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For $\mathbb Q$-factorial klt algebraically integrable adjoint foliated structures, we prove the cone theorem, the contraction theorem, and the existence of flips. Therefore, we deduce the existence of the minimal model program for such structures. We also prove the base-point-freeness theorem for such structures of general type and establish an adjunction formula and the existence of $\mathbb Q$-factorial quasi-dlt modifications for algebraically integrable adjoint foliated structures., Comment: 50 pages

Based on the PubMed database, there are around 260 manuscripts describing nanothermometers. These research articles detail the synthesis, performance, and application of intracellular nanothermometers. This intracellular prevalence is due to the significant importance, complexity, and utility of the intracellular compartments for understanding cell metabolism and disease treatment. However, in recent years, the extracellular environment of the cell has emerged as a crucial factor in medicine, particularly in hyperthermia and immunotherapy. Despite this, we have not seen evidence in the literature describing the utilization or performance of a nanothermometer designed for extracellular temperature measurements. This oversight not only neglects the potential for measuring extracellular temperature but also fails to address the extracellular environment of the cell. Here, we introduce a nanothermometer designed specifically for measuring extracellular temperature by directly converting serum proteins into nanothermometers (either unmodified or labeled with the clinically approved dye Fluorescein). Additionally, leveraging the extracellular localization of these nanothermometers, we demonstrate (1) the enhancement of their temperature sensitivity by combining them with gold nanorods, and (2) their capability to generate damage and disrupt the plasma membrane, thus opening the door to their use as photodynamic therapy agents. We firmly believe that these advancements represent not only a broadening of the applications of nanothermometry but also a pioneering step in showcasing the ability of nanothermometers to induce cell death., Comment: 18 pages, 5 figures

Simon's algorithm was one of the first problems to demonstrate a genuine quantum advantage. The algorithm, however, assumes access to noise-free qubits. In our work we use Simon's algorithm to benchmark the error rates of devices currently available in the "quantum cloud." As a main result we obtain an objective comparison between the different physical platforms made available by IBM and IonQ. Our study highlights the importance of understanding the device architectures and chip topologies when transpiling quantum algorithms onto hardware. For instance, we demonstrate that two-qubit operations on spatially separated qubits on superconducting chips should be avoided.

We introduce the AI Security Pyramid of Pain, a framework that adapts the cybersecurity Pyramid of Pain to categorize and prioritize AI-specific threats. This framework provides a structured approach to understanding and addressing various levels of AI threats. Starting at the base, the pyramid emphasizes Data Integrity, which is essential for the accuracy and reliability of datasets and AI models, including their weights and parameters. Ensuring data integrity is crucial, as it underpins the effectiveness of all AI-driven decisions and operations. The next level, AI System Performance, focuses on MLOps-driven metrics such as model drift, accuracy, and false positive rates. These metrics are crucial for detecting potential security breaches, allowing for early intervention and maintenance of AI system integrity. Advancing further, the pyramid addresses the threat posed by Adversarial Tools, identifying and neutralizing tools used by adversaries to target AI systems. This layer is key to staying ahead of evolving attack methodologies. At the Adversarial Input layer, the framework addresses the detection and mitigation of inputs designed to deceive or exploit AI models. This includes techniques like adversarial patterns and prompt injection attacks, which are increasingly used in sophisticated attacks on AI systems. Data Provenance is the next critical layer, ensuring the authenticity and lineage of data and models. This layer is pivotal in preventing the use of compromised or biased data in AI systems. At the apex is the tactics, techniques, and procedures (TTPs) layer, dealing with the most complex and challenging aspects of AI security. This involves a deep understanding and strategic approach to counter advanced AI-targeted attacks, requiring comprehensive knowledge and planning., Comment: SPIE DCS 2024

Estimation of nearshore bathymetry is important for accurate prediction of nearshore wave conditions. However, direct data collection is expensive and time-consuming while accurate airborne lidar-based survey is limited by breaking waves and decreased light penetration affected by water turbidity. Instead, tower-based platforms or Unmanned Aircraft System (UAS) can provide indirect video-based observations. The video-based time-series imagery provides wave celerity information and time-averaged (timex) or variance enhanced (var) images identify persistent regions of wave breaking. In this work, we propose a rapid and improved bathymetry estimation method that takes advantage of image-derived wave celerity and a first-order bathymetry estimate from Parameter Beach Tool (PBT), software that fits parameterized sandbar and slope forms to the timex or var images. Two different sources of the data, PBT and wave celerity, are combined or blended optimally based on their assumed accuracy in a statistical framework. The PBT-derived bathymetry serves as "prior" coarse-scale background information and then is updated and corrected with the imagery-derived wave data through the dispersion relationship, which results in a better bathymetry estimate that is consistent with imagery-based wave data. To illustrate the accuracy of our proposed method, imagery data sets collected in 2017 at the US Army EDRC's Field Research Facility in Duck, NC under different weather and wave height conditions are tested. Estimated bathymetry profiles are remarkably close to the direct survey data. The computational time for the estimation from PBT-based bathymetry and imagery-derived wave celerity is only about five minutes on a free Google Cloud node with one CPU core. These promising results indicate the feasibility of reliable real-time bathymetry imaging during a single flight of UAS., Comment: 21 pages, 14 figures, preprints

We present an adjunction formula for foliations on varieties and we consider applications of the adjunction formula to the cone theorem for rank one foliations and the study of foliation singularities., Comment: 37 pages. Exposition improved based on referee's suggestions. Final version. Mathematische Annalen (to appear)

