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We study the decay scenario of a codimension-2 NHIM in a three degrees of freedom Hamiltonian system under increasing perturbation when the NHIM loses its normal hyperbolicity. On one hand, we follow this decay in the Poincar\'e map for the internal dynamics of the NHIM. On the other hand, we also follow the decay in a time delay function calculated on a 2-dimensional plane in the phase space of the system. In addition, we observe the role of tangential transient effects on the decaying NHIM and their manifestation in the delay time indicator function. Thereby we obtain ideas on how the decay of NHIMs and the tangential transient effects are encoded in indicator functions. As an example of demonstration, we use the motion of an electron in a perturbed magnetic dipole field.

Polynomial invariants constitute a dynamic and essential area of study in the mathematical theory of knots. From the pioneer Alexander polynomial, the revolutionary Jones polynomial, to the collectively discovered HOMFLYPT polynomial, just to mention a few, these algebraic expressions have been central to the understanding of knots and links. The introduction of Khovanov homology has sparked significant interest in the categorification of these polynomials, offering deeper insights into their topological and algebraic properties. In this work, we revisit two prominent polynomial invariants, the Alexander-Conway and the Kauffman bracket polynomials, and focus specifically on the polynomials associated with the family of three strand pretzel links $P(1,1,n)$., Comment: 10 pages, 18 figures

We take a first step towards the classification of singular Mori dream $K3$ surfaces. We prove that if the Picard lattice of a singular $K3$ surface is Mori dream, then the surface is Mori dream. Moreover, we show that for singular $K3$ surfaces, of Picard rank two, being Mori dream is equivalent to contain two negative curves intersecting each other, and apply this result to study Mori dreamness of $K3$ surfaces with a singular point of type $A_n$., Comment: 15 pages

We measure the average spin of $^{144}$Ba, a common fragment produced in $^{252}$Cf(sf), as a function of the total kinetic energy (TKE). We combined for the first time a twin Frisch-gridded ionization chamber with a world-class $\gamma$-ray spectrometer that was designed to measure high-multiplicity $\gamma$-ray events, Gammasphere. The chamber, loaded with a $^{252}$Cf(sf) source, provides a fission trigger, the TKE of the fragments, the approximate fragment masses, and the polar angle of the fission axis. Gammasphere provides the total $\gamma$-ray yield, fragment identification through the tagging of decay $\gamma$ rays, and the feeding of rotational bands in the fragments. We determine the dependence of the average spin of $^{144}$Ba on the fragments' TKE by correlating the fragment properties with the distribution of discrete levels that are fed. We find that the average spin only changes by about $0.5$ $\hbar$ across the TKE range of 158-203 MeV. The virtual independence of the spin on TKE suggests that spin is not solely generated through the statistical excitation of rotational modes, and more complex mechanisms are required., Comment: Accepted for publication in Phys. Rev. C

We present results from commissioning observations of the mid-IR instrument, MIRAC-5, on the 6.5-m MMT telescope. MIRAC-5 is a novel ground-based instrument that utilizes a state-of-the-art GeoSnap (2 - 13 microns) HgCdTe detector with adaptive optics support from MAPS to study protoplanetary disks, wide-orbit brown dwarfs, planetary companions in the contrast-limit, and a wide range of other astrophysical objects. We have used MIRAC-5 on six engineering observing runs, improving its performance and defining operating procedures. We characterize key aspects of MIRAC-5's performance, including verification that the total telescope, atmosphere, instrument, and detector throughput is approximately 10%. Following a planned dichroic upgrade, the system will have a throughput of 20% and background limiting magnitudes (for SNR = 5 and 8 hour exposure times) of 18.0, 15.6, and 12.6 for the L', M', and N' filters, respectively. The detector pixels experience 1/f noise but, if the astrophysical scene is properly modulated via chopping and nodding sequences, it is less than 10% the Poisson noise from the observed background in an 85 Hz frame. We achieve close to diffraction-limited performance in the N-band and all bands are expected to reach diffraction-limited performance following the adaptive optics system commissioning. We also present an exposure time calculator calibrated to the on-sky results. In its current state, MIRAC-5 will be capable of achieving several scientific objectives including the observation of warm wide-orbit companions. Once the adaptive optics is commissioned and a coronagraph installed in 2025, MIRAC-5 will have contrast-limited performance comparable to JWST, opening new and complementary science investigations for close-in companions., Comment: 23 pages, 12 figures, 9 tables, Accepted into PASP, Exposure Time Calculator will be made publicly available soon

