Search

The virtual cohomological dimension of $\operatorname{Out}(F_n)$ is given precisely by the dimension of the spine of Culler--Vogtmann Outer space. However, the dimension of the spine of untwisted Outer space for a general right-angled Artin group $A_\Gamma$ does not necessarily match the virtual cohomological dimension of the untwisted subgroup $U(A_\Gamma) \leq \operatorname{Out}(A_\Gamma)$. Under certain graph-theoretic conditions, we perform an equivariant deformation retraction of this spine to produce a new contractible cube complex upon which $U(A_\Gamma)$ acts properly and cocompactly. Furthermore, we give conditions for when the dimension of this complex realises the virtual cohomological dimension of $U(A_\Gamma)$., Comment: 36 pages, 13 figures. Comments welcome!

Recent advances in neural recording technology allow simultaneously recording action potentials from hundreds to thousands of neurons in awake, behaving animals. However, characterizing spike patterns in the resulting data, and linking these patterns to behaviour, remains a challenging task. The lack of a rigorous mathematical language for variable numbers of events (spikes) emitted by multiple agents (neurons) is an important limiting factor. We introduce a new mathematical operation to decompose complex spike patterns into a set of simple, structured elements. This creates a mathematical language that allows comparing spike patterns across trials, detecting sub-patterns, and making links to behaviour via a clear distance measure. We apply the method to dual Utah array recordings from macaque prefrontal cortex, where this technique reveals previously unseen structure that can predict both memory-guided decisions and errors in a virtual-reality working memory task. These results demonstrate that this technique provides a powerful new approach to understand structure in the spike times of neural populations, at a scale that will continue to grow more and more rapidly in upcoming years.

Magnetic resonance (MR)-guided radiation therapy (RT) is enhancing head and neck cancer (HNC) treatment through superior soft tissue contrast and longitudinal imaging capabilities. However, manual tumor segmentation remains a significant challenge, spurring interest in artificial intelligence (AI)-driven automation. To accelerate innovation in this field, we present the Head and Neck Tumor Segmentation for MR-Guided Applications (HNTS-MRG) 2024 Challenge, a satellite event of the 27th International Conference on Medical Image Computing and Computer Assisted Intervention. This challenge addresses the scarcity of large, publicly available AI-ready adaptive RT datasets in HNC and explores the potential of incorporating multi-timepoint data to enhance RT auto-segmentation performance. Participants tackled two HNC segmentation tasks: automatic delineation of primary gross tumor volume (GTVp) and gross metastatic regional lymph nodes (GTVn) on pre-RT (Task 1) and mid-RT (Task 2) T2-weighted scans. The challenge provided 150 HNC cases for training and 50 for testing, hosted on Grand Challenge using a Docker submission framework. In total, 19 independent teams from across the world qualified by submitting both their algorithms and corresponding papers, resulting in 18 submissions for Task 1 and 15 submissions for Task 2. Evaluation using the mean aggregated Dice Similarity Coefficient showed top-performing AI methods achieved scores of 0.825 in Task 1 and 0.733 in Task 2. These results surpassed clinician interobserver variability benchmarks, marking significant strides in automated tumor segmentation for MR-guided RT applications in HNC., Comment: For HNTS-MRG 2024 volume of Lecture Notes in Computer Science

Millimeter-wave refracting telescopes targeting the degree-scale structure of the cosmic microwave background (CMB) have recently grown to diffraction-limited apertures of over 0.5 meters. These instruments are entirely housed in vacuum cryostats to support their sub-kelvin bolometric detectors and to minimize radiative loading from thermal emission due to absorption loss in their transmissive optical elements. The large vacuum window is the only optical element in the system at ambient temperature, and therefore minimizing loss in the window is crucial for maximizing detector sensitivity. This motivates the use of low-loss polymer materials and a window as thin as practicable. However, the window must simultaneously meet the requirement to keep sufficient vacuum, and therefore must limit gas permeation and remain mechanically robust against catastrophic failure under pressure. We report on the development of extremely thin composite polyethylene window technology that meets these goals. Two windows have been deployed for two full observing seasons on the BICEP3 and BA150 CMB telescopes at the South Pole. On BICEP3, the window has demonstrated a 6% improvement in detector sensitivity., Comment: 20 pages, 12 figures, 4 tables

In this report, we share insights from a Research-Practice-Industry Partnership (RPIP) that explored mathematics instructional practices with support of digital mathematics tools. RPIPs bring together researchers, practitioners, and product developers, with each party having an equal voice, in a rapid-cycle model for edtech research and development. We framed this RPIP using the principles of Universal Design for Learning (UDL): provide multiple means of Engagement, Representation, and Action & Expression. These principles support learner variability, improve accessibility, and are closely aligned with mathematics education research, which highlights the multimodal nature of mathematics and the need to use and connect multiple representations to help students develop understanding of mathematics concepts. [This report was produced in partnership with Creativity Labs with funding support from Texthelp.]