Flare frequency distributions represent a key approach to addressing one of the largest problems in solar and stellar physics: determining the mechanism that counter-intuitively heats coronae to temperatures that are orders of magnitude hotter than the corresponding photospheres. It is widely accepted that the magnetic field is responsible for the heating, but there are two competing mechanisms that could explain it: nanoflares or Alfv\'en waves. To date, neither can be directly observed. Nanoflares are, by definition, extremely small, but their aggregate energy release could represent a substantial heating mechanism, presuming they are sufficiently abundant. One way to test this presumption is via the flare frequency distribution, which describes how often flares of various energies occur. If the slope of the power law fitting the flare frequency distribution is above a critical threshold, $\alpha=2$ as established in prior literature, then there should be a sufficient abundance of nanoflares to explain coronal heating. We performed $>$600 case studies of solar flares, made possible by an unprecedented number of data analysts via three semesters of an undergraduate physics laboratory course. This allowed us to include two crucial, but nontrivial, analysis methods: pre-flare baseline subtraction and computation of the flare energy, which requires determining flare start and stop times. We aggregated the results of these analyses into a statistical study to determine that $\alpha = 1.63 \pm 0.03$. This is below the critical threshold, suggesting that Alfv\'en waves are an important driver of coronal heating., Comment: 1,002 authors, 14 pages, 4 figures, 3 tables, published by The Astrophysical Journal on 2023-05-09, volume 948, page 71

We show that termination of flips for $\mathbb Q$-factorial klt pairs in dimension $r$ implies existence of minimal models for algebraically integrable foliations of rank $r$ with log canonical singularities over a $\mathbb Q$-factorial klt projective variety., Comment: 14 pages

We discuss a conjecture of Shokurov on the semi-ampleness of the moduli part of a general fibration., Comment: 28 pages, comments welcome!

Ultra-high-temperature ceramics (UHTCs) are optimal structural materials for applications that require extreme temperature resilience, resistance to chemically aggressive environments, wear, and mechanical stress. Processing UHTCs with laser-based additive manufacturing (AM) has not been fully realized due to a variety of obstacles. In this work, selective laser reaction sintering (SLRS) techniques were investigated for the production of near net-shape UHTC ceramics such as HfC, ZrC, TiC, HfN, ZrN, and TiN. Group IV transition metal and metal oxide precursor materials were chemically converted and reaction-bonded into layers of UHTCs using single-step selective laser processing in CH4 or NH3 gas that might be compatible with prevailing powder bed fusion techniques. Conversion of either metals (Hf, Zr and Ti) or metal oxides (HfO2, ZrO2, and TiO2) particles was first investigated to examine reaction mechanisms and volume changes associated with SLRS of single-component precursor systems. SLRS processing of metal or metal oxide alone produced near stoichiometric UHTC phases with yields up to 100 wt% total for carbides and nitrides. However, for single component precursors, gas-solid reactivity induced volumetric changes resulted in residual stresses and cracking in the product layer. To mitigate conversion-induced stresses, composite metal/metal oxide precursors were employed to compensate for the volume changes of either the metal (which expands during conversion) or the metal oxide precursor (which contracts)., Comment: 58 pages, 17 figures

Selective laser reaction sintering techniques (SLRS) techniques were investigated for the production of near net-shape non-oxide ceramics including SiC, Si$_3$N$_4$, and HfC/SiC composites that might be compatible with prevailing powder bed fusion additive manufacturing processes. Reaction bonded layers of covalent ceramics were produced using in-situ reactions that occur during selective laser processing and layer formation. During SLRS, precursor materials composed of metal and/or metal oxide powders were fashioned into powder beds for conversion to non-oxide ceramic layers. Laser-processing was used to initiate simultaneous chemical conversion and local interparticle bonding of precursor particles in CH4 or NH3 gases. Several factors related to the reaction synthesis process (precursor chemistry, gas-solid and gas-liquid synthesis mechanisms, precursor vapor pressures) were investigated in relation to resulting microstructures and non-oxide yields. Results indicated that the volumetric changes which occurred during in-situ conversion of single component precursors negatively impacted the surface layer microstructure. To circumvent the internal stresses and cracking that accompanied the conversion of Si or Hf (that expands upon conversion) or SiO$_x$ (that contracts during conversion), optimized ratios of the precursor constituents were used to produce near isovolumetric conversion to the product phase. The results demonstrate that under appropriate processing conditions and precursor selection, the formation of near net-shape SiC and SiC composites might be achieved through single-step AM-compatible techniques., Comment: 31 pages, 11 figures