We develop a probabilistic variant of Partial Least Squares (PLS) we call Probabilistic Targeted Factor Analysis (PTFA), which can be used to extract common factors in predictors that are useful to predict a set of predetermined target variables. Along with the technique, we provide an efficient expectation-maximization (EM) algorithm to learn the parameters and forecast the targets of interest. We develop a number of extensions to missing-at-random data, stochastic volatility, and mixed-frequency data for real-time forecasting. In a simulation exercise, we show that PTFA outperforms PLS at recovering the common underlying factors affecting both features and target variables delivering better in-sample fit, and providing valid forecasts under contamination such as measurement error or outliers. Finally, we provide two applications in Economics and Finance where PTFA performs competitively compared with PLS and Principal Component Analysis (PCA) at out-of-sample forecasting.

The synergy between different detection methods is a key asset in exoplanetology, allowing for both precise characterization of detected exoplanets and robust constraints even in the case of non-detection. Recently, the interplay between imaging, radial velocities and astrometry has produced significant advancements in exoplanetary science. We report a first result of an ongoing survey performed with SHARK-NIR, the new high-contrast near-infrared imaging camera at the Large Binocular Telescope, in parallel with LBTI/LMIRCam in order to detect planetary companions around stars with significant proper motion anomaly. In this work we focus on HD 57625, a F8 star for which we determine a $4.8^{+3.7}_{-2.9}$Ga age, exhibiting significant astrometric acceleration and for which archival radial velocities hint at the presence of a previously undetected massive long-period companion. We analyse the imaging data we collected with SHARK-NIR and LMIRCam in synergy with the available public SOPHIE radial velocity time series and Hipparcos-Gaia proper motion anomaly. With this joint multi-technique analysis, we aim at characterizing the companion responsible for the astrometric and radial velocity signals. The imaging observations result in a non-detection, indicating the companion to be in the substellar regime. This is confirmed by the synergic analysis of archival radial velocity and astrometric measurements resulting in the detection of HD 57625 b, a ${8.43}_{-0.91}^{+1.10}$M$_{\rm Jup}$ planetary companion with an orbital separation of ${5.70}_{-0.13}^{+0.14}$au and ${0.52}_{-0.03}^{+0.04}$ eccentricity. HD 57625 b joins the small but growing population of giant planets in outer orbits with true mass determination provided by the synergic usage of multiple detection methods, proving once again the importance of multi-technique analysis in providing robust characterization of planetary companions., Comment: 12 pages, 8 figures, accepted for publication in A&A

Precision radial velocity (RV) spectrographs that use adaptive optics (AO) show promise to advance telescope observing capabilities beyond those of seeing-limited designs. We are building a spectrograph for the Large Binocular Telescope (LBT) named iLocater that uses AO to inject starlight directly into single mode fibers (SMF). iLocater's first acquisition camera system (the `SX' camera), which receives light from one of the 8.4m diameter primary mirrors of the LBT, was initially installed in summer 2019 and has since been used for several commissioning runs. We present results from first-light observations that include on-sky measurements as part of commissioning activities. Imaging measurements of the bright B3IV star 2 Cygni ($V=4.98$) resulted in the direct detection of a candidate companion star at an angular separation of only $\theta = 70$ mas. Follow-up AO measurements using Keck/NIRC2 recover the candidate companion in multiple filters. An $R\approx1500$ miniature spectrograph recently installed at the LBT named ``Lili'' provides spatially resolved spectra of each binary component, indicating similar spectral types and strengthening the case for companionship. Studying the multiplicity of young runaway star systems like 2 Cygni ($36.6 \pm 0.5$ Myr) can help to understand formation mechanisms for stars that exhibit anomalous velocities through the galaxy. This on-sky demonstration illustrates the spatial resolution of the iLocater SX acquisition camera working in tandem with the LBT AO system; it further derisks a number of technical hurdles involved in combining AO with Doppler spectroscopy., Comment: Accepted to AJ