Intels efforts to build a practical quantum computer are focused on developing a scalable spin-qubit platform leveraging industrial high-volume semiconductor manufacturing expertise and 300 mm fabrication infrastructure. Here, we provide an overview of the design, fabrication, and demonstration of a new customized quantum test chip, which contains 12-quantum-dot spin-qubit linear arrays, code named Tunnel Falls. These devices are fabricated using immersion and extreme ultraviolet lithography (EUV), along with other standard high-volume manufacturing (HVM) processes, as well as production-level process control. We present key device features and fabrication details, as well as qubit characterization results confirming device functionality. These results corroborate our fabrication methods and are a crucial step towards scaling of extensible 2D qubit array schemes.

In this article, we establish a large sieve inequality for additive characters to moduli in the range of appropriate integer polynomials of degree two. As an application, we derive a weighted zero-density estimate for twists of $L$-functions associated to multiplicative characters with conductor of this form.

Latching techniques are widely used to enhance readout of qubits. These methods require precise tuning of multiple tunnel rates, which can be challenging to achieve under realistic experimental conditions, such as when a qubit is coupled to a single reservoir. Here, we present a method for single-shot measurement of a quantum dot qubit with a single reservoir using a latched-readout scheme. Our approach involves pulsing a barrier gate to dynamically control qubit-to-reservoir tunnel rates, a method that is readily applicable to the latched readout of various spin-based qubits. We use this method to enable qubit state latching and to reduce the qubit reset time in measurements of coherent Larmor oscillations of a Si/SiGe quantum dot hybrid qubit., Comment: 6 pages, including supplemental materials

In the initial stages of ITER operation, ELM mitigation systems need to be commissioned. This requires controlled flat-top operation in type-I ELMy H-mode regimes. Hydrogen or helium plasma discharges are used exclusively in these stages to ensure negligible production of neutrons from fusion reactions. With the expected higher L-H power threshold of hydrogen and helium plasmas compared to corresponding D and D/T plasmas, it is uncertain whether available auxiliary power systems are sufficient to operate in stable type-I ELMy H-mode. This has been investigated using integrated core and edge/SOL/divertor modelling with JINTRAC. Assuming that the L-H power threshold is well captured by the Martin08 scaling law, the presented simulations have found that 30 MW of ECRH power is likely required for the investigated hydrogen plasma scenarios, rather than the originally planned 20 MW in the 2016 Staged Approach ITER Baseline. However, past experiments have shown that a small helium fraction (~10 %) can considerably reduce the hydrogen plasma L-H power threshold. Assuming that these results extrapolate to ITER operation regimes, the 7.5MA/2.65T hydrogen plasma scenario is likely to access stable type-I ELMy H-mode operation also at 20 MW of ECRH., Comment: 22 pages, 10 figures

We perform readout of a quantum-dot hybrid qubit coupled to a superconducting resonator through a parametric, longitudinal interaction mechanism. Our experiments are performed with the qubit and resonator frequencies detuned by $\sim$10 GHz, demonstrating that longitudinal coupling can facilitate semiconductor qubit operation in the 'ultra-dispersive' regime of circuit quantum electrodynamics., Comment: Main text and Supplementary Information; 13 pages, 7 figures

We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded Kolmogorov maps and coupling terms are defined by nonlinear functions taking values in $(0,1)$. These couplings describe the proportions of individuals dispersing between regions. We first give a brief survey of similar discrete-time dispersal models. We then derive sufficient conditions for the stability/instability of the extinction equilibrium, for the existence of a positive fixed point and for ensuring uniform strong persistence. Finally we numerically explore a planar version of our model in a source-sink context, to show some of the qualitative behaviour that the model we consider can capture: for example, periodic behaviour and dynamics reminiscent of chaos.

The rapid development of quantum dot (QD) devices for quantum computing has necessitated more efficient and automated methods for device characterization and tuning. This work demonstrates the feasibility and advantages of applying explainable machine learning techniques to the analysis of quantum dot measurements, paving the way for further advances in automated and transparent QD device tuning. Many of the measurements acquired during the tuning process come in the form of images that need to be properly analyzed to guide the subsequent tuning steps. By design, features present in such images capture certain behaviors or states of the measured QD devices. When considered carefully, such features can aid the control and calibration of QD devices. An important example of such images are so-called $\textit{triangle plots}$, which visually represent current flow and reveal characteristics important for QD device calibration. While image-based classification tools, such as convolutional neural networks (CNNs), can be used to verify whether a given measurement is $\textit{good}$ and thus warrants the initiation of the next phase of tuning, they do not provide any insights into how the device should be adjusted in the case of $\textit{bad}$ images. This is because CNNs sacrifice prediction and model intelligibility for high accuracy. To ameliorate this trade-off, a recent study introduced an image vectorization approach that relies on the Gabor wavelet transform (Schug $\textit{et al.}$ 2024 $\textit{Proc. XAI4Sci: Explainable Machine Learning for Sciences Workshop (AAAI 2024) (Vancouver, Canada)}$ pp 1-6). Here we propose an alternative vectorization method that involves mathematical modeling of synthetic triangles to mimic the experimental data. Using explainable boosting machines, we show that this new method offers superior explainability of model prediction without sacrificing accuracy., Comment: 20 pages, 5 figures, abbreviated version published in Proceedings of the XAI4Sci: Explainable machine learning for sciences workshop at AAAI 2024, (Vancouver, Canada)