Ultra-high-temperature ceramics (UHTCs) are candidate structural materials for applications that require resiliency to extreme temperature (>2000{\deg}C), high mechanical loads, or aggressive oxidizing environments. Processing UHTC transition metal carbides as standalone materials using additive manufacturing (AM) methods has not been fully realized due to their extremely slow atomic diffusivities that impede sintering and large volume changes during indirect AM that can induce defect structures. In this work, a two-step, reactive AM approach was studied for the formation of the ultra-high temperature ceramic TiCx. Readily available equipment including a polymer powder bed fusion AM machine and a traditional tube furnace were used to produce UHTC cubes and lattice structures with sub-millimeter resolution. This processing scheme incorporated, (1) selective laser sintering of a Ti precursor mixed with a phenolic binder for green body shaping, and (2) ex-situ, isothermal gas-solid conversion of the green body in CH4 to form TiCx structures. Reactive post-processing in CH4 resulted in up to 98.2 wt% TiC0.90 product yield and a reduction in net-shrinkage during consolidation due to the volume expansion associated with the conversion of Ti to TiC. Results indicated that reaction bonding associated with the Gibbs free energy release associated with TiC formation produced interparticle adhesion at low furnace processing temperatures. The ability to bond highly refractory materials through this type of process resulted in structures that were crack-free and resisted fracture during thermal shock testing. Broadly, the additive manufacturing approach presented could be useful for the production of many UHTC carbides that might otherwise be incompatible with prevailing AM techniques that do not include reaction synthesis., Comment: 23 pages,14 figures, one figure with link to external video

Micromotor and nanomotor particles are typically made using dense solid particles that can sediment or be trapped in confined flow environments. Creation of much larger motors should be possible if a very low-density system is used with sufficient strength to carry liquid and still experience propulsive motion. Light, dense millimotors should also be able to deform more than dense solid ones in constrictions. Millimotors are created from permeable capsules of bacterial cellulose that are coated with catalase-containing metal-organic frameworks, enabling reactive propulsion in aqueous hydrogen peroxide. The motion of the motors is quantified using particle tracking and the deformation is measured using microcapillary compression and flow through confined channels. Two different propulsion mechanisms are dominant depending on the motor surface chemistry: oxygen bubbles are expelled from hydrophilic millimotors, driving motion via reaction force and buoyancy. Hydrophobic millimotors remain attached to growing bubbles and move by buoyancy alone. Despite their large size, the low-density capsules compress to pass through contractions that would impede and be blocked by solid motors. The sparse structure but relatively large size of the motors enables them to transport significant volumes of liquid using minimal solid mass as a motor support structure.

Bacterial cellulose biofilms are complex networks of strong interwoven nanofibers that control transport and protect bacterial colonies in the film. Design of diverse applications of bacterial cellulose films also relies on understanding and controlling transport through the fiber mesh, and transport simulations of the films are most accurate when guided by experimental characterization of the structures and the resultant diffusion inside. Diffusion through such films is a function of their key microstructural length scales, determining how molecules, as well as particles and microorganisms, permeate them. We use microscopy to study the unique bacterial cellulose film structure and quantify the mobility dynamics of various sizes of tracer particles and macromolecules. Mobility is hindered within the films, as confinement and local movement strongly depend on void size relative to diffusing tracers. The biofilms have a naturally periodic structure of alternating dense and porous layers of nanofiber mesh, and we tune the magnitude of the spacing via fermentation conditions. Micron-sized particles can diffuse through the porous layers, but can not penetrate the dense layers. Tracer mobility in the porous layers is isotropic, indicating a largely random pore structure there. Molecular diffusion through the whole film is only slightly reduced by the structural tortuosity. Knowledge of transport variations within bacterial cellulose networks can be used to guide design of symbiotic cultures in these structures and enhance their use in applications biomedical implants, wound dressings, lab-grown meat, and sensors.

We prove the Cone Theorem for algebraically integrable foliations. As a consequence, we show that termination of flips implies the b-nefness of the moduli part of a log canonical pair with respect to a contraction, generalising the case of lc trivial fibrations., Comment: 36 pages. General improvements, e.g. several results do not require termination of flips anymore

$\bf{Purpose:}$ The goal of this study was (i) to use artificial intelligence to automate the traditionally labor-intensive process of manual segmentation of tumor regions in pathology slides performed by a pathologist and (ii) to validate the use of a well-known and readily available deep learning architecture. Automation will reduce the human error involved in manual delineation, increase efficiency, and result in accurate and reproducible segmentation. This advancement will alleviate the bottleneck in the workflow in clinical and research applications due to a lack of pathologist time. Our application is patient-specific microdosimetry and radiobiological modeling, which builds on the contoured pathology slides. $\bf{Methods:}$ A U-Net architecture was used to segment tumor regions in pathology core biopsies of lung tissue with adenocarcinoma stained using hematoxylin and eosin. A pathologist manually contoured the tumor regions in 56 images with binary masks for training. Overlapping patch extraction with various patch sizes and image downsampling were investigated individually. Data augmentation and 8-fold cross-validation were used. $\bf{Results:}$ The U-Net achieved accuracy of 0.91$\pm$0.06, specificity of 0.90$\pm$0.08, sensitivity of 0.92$\pm$0.07, and precision of 0.8$\pm$0.1. The F1/DICE score was 0.85$\pm$0.07, with a segmentation time of 3.24$\pm$0.03 seconds per image, achieving a 370$\pm$3 times increased efficiency over manual segmentation. In some cases, the U-Net correctly delineated the tumor's stroma from its epithelial component in regions that were classified as tumor by the pathologist. $\bf{Conclusion:}$ The U-Net architecture can segment images with a level of efficiency and accuracy that makes it suitable for tumor segmentation of histopathological images in fields such as radiotherapy dosimetry, specifically in the subfields of microdosimetry., Comment: 17 pages, 5 figures, 2 tables

We explore the birational structure and invariants of a foliated surface $(X, \mathcal F)$ in terms of the adjoint divisor $K_{\mathcal F}+\epsilon K_X$, $0< \epsilon \ll 1$. We then establish a bound on the automorphism group of an adjoint general type foliated surface $(X, \mathcal F)$, provide a bound on the degree of a general curve invariant by an algebraically integrable foliation on a surface and prove that the set of $\epsilon$-adjoint canonical models of foliations of general type and with fixed volume form a bounded family., Comment: v2: 43 pages. Expanded and improved the exposition. Main results are unchanged; v1: 32 pages. Comments are welcome!