Independence complexes of circle graphs are purely combinatorial objects. However, when constructed from some diagram of a link $L$, they reveal topological properties of $L$, more specifically, of its Khovanov homology. We analyze the homotopy type of independence complexes of circle graphs, with a focus on those arising when the graph is bipartite. Moreover, we compute (real) extreme Khovanov homology of a $4$-strand pretzel knot using chord diagrams and independence complexes., Comment: 11 pages, 7 figures

Detecting and characterizing decoherence-inducing noise sources is critical for developing scalable quantum technologies and deploying quantum sensors that operate at molecular scales. Yet, existing methods for such noise spectroscopy face fundamental difficulties, including their reliance on severe approximations and the need for extensively averaged measurements. Here, we propose an alternative approach that processes the commonly performed dynamical decoupling-based coherence measurements using a novel self-consistent optimization framework to extract the noise power spectrum that characterizes the interaction between a qubit or quantum sensor and its environment. Our approach adopts minimal assumptions and is robust to the presence of measurement errors. We introduce a protocol to quantify confidence intervals and a physically motivated heuristic to determine which new dynamical decoupling measurement can improve spectral reconstruction. We employ our method to reconstruct the noise spectrum of a nitrogen-vacancy sensor in diamond, resolving previously undetected nuclear species at the diamond surface and revealing that the previous measurements of low-frequency noise had overestimated its strength by an order of magnitude. Our method's noise spectrum reconstructions uncover previously unsuspected structure and offer unprecedented accuracy, setting the stage for precision noise spectroscopy-based quantum metrology., Comment: 16 pages, 5 figures

Predicting the exact many-body quantum dynamics of polarons in materials with strong carrier-phonon interactions presents a fundamental challenge, often necessitating one to adopt approximations that sacrifice the ability to predict the transition from nonequilibrium relaxation to thermodynamic equilibrium. Here, we exploit a recent breakthrough that generalizes the concept of memory beyond its conventional temporal meaning to also encompass space. Specifically, we leverage our discovery that the dynamics of observables in systems with local couplings satisfy Green's functions with kernels that are local in time and space. This enables us to employ the dynamics of small lattices over short times to predict the dynamics of thermodynamically large lattices over arbitrarily long timescales while circumventing the deleterious impacts of finite-size effects. We thus interrogate the \textit{exact} nonequilibrium formation and migration of polarons in one- (1D) and two-dimensional (2D) systems, revealing that their motion approaches diffusive transport only asymptotically in time and system size. We also compare transport in 1D and 2D systems to investigate the effect of dimension in polaron migration physics, illustrating how energy variations can cause localization -- a phenomenon observable via current microscopy experiments.