We have carried out a SEM-EPMA-TEM study to determine the textures and compositions of relict primary iron sulfides and their alteration products in a suite of moderately to heavily-altered CM1 carbonaceous chondrites. We observed four textural groups of altered primary iron sulfides: 1) pentlandite+phyllosilicate (2P) grains, characterized by pentlandite with submicron lenses of phyllosilicates, 2) pyrrhotite+pentlandite+magnetite (PPM) grains, characterized by pyrrhotite-pentlandite exsolution textures with magnetite veining and secondary pentlandite, 3) pentlandite+serpentine (PS) grains, characterized by relict pentlandite exsolution, serpentine, and secondary pentlandite, and 4) pyrrhotite+pentlandite+magnetite+serpentine (PPMS) grains, characterized by features of both the PPM and PS grains. We have determined that all four groups were initially primary iron sulfides, which formed from crystallization of immiscible sulfide melts within silicate chondrules in the solar nebula. The fact that such different alteration products could result from the same precursor sulfides within even the same meteorite sample further underscores the complexity of the aqueous alteration environment for the CM chondrites. The different alteration reactions for each textural group place constraints on the mechanisms and conditions of alteration with evidence for acidic environments, oxidizing environments, and changing fluid compositions (Ni-bearing and Si-Mg-bearing)., Comment: 53 pages, 10 figures, 2 tables, appendix containing 3 additional figures and 5 additional tables

The moving discontinuous Galerkin method with interface condition enforcement (MDG-ICE) is a high-order, r-adaptive method that treats the grid as a variable and weakly enforces the conservation law, constitutive law, and corresponding interface conditions in order to implicitly fit high-gradient flow features. In this paper, we develop an optimization solver based on the Levenberg-Marquardt algorithm that features an anisotropic, locally adaptive penalty method to enhance robustness and prevent cell degeneration in the computation of hypersonic, viscous flows. Specifically, we incorporate an anisotropic grid regularization based on the mesh-implied metric that inhibits grid motion in directions with small element length scales, an element shape regularization that inhibits nonlinear deformations of the high-order elements, and a penalty regularization that penalizes degenerate elements. Additionally, we introduce a procedure for locally scaling the regularization operators in an adaptive, elementwise manner in order to maintain grid validity. We apply the proposed MDG-ICE formulation to two- and three-dimensional test cases involving viscous shocks and/or boundary layers, including Mach 17.6 hypersonic viscous flow over a circular cylinder and Mach 5 hypersonic viscous flow over a sphere, which are very challenging test cases for conventional numerical schemes on simplicial grids. Even without artificial dissipation, the computed solutions are free from spurious oscillations and yield highly symmetric surface heat-flux profiles.

In this paper, we use the Weyl-bound for Dirichlet $L$-functions to derive zero-density estimates for $L$-functions associated to families of fixed-order Dirichlet characters. The results improve on previous bounds given by the author when $\sigma$ is sufficiently distanced from the critical line.

The main purpose of this paper is to establish bounds on the second moment of $L\big(\tfrac{1}{2}+it,\chi\big)$, averaged over families of fixed order characters. A discrete version of the main result is also stated, from which zero-density estimates pertaining to fixed order characters are derived.

This study examines the complex interplay of gender and other demographics on continuation rates in high school physics. Using a diverse dataset that combines demographics from the Canadian Census and eleven years of gendered enrolment data from the Ontario Ministry of Education, we track student cohorts as they transition from mandatory science to elective physics courses. We then employ hierarchical linear modelling to quantify the interaction effects between gender and other demographics, providing a detailed perspective on the on continuation in physics. Our results indicate the racial demographics of a school's neighbourhood have a limited impact on continuation once controlling for other factors such as socioeconomic status, though neighbourhoods with a higher Black population were a notable exception, consistently exhibiting significantly lower continuation rates for both male and female students. A potential role model effect related to parental education was also found as the proportion of parents with STEM degrees correlates positively with increased continuation, whereas an increase in non-STEM degrees corresponds with a reduced SCR. The most pronounced effects are school-level factors. Continuation rates in physics are very strongly correlated with continuation in chemistry or calculus - effects which are much stronger for male than female students. Conversely, continuation in biology positively correlates with the continuation of female students in physics, with little to no effect found for male students. Nevertheless, the effect sizes observed for chemistry and calculus markedly outweigh that for biology. This is further evidence that considering STEM as a homogeneous subject when examining gender disparities is misguided. These insights can guide future education policies and initiatives to increase continuation rates and foster greater gender equity in physics education., Comment: 17 pages, 5 figures, 2 tables