There remains a need for techniques to monitor thermal processes at high spatiotemporal resolution, with myriad potential applications in chemistry, biology, and engineering. Measurement of temperature from nanoscale molecular phenomena are particularly promising due to their general compatibility with biological systems. Among these phenomena, fluorescence polarization anisotropy is particularly attractive due to its high sensitivity to thermal and photophysical information, and its general utility with a wide spectrum of fluorophores. In this work, we propose that the measurement of the intrinsic fluorescence polarization anisotropy of tryptophan can be used to measure label-free temperature at the nanoscale in a variety of tryptophan-containing proteins. We present a theoretical model of the temperature sensitivity of fluorescence polarization in free tryptophan and tryptophan-containing proteins, empirically explore these properties, and discuss the potential development of proteins as thermal memory sensors., Comment: 11 pages, 3 figures and 3 tables

Novel view synthesis is a challenging and ill-posed inverse rendering problem. Neural rendering techniques have recently achieved photorealistic image quality for this task. State-of-the-art (SOTA) neural volume rendering approaches, however, are slow to train and require minutes of inference (i.e., rendering) time for high image resolutions. We adopt high-capacity neural scene representations with periodic activations for jointly optimizing an implicit surface and a radiance field of a scene supervised exclusively with posed 2D images. Our neural rendering pipeline accelerates SOTA neural volume rendering by about two orders of magnitude and our implicit surface representation is unique in allowing us to export a mesh with view-dependent texture information. Thus, like other implicit surface representations, ours is compatible with traditional graphics pipelines, enabling real-time rendering rates, while achieving unprecedented image quality compared to other surface methods. We assess the quality of our approach using existing datasets as well as high-quality 3D face data captured with a custom multi-camera rig., Comment: Project website: http://www.computationalimaging.org/publications/nlr/

We prove existence of flips and the base point free theorem for log canonical foliated pairs of rank one on a Q-factorial projective klt threefold. This, in particular, provides a proof of the existence of a minimal model for a rank one foliation on a threefold for a wider range of singularities, after McQuillan. Moreover, we show abundance in the case of numerically trivial log canonical foliated pairs of rank one., Comment: 82 pages

We provide several applications of the minimal model program to the local and global study of co-rank one foliations on threefolds. Locally, we prove a singular variant of Malgrange's theorem, a classification of terminal foliation singularities and the existence of separatrices for log canonical singularities. Globally, we prove termination of flips, a connectedness theorem on lc centres, a non-vanshing theorem and some hyperbolicity properties of foliations., Comment: 55 pages; new version taking into account referee comments, to appear in JEMS

An important strategy to stabilize emulsions is to arrest coalescence of the constituent droplets with an opposing rheological force. Colloidal particles adsorbed on the surface of emulsion droplets in a Pickering emulsion become increasingly crowded during successive coalescence events because the combined surface area of coalescing droplets is less than that of the constituent droplets. Beyond a critical density, the particles form a rigid shell around the droplet and inhibit both relaxation of the droplet shape and further coalescence. The resulting droplets have a nonuniform distribution of curvature and, depending on the initial coverage, may incorporate a region with negative Gaussian curvature around the neck that bridges the two droplets. Here, we resolve the relative influence of the curvature and the kinetic process of arrest on the microstructure of the final state. Identifying the dimensionless ratio of the rate of area change \dot{A} to the diffusion constant D as a measure of the importance of kinetics in this system, we show that this depends on the extrinsic geometry of the surface as opposed to the static packings that depend solely on intrinsic geometry., Comment: 9 pages, 5 figures