Early and accurate melanoma detection is crucial for improving patient outcomes. Recent advancements in artificial intelligence AI have shown promise in this area, but the technologys effectiveness across diverse skin tones remains a critical challenge. This study conducts a systematic review and preliminary analysis of AI based melanoma detection research published between 2013 and 2024, focusing on deep learning methodologies, datasets, and skin tone representation. Our findings indicate that while AI can enhance melanoma detection, there is a significant bias towards lighter skin tones. To address this, we propose including skin hue in addition to skin tone as represented by the LOreal Color Chart Map for a more comprehensive skin tone assessment technique. This research highlights the need for diverse datasets and robust evaluation metrics to develop AI models that are equitable and effective for all patients. By adopting best practices outlined in a PRISMA Equity framework tailored for healthcare and melanoma detection, we can work towards reducing disparities in melanoma outcomes., Comment: 22 pages, 4 figures, 7 tables,accepted for publication in Future of Information and Communication Conference (FICC) 2025, whose proceedings will be published in 'Lecture Notes in Networks and Systems' by Springer Nature

Materials science datasets are inherently heterogeneous and are available in different modalities such as characterization spectra, atomic structures, microscopic images, and text-based synthesis conditions. The advancements in multi-modal learning, particularly in vision and language models, have opened new avenues for integrating data in different forms. In this work, we evaluate common techniques in multi-modal learning (alignment and fusion) in unifying some of the most important modalities in materials science: atomic structure, X-ray diffraction patterns (XRD), and composition. We show that structure graph modality can be enhanced by aligning with XRD patterns. Additionally, we show that aligning and fusing more experimentally accessible data formats, such as XRD patterns and compositions, can create more robust joint embeddings than individual modalities across various tasks. This lays the groundwork for future studies aiming to exploit the full potential of multi-modal data in materials science, facilitating more informed decision-making in materials design and discovery.

The exact quantum dynamics of lattice models can be computationally intensive, especially when aiming for large system sizes and extended simulation times necessary to converge transport coefficients. By leveraging finite memory times to access long-time dynamics using only short-time data, generalized master equations (GMEs) can offer a route to simulating the dynamics of lattice problems efficiently. However, such simulations are limited to small lattices whose dynamics exhibit finite-size artifacts that contaminate transport coefficient predictions. To address this problem, we introduce a novel approach that exploits finite memory in time \textit{and} space to efficiently predict the many-body dynamics of dissipative lattice problems involving short-range interactions. This advance enables one to leverage the short-time dynamics of small lattices to simulate arbitrarily large systems over long times. We demonstrate the strengths of this method by focusing on nonequilibrium polaron relaxation and transport in the dispersive Holstein model, successfully simulating lattice dynamics in one and two dimensions free from finite-size effects, reducing the computational expense of such simulations by multiple orders of magnitude. Our method is broadly applicable and provides an accurate and efficient means to investigate nonequilibrium relaxation with microscopic resolution over mesoscopic length and time scales that are relevant to experiment.

Porphyrins offer a malleable and cost-efficient platform to sculpt bioinspired technologies with tunable charge transfer, energy conversion, and photocatalytic properties. Yet, despite decades of research, the physical mechanisms that determine their electronic spectra remain elusive. Even for metal-free porphyrins, no consensus exists on the origin of the splitting of their $Q$-bands, an energetic region critical in photosynthesis. We leverage our recent statistical treatment of molecular motions in the condensed phase to predict their linear absorption spectra. By bridging exact quantum-dynamical expressions with atomistic simulations, our theory is the first to capture the spectra of representative porphyrins in solution: porphine, tetraphenylporphyrin, and tetraphenylporpholactone. Our work reveals that $Q$-band splitting arises from extreme timescale separation of nuclear motions that turn symmetry-forbidden transitions bright. We exploit these insights to propose and confirm how chemical modifications tune the optical properties of porphyrins, demonstrating the potential for developing design principles to tailor their optoelectronic behavior., Comment: 14 pages, 5 figures

