from the two passes are aligned to be indistinguishable. Dichroic mirror 1 (DM1) transmits the signal photons while discarding the pump and idler. DM3 spatially separates the signal wavelength. The interference bandpass filters (IF) select the signal wavelengths of interest to be imaged on different regions of the CMOS detector. The total intensity Itot recorded by the camera is the sum of the zero order background from the signal photons, Isig,1 + Isig,2, and an interference term as shown in Eq 1. Itot = Isig,1 + Isig,2 + 2 Re hAsig,1(r) Asig,2(r) exp(i ktilt · r) (T (r) exp(iφobj(r))]2i (1) The interference term contains Asig,1(r) and Asig,2(r), the amplitude profiles of the first- and second-pass signal beams. Crucially, it also contains the complex object field T (r) exp(iφobject(r)), where T (r) is the object’s Fig. 1. A) Experimental setup: L1,L2 - lenses; M1-M3 - mirrors; DM1-DM3 - dichroic mirrors; IF1, IF2: interference filters B) Fourier Transform Plane: The separation of +1, -1, and zero order terms for filtering C) The OPD contour plot of the photoresist square sample reconstructed transmission and φobject(r) is the phase it imparts. The squaring occurs because the object is passed twice in the Michelson interferometer. A spatial carrier frequency exp(iktilt · r) is introduced by tilting the idler mirror, creating straight fringe patterns. This separates the +1, −1, and zero-order diffraction orders in the Fourier domain. Thus, by filtering for the +1 term, the object’s complete phase φobj and transmission profiles T can be directly reconstructed from one image as shown in Fig 1b. Moreover, due to the bandpass filters before the detector, two selected narrow wavelength windows within the SPDC signal spectrum are imaged onto two spatially separated areas of the camera pixel array. In so doing, the off-axis single-short scheme resolves the phase wrapping limitation without sacrificing depth/phase resolution, as each frame captures the interference profiles from both wavelengths simultaneously. Thus, two sets of T (x, y, λ ) and φ (x, y, λ ) corresponding to the two wavelengths λ1 and λ2 can be obtained. Our algorithm uses the difference of the two T (x, y, λ ) to compute the spectral-contrast information and the optical-path-difference (LOPD) map. We obtain the phase-unwrapped axial profile of the sample, which is instead limited by the synthetic wavelength Λ = λ1λ2 [3]. A reconstruction of a calibration object—an S1818 photoresist sample patterned into 1 mm squares via lithographic patterning—is shown in Figure 1c. While noting the absence of cryogenic IR and single-photon counting in this system, for field-deployment, we counter the image degradation scatterings and the camera pixel noises by adding a neuromorphic-computational approach [4] at the backend of image processing. This is especially meaningful for quantum holography under photon-starved and indirect detection conditions. The deep learning stage is introduced as an algorithm, data-driven step to refine the experimentally obtained ghost/holographic images. Using paired datasets of quantum/ghost acquisitions and their corresponding high-quality microscopic references, the neural network learns both the measurement-induced degradations and the structural priors of biological samples through end-to-end supervised learning. Thus, the pipeline serves as a learned post-detection resolution enhancer, yielding cleaner backgrounds, higher contrast, sharper boundaries, and effectively improved spatial resolution, thereby enabling meaningful reconstructions even when measurements are constrained by low photon counts and restricted spatial frequencies. This work is supported by ARO W911NF2410138, AOARD FA2386-24-1-4068, NSF 2231901 References 1. S. To¨pfer, M. G. Basset, J. Fuenzalida, F. Steinlechner, J. P. Torres, and M. Gra¨fe, “Quantum holography with unde-tected light,” Sci. Adv. 8, eabl4301 (2022). 2. L. J. Wang, X. Y. Zou, and L. Mandel, “Induced coherence without induced emission,” PRA 44, 4614–4622 (1991). 3. Y. Zhang, W. Liu, P. Moroshkin, and J. Xu, “Multiwavelength quantum holography with noninteracting photons,” in Conference on Lasers and Electro-Optics (CLEO) (Optica, 2025), pp. 1–2. N. Zhang, T. Shea, and A. Nurmikko, “Event-based tracking and imaging of randomly moving objects in dense dy-namical scattering media,” in Proc.IEEE/CVF Conf. on CVPR (IEEE, 2025) pp. 5114-512 

Age-related changes in hemodynamics and leaflet mechanics progressively reduce tissue flexibility and lead to structural valve degeneration (SVD) in bioprosthetic transcatheter aortic valve replacement (TAVR) devices. A novel pulmonary visceral pleura (PVP) tissue, which exhibits a substantially higher elastin-to-collagen ratio than bovine or porcine pericardium used in current commercial valves, has shown strong potential for improving resilience, biocompatibility, and long-term performance in next-generation TAVR designs. In this study, the dynamic behavior of a prototype PVP bioprosthetic valve was evaluated in vitro using a benchtop pulsatile flow loop that integrates optical and acoustic imaging modalities. Physiological aortic flow conditions were reproduced by a programmable pulsatile pump, and simultaneous measurements of pressure and flow were obtained using pressure transducers and flow instrumentation. High-speed optical imaging was used to quantify leaflet kinematics, while B-mode ultrasound, Doppler, and Particle Image Velocimetry (PIV) provided complementary characterization of leaflet motion and near-valvular flow. A comparative assessment was performed against a stented valve with stiff silicone leaflets to evaluate hemodynamic differences associated with the PVP material. Analysis of the valve opening area, timing, and corresponding flow waveform demonstrated that the PVP valve achieved a substantially larger effective orifice area, lower peak jet velocity and turbulence, and lower pressure gradient than the silicone leaflet control. The combined use of ultrasound imaging and optical PIV enabled versatile noninvasive characterization of these hemodynamic features, which establishes a robust experimental framework for evaluating emerging bioprosthetic valve materials and provides essential data to support future fluid–structure interaction simulations and the continued optimization of next generation TAVR designs. 

Helical flow structures play an important role in transport processes in engineered and physiological systems, where cur-vature and torsion generate secondary motions that influence momentum transport, mixing, and wall interactions. This study presents a computational investigation of steady helical pipe flows using the curvature-corrected k–ω SST turbulence model combined with an intermittency-based transition formulation to capture transition and laminarization effects. The numeri-cal framework is validated against experimental velocity measurements obtained downstream of a baseline helical con-figuration, showing good agreement at the measurement plane. Following validation, a parametric study is conducted across three helical geometries with physiologically relevant pitch and curvature ratios (r/D = 1.5–3.0, P/D = 6–12) at Reynolds numbers of 1800 and 3000. Helicity-based visualiza-tion and quantitative cross-sectional metrics are used to char-acterize secondary-flow evolution. The configuration with the smallest pitch and curvature ratios consistently exhibits the largest helicity imbalance between counter-rotating vortices while maintaining the lowest turbulent kinetic energy and intermittency across all cross-sections and Reynolds numbers, indicating an inverse relationship between vortex asymmetry and turbulence intensity under transitional conditions. Reynolds-number sensitivity is also shown to depend strongly on the turbulence modeling approach: while fully turbulent SST predictions remain largely Reynolds-number independent, the transitional formulation captures pronounced Reynolds-number effects in the entrance and mid-helix regions. These findings show that vessel geometry governs an inverse relationship between secondary-flow asymmetry and turbulence, which can be used to identify critical regions of uneven mixing and localized wall interactions in physiological flow systems.