Background: Over the past decade, schools across the United States increasingly turned to online learning (Gemin, Pape, Vashaw, & Watson, 2015; Queen & Lewis, 2011). While many espouse the promise of online credit recovery (OCR) courses, the abrupt shift to online learning during the COVID-19 pandemic renewed concerns about theses courses' effectiveness as tools for equitable outcomes (Tate & Warschauer, 2022). These concerns are exacerbated by a dearth of rigorous and mixed evidence about the effectiveness of OCR courses (Viano, 2018). A correlational study of OCR in Florida found that students in online courses were more likely to earn a C or better than students in face-to-face courses (Hughes, Zhou & Petscher, 2015). A study of North Carolina high school students who failed a course found that students who enrolled in OCR were more likely to graduate but had lower test scores than students who repeated the face-to-face version of the course (Viano & Henry, 2020). In addition, Heinrich et al. (2019) found that in a large urban midwestern district "online course-taking is not benefiting students or reflecting real learning" (p. 2,174). To date, there have been two randomized controlled trials of OCR. The first study found that students who took an OCR course in Chicago were less likely to earn credit and learned less than students who took a face-to-face course (Heppen et al., 2017), but found no statistically significant differences in longer-term outcomes, including high school graduation (Rickles et al., 2018). The second study found that students who took an OCR course in a large, urban school district were, on average, less likely to earn credit for ninth grade English than students who took a teacher-directed course but found no statistically significant differences in credit recovery rates in Algebra 1 or in content knowledge across both subject areas (Rickles et al., in press). Purpose: This paper builds off the second randomized study to examine how OCR affects longer-term high school outcomes relative to the business-as-usual (BAU) teacher-directed credit recovery classes. We address the following research questions: (1) What was the impact of taking OCR on students' credit accumulation over four years of high school?; (2) What was the impact of taking OCR on students' probability of on-time high school graduation?; (3) How did the longer-term effects of OCR vary across sites?; and (4) How did students' prior academic performance and engagement moderate the longer-term effects of OCR? Intervention: The intervention for this study was an Algebra 1 or English 9 online curriculum for the credit recovery course, where an online provider supplied the main course content and curriculum, and the school provided the credentialed in-class teacher who could supplement the digital instruction. The BAU classes primarily relied on traditional teacher-directed instruction, where teachers had latitude in the curriculum and instructional materials for the class. For both the intervention and BAU conditions, students took the class within a standard classroom during the district's 5-week summer session. Key characteristics of the online learning model tested in this study are presented in Exhibit A.1. The theory of action for the study is presented in Exhibit A.2. Population and Setting: The analyses in this paper are based on 613 students in 28 Algebra 1 classes across 13 high schools and 1,124 students in 70 English 9 classes across 19 high schools, all within a large urban district. All students entered 9th grade in the 2017-18 school year (Cohort 1) or the 2018-19 school year (Cohort 2) and failed their Algebra 1 and/or at least one semester of their English 9 course and enrolled in a credit recovery course the summer between their 9th and 10th grade year. For both cohorts, the credit recovery classes took place before the COVID-19 pandemic. Exhibit A.3 presents descriptive statistics and baseline equivalence for the Algebra 1 and English 9 student samples. Research Design: Students were randomly assigned to take their credit recovery course in an online class (treatment) or a BAU class (control). Random assignment took place within blocks defined by school, course, and cohort. In some schools, blocks were further defined by which semesters of the course the students failed during their 9th grade year. Data Collection and Analysis: We utilized extant district student background and course data for all analyses in this paper. Measures are described in Exhibit A.4. All analyses were conducted separately for Algebra and English. We estimated average treatment effects for the intent-to-treat student sample using regression models that control for student characteristics and randomization blocks. For the analysis of between-site heterogeneity, we estimated site-specific treatment effects by adding site-by-treatment interaction terms (fixed effects) to the main impact model specification. For the student-level moderator analysis we estimated separate moderation models for two indicators of prior academic performance (8th grade assessment scores and 9th grade GPA) and an indicator of school engagement (9th grade attendance). Findings: We are conducting analyses for this paper and therefore do not currently have findings to present. We expect to have full results by August 2023. Conclusions: The findings will provide needed evidence about the relative effectiveness of OCR to keep students on track toward graduation over time and obtain a high school degree. While earlier results from this study indicate that the online classes were more difficult to pass but may have improved short-term content knowledge for certain students in certain subject areas, it is not clear whether those proximal effects had implications for students' progress toward graduation. To help interpret the findings, the paper will use data from a larger sample of the district's students, focus group data from participating teachers, and interview data from students who took credit recovery during the pandemic to help situate the impact findings within the broader context of teaching, learning, and high school progression during the pandemic. Within this context, findings about the longer-term effects of OCR should inform future efforts to address the needs of students who fall behind early in their high school career.

We prove existence of flips, special termination, the base point free theorem and, in the case of log general type, the existence of minimal models for F-dlt foliated pairs of co-rank one on a $\mathbb Q$-factorial projective threefold. As applications, we show the existence of F-dlt modifications and F-terminalisations for foliated pairs and we show that foliations with canonical or F-dlt singularities admit non-dicritical singularities. Finally, we show abundance in the case of numerically trivial foliated pairs., Comment: 89 pages. Revision based on comments from the referee. Inventiones Math. (to appear)

The stable configurations formed by two viscoelastic, ellipsoid-shaped droplets during their arrested coalescence has been investigated using micromanipulation experiments. Ellipsoidal droplets are produced by millifluidic emulsification of petrolatum into a yield stress fluid that preserves their elongated shape. The liquid meniscus between droplets can transmit stress and instigate movement of the droplets, from their initial relative position, in order to minimize doublet surface energy. The action of the liquid meniscus causes the ellipsoidal droplets to undergo rolling and restructuring events because of their unique ellipsoid shape and associated variation in surface curvature. The final configuration of the droplets is shown to be controlled by the balance between interfacial Laplace pressure and internal elasticity, as well as a constraint force that resists complete minimization of surface energy. Geometric and surface energy calculations are used to map the possible and most likely configurations of the droplet pairs. Experimental deviations from the calculations indicate the magnitude and potential origin of the constraint force resisting full equilibration. Droplet aspect ratio and elasticity are both shown to influence the degree of restructuring and stability of the droplets at energy extrema. Higher aspect ratios drive greater restructuring and better agreement with final doublet configurations predicted by energy minimization. Lower elasticity droplets undergo secondary deformations at high aspect ratios, further broadening the space of possible morphologies., Comment: 22 pages, 6 figures

Injection of a radio frequency (RF) current was used to phase lock the SHNO to the TRSKM. The out of plane magnetization was detected by means of the polar magneto optical Kerr effect (MOKE). However, longitudinal MOKE images were dominated by an artifact arising from the edges of the Au NCs. Time resolved imaging revealed the simultaneous excitation of a non-linear `bullet' mode at the centre of the device, once the DC current exceeded a threshold value, and ferromagnetic resonance (FMR) induced by the RF current. However, the FMR response observed for sub-critical DC current values exhibits an amplitude minimum at the centre, which is attributed to spreading of the RF spin current due to the reactance of the device structure. This FMR response can be subtracted to yield images of the bullet mode. As the DC current is increased above threshold, the bullet mode appears to increase in size, suggesting increased translational motion. The reduced spatial overlap of the bullet and FMR modes, and this putative translational motion, may impede the injection locking and contribute to the reduced locking range observed within NC-SHNO devices. This illustrates a more general need to control the geometry of an injection-locked oscillator so that the autonomous dynamics of the oscillator exhibit strong spatial overlap with those resulting from the injected signal.