Quantum computing is a rapidly advancing field facing a significant shortage of qualified experts, creating an urgent demand for skilled professionals. In Latin America, quantum education remains in its early stages, further exacerbating the regional talent gap due to deficiencies in educational infrastructure and limited financial support. This work presents the efforts of the Quantum Computing and Artificial Intelligence research group at Universidad Nacional de Colombia to integrate quantum computing into higher education using the European Competence Framework for Quantum Technologies, which offers a standardized approach to defining competency requirements and assessing essential skills in the field. We propose introductory courses aligned with the frameworks guidelines, designed to meet industry standards and reach a broad audience. Additionally, we introduce supplementary resources, including team dynamics and evaluation methodologies, to enhance the educational ecosystem. These initiatives aim to create a sustainable and comprehensive quantum education model across Latin America, to close the regional skills gap, foster inclusivity, and prepare a diverse workforce to contribute innovative solutions on the global stage., Comment: 9 pages, 6 figures

In recent years, the financial sector has faced growing pressure to adopt advanced machine learning models to derive valuable insights while preserving data privacy. However, the highly sensitive nature of financial data presents significant challenges to sharing and collaboration. This paper presents DPFedBank, an innovative framework enabling financial institutions to collaboratively develop machine learning models while ensuring robust data privacy through Local Differential Privacy (LDP) mechanisms. DPFedBank is designed to address the unique privacy and security challenges associated with financial data, allowing institutions to share insights without exposing sensitive information. By leveraging LDP, the framework ensures that data remains confidential even during collaborative processes, providing a crucial solution for privacy-aware machine learning in finance. We conducted an in-depth evaluation of the potential vulnerabilities within this framework and developed a comprehensive set of policies aimed at mitigating these risks. The proposed policies effectively address threats posed by malicious clients, compromised servers, inherent weaknesses in existing Differential Privacy-Federated Learning (DP-FL) frameworks, and sophisticated external adversaries. Unlike existing DP-FL approaches, DPFedBank introduces a novel combination of adaptive LDP mechanisms and advanced cryptographic techniques specifically tailored for financial data, which significantly enhances privacy while maintaining model utility. Key security enhancements include the implementation of advanced authentication protocols, encryption techniques for secure data exchange, and continuous monitoring systems to detect and respond to malicious activities in real-time., Comment: 9 pages, 1 figure

The Fourier Transform (FT) is a fundamental tool that permeates modern science and technology. While chemistry undergraduates encounter the FT as early as second year, their courses often only mention it in passing because computers frequently perform it automatically behind the scenes. Although this automation enables students to focus on `the chemistry', students miss out on an opportunity to understand and use one of the most powerful tools in the scientific arsenal capable of revealing how time-dependent signals encode chemical structure. Although many educational resources introduce chemists to the FT, they often require familiarity with sophisticated mathematical and computational concepts. Here, we present a series of three self-contained, Python-based laboratory activities for undergraduates to understand the FT and apply it to analyze audio signals, an infrared (IR) spectroscopy interferogram, and a nuclear magnetic resonance (NMR) free induction decay (FID). In these activities, students observe how the FT reveals and quantifies the contribution of each frequency present in a temporal signal and how decay timescales dictate signal broadening. Our activities empower students with the tools to transform their own temporal datasets (e.g., FID) to a frequency spectrum. To ensure accessibility of the activities and lower the barrier to implementation, we utilize Google Colab's open-source, cloud-based platform to run Jupyter notebooks. We also offer a pre-laboratory activity that introduces students to the basics of Python and the Colab platform, and reviews the math and programming skills needed to complete the lab activities. These lab activities help students build a qualitative, quantitative, and practical understanding of the FT., Comment: 11 pages, 5 figures

The MMT Adaptive optics exoPlanet characterization System (MAPS) is currently in its engineering phase, operating on-sky at the MMT Telescope on Mt. Hopkins in southern Arizona. The MAPS Adaptive Secondary Mirror's actuators are controlled by a closed loop modified PID control law and an open loop feed-forward law, which in combination allows for faster actuator response time. An essential element of achieving the secondary's performance goals involves the process of PID gain tuning. To start, we briefly discuss the design of the MAPS ASM and its actuators. We then describe the actuator positional control system and control law. Next, we discuss a few of the issues that make ASM tuning difficult. We then outline our initial attempts at tuning the actuator controllers and discuss the use of actuator positional power spectra for both tuning and determining the health and failure states of individual actuators. We conclude by presenting the results of our latest round of tuning configuration trials, which have been successful at decreasing mirror latency, increasing operational mirror modes and improving image PSF., Comment: To be published in Proceedings of SPIE, Optics and Photonics 2024. 24 pages, 16 figures, 5 tables. Lead Author, J. Johnson. Second Lead Author, A. Vaz. Project P.I., K. Morzinski. Project Second P.I.s, J. Patience and S. Sivanandam, Project Manager, M. Montoya

The growth of the tech startup ecosystem in Latin America (LATAM) is driven by innovative entrepreneurs addressing market needs across various sectors. However, these startups encounter unique challenges and risks that require specific management approaches. This paper explores a case study with the Total Addressable Market (TAM), Serviceable Available Market (SAM), and Serviceable Obtainable Market (SOM) metrics within the context of the online food delivery industry in LATAM, serving as a model for valuing startups using the Discounted Cash Flow (DCF) method. By analyzing key emerging powers such as Argentina, Colombia, Uruguay, Costa Rica, Panama, and Ecuador, the study highlights the potential and profitability of AI-driven startups in the region through the development of a ranking of emerging powers in Latin America for tech startup investment. The paper also examines the political, economic, and competitive risks faced by startups and offers strategic insights on mitigating these risks to maximize investment returns. Furthermore, the research underscores the value of diversifying investment portfolios with startups in emerging markets, emphasizing the opportunities for substantial growth and returns despite inherent risks., Comment: 21 pages, 7 figures, 8 tables, Accepted for publication to the International Association for Applied Business Research Journal (IAABR)

Bell's states are among the most useful in quantum computing. These state are an orthonormal base of entagled states with two qubits. We propose alternative bases of entangled states. Some of these states depend on a continuous parameter. We present the quantum circuit and code of these alternative bases. In addition, we study quantum teleportation with these entangled states and present their quantum circuits and codes associated., Comment: 39 pages, 15 figures, minor corrections. Comments welcome

As wavefront quality demands tighten on space systems for applications such as astronomy and laser communication, mounting small optics such that the wavefront is undisturbed, positioning is adjustable and the design is producible, while surviving harsh space environments, is a continuing challenge. We designed multiple candidate flexure mounts to support small optics (up to 50 mm diameter, and over 100 grams) to survive the qualification and acceptance tests of small spacecraft and units as defined in ISO 19683 and a mounting structure which is adjustable in decenter [+/-0.5mm], tip/tilt +/-0.5deg, and piston [+/-0.25mm]. We will present design details along with measurements showing less than approximately lambda/10 wavefront contribution from the optic bonding process, along with thermal and multi-axis vibration test data showing the mounted optics survived the acceptance testing loads and are suitable for operation in a wide range of harsh environments.

Many interventions are both beneficial to initiate and harmful to stop. Traditionally, to determine whether to deploy that intervention in a time-limited way depends on if, on average, the increase in the benefits of starting it outweigh the increase in the harms of stopping it. We propose a novel causal estimand that provides a more nuanced understanding of the effects of such treatments, particularly, how response to an earlier treatment (e.g., treatment initiation) modifies the effect of a later treatment (e.g., treatment discontinuation), thus learning if there are effects among the (un)affected. Specifically, we consider a marginal structural working model summarizing how the average effect of a later treatment varies as a function of the (estimated) conditional average effect of an earlier treatment. We allow for estimation of this conditional average treatment effect using machine learning, such that the causal estimand is a data-adaptive parameter. We show how a sequentially randomized design can be used to identify this causal estimand, and we describe a targeted maximum likelihood estimator for the resulting statistical estimand, with influence curve-based inference. Throughout, we use the Adaptive Strategies for Preventing and Treating Lapses of Retention in HIV Care trial (NCT02338739) as an illustrative example, showing that discontinuation of conditional cash transfers for HIV care adherence was most harmful among those who most had an increase in benefits from them initially.