Time-resolved scanning Kerr microscopy (TRSKM) was used to study precessional magnetization dynamics induced by a radio frequency (RF) current within a Al$_2$O$_3$/Py(5 nm)/Pt(6 nm)/Au(150 nm) spin Hall nano-oscillator structure. The Au layer was formed into two needle-shaped electrical contacts that concentrated the current in the centre of a Py/Pt mesa of 4 $\mu$m diameter. Due to the spin Hall effect, current within the Pt layer drives a spin current into the Py layer, exerting a spin transfer torque (STT). By injecting RF current, and exploiting the phase-sensitivity of TRSKM and the symmetry of the device structure, the STT and Oersted field torques have been separated and spatially mapped. The STT and torque due to the in-plane Oersted field are observed to exhibit minima at the device centre that is ascribed to spreading of RF current that is not observed for DC current. Torques associated with the RF current may destabilise the position of the self-localised bullet mode excited by the DC current, and inhibit injection locking. The present study demonstrates the need to characterise both DC and RF current distributions carefully.

We present a variant of the classical Darboux-Jouanolou Theorem. Our main result provides a characterization of foliations which are pull-backs of foliations on surfaces by rational maps. As an application, we provide a structure theorem for foliations on 3-folds admitting an infinite number of extremal rays.

We develop some basic results in a higher dimensional foliated Mori theory, and show how these results can be used to prove a structure theorem for the Kleiman-Mori cone of curves in terms of the numerical properties of $K_{\mathcal{F}}$ for rank 2 foliations on threefolds. We also make progress toward realizing a minimal model program for rank 2 foliations on threefolds., Comment: 50 pages, new version taking into account referee suggestions, published version to appear in Compositio Math

The stability of shapes formed by three viscoelastic droplets during their arrested coalescence has been investigated using micromanipulation experiments. Addition of a third droplet to arrested droplet doublets is shown to be controlled by the balance between interfacial pressures driving coalescence and internal elasticity that resists total consolidation. The free fluid available within the droplets controls the transmission of stress during droplet combination and allows connections to occur via formation of a neck between the droplets. The anisotropy of three-droplet systems adds complexity to the symmetric case of two-droplet aggregates because of the multiplicity of orientations possible for the third droplet. When elasticity dominates, the initial orientation of the third droplet is preserved in the triplet's final shape. When elasticity is dominated by the interfacial driving force, the final shape can deviate strongly from the initial positioning of droplets. Movement of the third droplet to a more compact packing occurs, driven by liquid meniscus expansion that minimizes the surface energy of the triplet. A range of compositions and orientations are examined and the resulting domains of restructuring and stability are mapped based on the final triplet structure. A geometric and a physical model are used to explain the mechanism driving meniscus-induced restructuring and are related to the impact of these phenomena on multiple droplet emulsions.

We construct an order reconstruction (OR)-type Landau-de Gennes critical point on a square domain of edge length $\lambda$, motivated by the well order reconstruction solution numerically reported by Kralj and Majumdar. The OR critical point is distinguished by an uniaxial cross with negative scalar order parameter along the square diagonals. The OR critical point is defined in terms of a saddle-type critical point of an associated scalar variational problem. The OR-type critical point is globally stable for small $\lambda$ and undergoes a supercritical pitchfork bifurcation in the associated scalar variational setting. We consider generalizations of the OR-type critical point to a regular hexagon, accompanied by numerical estimates of stability criteria of such critical points on both a square and a hexagon in terms of material-dependent constants., Comment: 29 pages, 12 figures

Most systematic tables of data associated to ranks of elliptic curves order the curves by conductor. Recent developments, led by work of Bhargava-Shankar studying the average sizes of $n$-Selmer groups, have given new upper bounds on the average algebraic rank in families of elliptic curves over $\mathbb{Q}$ ordered by height. We describe databases of elliptic curves over $\mathbb{Q}$ ordered by height in which we compute ranks and $2$-Selmer group sizes, the distributions of which may also be compared to these theoretical results. A striking new phenomenon observed in these databases is that the average rank eventually decreases as height increases., Comment: 20 pages; to appear in ANTS XII. Data available at http://wstein.org/papers/2016-height/

We study the gradient flow model for the Landau-de Gennes energy functional for nematic liquid crystals at the nematic-isotropic transition temperature on prototype geometries. We study the dynamic model on a three-dimensional droplet and on a disc with Dirichlet boundary conditions and different types of initial conditions. In the case of a droplet with radial boundary conditions, a large class of physically relevant initial conditions generate dynamic solutions with a well-defined isotropic-nematic interface which propagates according to mean curvature for small times. On a disc, we make a distinction between "planar" and "non-planar" initial conditions and "minimal" and "non-minimal" Dirichlet boundary conditions. Planar initial conditions generate solutions with an isotropic core for all times whereas non-planar initial conditions generate solutions which escape into the third dimension. Non-minimal boundary conditions generate solutions with boundary layers and these solutions can either have a largely ordered interior profile or an almost entirely disordered isotropic interior profile. Our examples suggest that whilst critical points of the Landau-de Gennes energy typically have highly localized disordered-ordered interfaces, the transient dynamics exhibit observable isotropic-nematic interfaces of potential experimental relevance.

Non-spherical emulsion droplets can be stabilized by densely packed colloidal particles adsorbed at their surface. In order to understand the microstructure of these surface packings, the ordering of hard spheres on ellipsoidal surfaces is determined through large scale computer simulations. Defects in the packing are shown generically to occur most often in regions of strong curvature; however, the relationship between defects and curvature is nontrivial, and the distribution of defects shows secondary maxima for ellipsoids of sufficiently high aspect ratio. As with packings on spherical surfaces, additional defects beyond those required by topology are observed as chains or 'scars'. The transition point, however, is found to be softened by the anisotropic curvature which also partially orients the scars. A rich library of symmetric commensurate packings are identified for low particle number. We verify experimentally that ellipsoidal droplets of varying aspect ratio can be arrested by surface-adsorbed colloids., Comment: 11 pages, 7 figures

We continue the study of constructing invariant Laplacians on Julia sets, and studying properties of their spectra. In this paper we focus on two types of examples: 1) Julia sets of cubic polynomials $z^3 + c$ with a single critical point; 2) formal matings of quadratic Julia sets. The general scheme introduced in earlier papers in this series involves realizing the Julia set as a circle with identifications, and attempting to obtain the Laplacian as a renormalized limit of graph Laplacians on graphs derived form the circle with identifications model. In the case of cubic Julia sets the details follows the pattern established for quadratic Julia sets, but for matings the details are quite challenging, and we have only been completely successful for one example. Once we have constructed the Laplacian, we are able to use numerical methods to approximate the eigenvalues and eigenfunctions. One striking observation from the data is that for the cubic Julia sets the multiplicities of all eigenspaces (except for the trivial eigenspace of constants) are even numbers. Nothing like this is valid for the quadratic julia sets studied earlier. We are able to explain this, based on the fact that three is an odd number, and more precisely because the dihedral-3 symmetry group has only two distinct one-dimensional irreducible representations.

The discrete-time Toda equation arises as a universal equation for the relevant Hankel determinants associated with one-variable orthogonal polynomials through the mechanism of adjacency, which amounts to the inclusion of shifted weight functions in the orthogonality condition. In this paper we extend this mechanism to a new class of two-variable orthogonal polynomials where the variables are related via an elliptic curve. This leads to a `Higher order Analogue of the Discrete-time Toda' (HADT) equation for the associated Hankel determinants, together with its Lax pair, which is derived from the relevant recurrence relations for the orthogonal polynomials. In a similar way as the quotient-difference (QD) algorithm is related to the discrete-time Toda equation, a novel quotient-quotient-difference (QQD) scheme is presented for the HADT equation. We show that for both the HADT equation and the QQD scheme, there exists well-posed $s$-periodic initial value problems, for almost all $\s\in\Z^2$. From the Lax-pairs we furthermore derive invariants for corresponding reductions to dynamical mappings for some explicit examples., Comment: 38 pages

A semi-discrete Lax pair formed from the differential system and recurrence relation for semi-classical orthogonal polynomials, leads to a discrete integrable equation for a specific semi-classical orthogonal polynomial weight. The main example we use is a semi-classical Laguerre weight to derive a third order difference equation with a corresponding Lax pair., Comment: 11 pages

We apply the direct method of obtaining reductions to the Toda hierarchy of equations. The resulting equations form a hierarchy of ordinary differential difference equations, also known as delay-differential equations. Such a hierarchy appears to be the first of its kind in the literature. All possible reductions, under certain assumptions, are obtained. The Lax pair associated to this reduced hierarchy is obtained., Comment: 11 pages

We investigate potential models that could explain why multiple proto-stellar systems predominantly show single jets. During their formation, stars most frequently produce energetic outflows and jets. However, binary jets have only been observed in a very small number of systems. We model numerically 3D binary jets for various outflow parameters. We also model the propagation of jets from a specific source, namely L1551 IRS 5, known to have two jets, using recent observations as constraints for simulations with a new MHD code. We examine their morphology and dynamics, and produce synthetic emission maps. We find that the two jets interfere up to the stage where one of them is almost destroyed or engulfed into the second one. We are able to reproduce some of the observational features of L1551 such as the bending of the secondary jet. While the effects of orbital motion are negligible over the jets dynamical timeline, their interaction has significant impact on their morphology. If the jets are not strictly parallel, as in most observed cases, we show that the magnetic field can help the collimation and refocusing of both of the two jets., Comment: accepted for publication in A&A