The rapid growth of quantum computing in the last few years has led many countries to make relevant public investments in that field. However, Colombia lacks any investment or legislation in this area. Most previous studies have focused on other countries, contributing to the region's significant lag. In this paper, we propose efforts to include quantum computing as a fundamental pillar of Colombia's development plan. In this research we involved three stakeholders: academia (Universidad Nacional de Colombia), industry (Alianza Team), and government (Vice Ministry of Digital Transformation). We anticipate that our work will provide a connection between all stakeholders involved in public investments in quantum technology in the country and will facilitate its legislation., Comment: 5 pages, 3 figures

We introduce a toric version of the sheaf of logarithmic vector fields along a divisor of a simplicial toric variety. The notion is also relevant for algebraically independent families of polynomials in the Cox ring. We provide a generalisation of the Saito criterion for the freeness of the toric logarithmic sheaf. We explain the relationship between this sheaf and the usual sheaf of logarithmic vector fields and the connection with holomorphic foliations on toric varieties., Comment: Comments welcome!

With the commissioning of the refurbished adaptive secondary mirror (ASM) for the 6.5-meter MMT Observatory under way, special consideration had to be made to properly calibrate the mirror response functions to generate an interaction matrix (IM). The commissioning of the ASM is part of the MMT Adaptive optics exoPlanet characterization System (MAPS) upgrade the observatory's legacy adaptive optics (AO) system. Unlike most AO systems, MAPS employs a convex ASM which prevents the introduction of a calibration source capable of simultaneously illuminating its ASM and wavefront sensor (WFS). This makes calibration of the AO system a significant hurdle in commissioning. To address this, we have employed a hybrid calibration strategy we call the Efficient Synthesis of Calibrations for Adaptive Optics through Pseudo-synthetic and Empirical methods (ESCAPE). ESCAPE combines the DO-CRIME on-sky calibration method with the SPRINT method for computing pseudo-synthetic calibration matrices. To monitor quasi-static system change, the ESCAPE methodology rapidly and continuously generates pseudo-synthetic calibration matrices using continual empirical feedback in either open or closed-loop. In addition, by measuring the current IM in the background while in close-loop, we are also able to measure the optical gains for pyramid wavefront sensor (PyWFS) systems. In this paper, we will provide the mathematical foundation of the ESCAPE calibration strategy and on-sky results from its application in calibrating the MMT Observatory's ASM. Additionally, we will showcase the validation of our approach from our AO testbed and share preliminary on-sky results from MMT., Comment: 16 pages, 9 figures, Submission to SPIE Adaptive Optics Systems IX

We study G-graded Artinian algebras having Poincar\'e duality and their Lefschetz properties. We prove the equivalence between the toric setup and the G-graded one, and a Hessian criterion in the G-graded setup. We provide an application to toric geometry., Comment: 21 pages. v2: we added some references to the previous literature. v3: same as v2, we disposed of some spurious files

Digital Breast Tomosynthesis (DBT) is an advanced breast imaging modality that offers superior lesion detection accuracy compared to conventional mammography, albeit at the trade-off of longer reading time. Accelerating lesion detection from DBT using deep learning is hindered by limited data availability and huge annotation costs. A possible solution to this issue could be to leverage the information provided by a more widely available modality, such as mammography, to enhance DBT lesion detection. In this paper, we present a novel framework, CoMoTo, for improving lesion detection in DBT. Our framework leverages unpaired mammography data to enhance the training of a DBT model, improving practicality by eliminating the need for mammography during inference. Specifically, we propose two novel components, Lesion-specific Knowledge Distillation (LsKD) and Intra-modal Point Alignment (ImPA). LsKD selectively distills lesion features from a mammography teacher model to a DBT student model, disregarding background features. ImPA further enriches LsKD by ensuring the alignment of lesion features within the teacher before distilling knowledge to the student. Our comprehensive evaluation shows that CoMoTo is superior to traditional pretraining and image-level KD, improving performance by 7% Mean Sensitivity under low-data setting. Our code is available at https://github.com/Muhammad-Al-Barbary/CoMoTo ., Comment: ADSMI @ MICCAI 2024

We show that quantum entanglement states are associated with multilinear polynomials that cannot be factored. By using these multilinear polynomials, we propose a geometric representation for entanglement states. In particular, we show that the Bell's states are associated with non-factorable real multilinear polynomial, which can be represented geometrically by three-dimensional surfaces. Furthermore, in this framework, we show that a quantum circuit can be seen as a geometric transformations of plane geometry. This phenomenon is analogous to gravity, where matter curves space-time. In addition, we show an analogy between quantum teleportation and operations involving multilinear polynomials., Comment: 16 pages, 2 figures. Minor corrections. Comments welcome

The real anisotropic Littlewood's $4 / 3$ inequality is an extension of a famous result obtained in 1930 by J. E. Littlewood. It asserts that, for $a , b \in ( 0 , \infty )$, the following conditions are equivalent: $\bullet$ There is an optimal constant $\mathsf{L}_{ a , b }^{ \mathbb{R} } \in [ 1 , \infty )$ such that \[ \Biggl ( \, \sum_{ k = 1 }^{ \infty } \biggl ( \, \sum_{ j = 1 }^{ \infty } \bigl \lvert A \bigl ( \boldsymbol{e}^{ (k) } , \boldsymbol{e}^{ (j) } \bigr ) \bigr \rvert^a \biggr )^{ \frac{b}{a} } \Biggr )^{ \frac{1}{b} } \leq \mathsf{L}_{ a , b }^{ \mathbb{R} } \cdot \lVert A \rVert \] for every continuous bilinear form $A \colon c_0 \times c_0 \to \mathbb{R}$. $\bullet$ The values $a , b$ satisfy $a , b \geq 1$ and $\frac{1}{a} + \frac{1}{b} \leq \frac{3}{2}$. Several authors have obtained the values of $\mathsf{L}_{ a , b }^{ \mathbb{R} }$ for diverse pairs $( a , b )$. In this paper we provide the complete list of such optimal values, as well as new estimates for $\mathsf{L}_{ a , b }^{ \mathbb{C} }$ (the analog for continuous $\mathbb{C}$-bilinear forms), which are exact in several cases. As an application we prove, in terms of the values $\mathsf{L}_{ 1 , r }^{ \mathbb{C} }$, a variant of Khinchin's inequality for Steinhaus variables, and we determine all the optimal $( q , s )$-cotype constants of the spaces $\ell_1 ( \mathbb{K} )$ (with $\mathbb{K} = \mathbb{R}$ or $\mathbb{C}$) in terms of the values $\mathsf{L}_{ 1 , q }^{ \mathbb{R} }$., Comment: Corrected typos and improved presentation and formatting. Added the section about cotype

Orthogonal arrays play a fundamental role in many applications. However, constructing orthogonal arrays with the required parameters for an application usually is extremely difficult and, sometimes, even impossible. Hence there is an increasing need for a relaxation of orthogonal arrays to allow a wider flexibility. The latter has lead to various types of arrays under the name of ``nearly-orthogonal arrays'', and less often ``almost orthogonal arrays''. The aim of this paper is twofold. On the one hand, we review all the existing relaxations, comparing and discussing them in depth. On the other hand, we explore how to find almost orthogonal arrays three ways: using integer programming, local search meta-heuristics and algebraic methods. We compare all our search results with the ones existing in the literature, and we show that they are competitive, improving some of the existing arrays for many non-orthogonality measures. All our found almost orthogonal arrays are available at a public repository., Comment: 59 pages