The Campus Profile is an annual publication designed to help faculty, staff, and students understand Glendale Community College's (California) diverse operations and make informed decisions. The publication is organized around the statewide accountability model. This year's Campus Profile includes more accountability performance measures than in previous years. In particular, it includes Key Performance Indicators (KPIs) defined in the college's Educational Master Plan. This report contains five sections and an index. Section 1 looks at the Glendale community profile, which describes housing characteristics, ethnicity, population by age cohorts, and area school information such as the Glendale Unified School District demographics and high school articulation. Section 2 reports on student access, with discussions on enrollment and demographics, student needs, and additional access-related KPIs. Total headcount for fall 1998 was 23,013 students. Section 3 discusses student success, which looks at course-taking, student outcomes/equity, educational goals, degree and certificate completion, time to goal completion, and additional success-related KPIs. Section 4 looks at staff composition, focusing on the present workforce, full-/part-time (AB 1725) ratios, staff development, and additional staff-related KPIs. Section 5 discusses the fiscal condition with a look at the general revenue, expenditures, general fund balances, and additional fiscal KPIs. (VWC)

Outlining the demography of the students and community served by Glendale Community College (GCC), in California, as well as providing indicators of institutional effectiveness, this five-part report is designed to assist faculty, staff, and students understand the college's diverse operations. Section I provides a community profile, including longitudinal data on housing characteristics, ethnicity, population by age, community growth and income, area schools, and GCC enrollees from area high schools. Section II focuses on student access and needs for fall 1993 to fall 1995, including credit and non-credit enrollment statistics by student age, gender, and ethnicity; assessment and placement results for 1995-96; financial aid statistics; and English as a Second Language and Basic Skills course enrollments. Section III provides data on student success for the same period, including information on academic standards; student retention and pass rates by division; student outcomes by ethnicity and other characteristics; characteristics of transfer, vocational preparation, and personal interest students; degrees completed by gender and ethnicity for 1995-96; and Associate in Arts, certificates, and Associate in Science Degrees completed by major from 1993-96. Section IV describes GCC staff by gender, ethnicity, full-time/part-time ratios, and staff development activities for 1995-96. Finally, section V reviews GCC's fiscal condition as of 1994-95, highlighting state, local, and federal general fund revenues; specific revenue sources; general fund expenditures from 1992-95; expenditures comparisons to state averages; and general fund balances from 1990-95. (BCY)

To gather data on attitudes related to the advisability of proposing a property tax increase to provide additional college support, Glendale Community College (GCC), in California, held four focus group meetings with classified employees. Following letters and electronic mail messages sent to all classified employees inviting them to participate, 29 full-time classified staff volunteered to participate in hour-long focus groups held at four times on July 1, 1996. All but one of the participants were residents of the District and would be affected by a tax increase. The focus groups discussed issues related to GCC's reputation, institutional needs, and advisability of seeking a property tax. An analysis of participants' comments revealed the following: (1) all four groups believed that having a community college in the community enhanced property values and contributed to the community by retraining the workforce and inexpensively educating students for transfer; (2) offering more classes, improving instructional technology, and performing seismic upgrades were identified as institutional needs; (3) participants raised concerns regarding trust and accountability, due to financial abuses of other local school districts; and (4) in general, there was a significantly negative reaction to the idea of a property tax increase. The focus group questions and suggested bond projects are appended. (TGI)

Established in 1927, Glendale Community College (GCC) in California is a public, open-enrollment institution dedicated to serving an increasingly diverse student and community population. In its effort to meet community needs, the college supports a strong transfer program, occupational programs, personal enrichment opportunities, and a variety of non-credit educational programs. As of 1996, the population of the college's district was estimated at 195,000, with growth estimated at 1% per year. While in 1970 the district population was 85% Caucasian, 1990 census data indicate that it is currently 64% Caucasian, one-third of which is Armenian; 21% Hispanic; 14% Asian; and 1% other. This diversity is reflected in the GCC student body, which is 30% Armenian, 21% Latino, 19% Caucasian, 14% Asian, 10% other, and 7% Filipino. Although total enrollment began to decline in 1992-93 in response to statewide community college fee increases, as of 1996 students were taking more units each term and semester-to-semester retention increased to approximately 75% from 64% in 1985. For credit enrollments, the number of continuing students declined for the first time in a decade in 1995, while the majority of credit students were 20 years old and under. Non-credit programs accounted or 5,817 students in fall 1996. Finally, GCC maintains active recruitment efforts with high schools and international students and transfers over 450 students yearly to institutions throughout the state and country. (Contains 15 graphs.) (HAA)

A panel of 46 experts from philosophy and education defines critical thinking as "purposeful, self-regulatory judgment which results in interpretation, analysis, evaluation, and inference, as well as explanation of the evidential, conceptual, methodological, criteriological, or contextual considerations upon which that judgment is based." At present, there are seven standardized critical thinking tests available, and several performance assessment approaches can be used as outcome measures within various subjects in communication. Standardized tests can provide useful information that is diagnostic and may help to guide instruction. However, multiple measures of critical thinking should be used in assessment. Critical thinking is not a general ability but rather a complex set of general and specific factors. Psychologists generally favor multiple measures of critical thinking because no single test covers the dimensions of a good conceptual definition of critical thinking. R. A. Ennis and S. P. Norris suggest that in lieu of appropriate multiple choice tests, open-ended assessment tests are needed; other measures could include interviews. College educators should first decide what students should be able to demonstrate and what they know and can do. Then, they should decide what to teach students. When educators are clear about the intended performance and results, they will have a set of criteria for selection of content. Then in devising their means of assessment, educators should consider guidelines concerning meaningful contexts in exams, novel situations, relevant products and performances, and the various levels of student ability. (Contains 21 references.) (TB)