cssi/SciSciGPT-SciSciNet huggingface dataset:
Demystifying “drop-outs” in single-cell UMI data

Many existing pipelines for scRNA-seq data apply pre-processing steps such as normalization or imputation to account for excessive zeros or “drop-outs." Here, we extensively analyze diverse UMI data sets to show that clustering should be the foremost step of the workflow. We observe that most drop-outs disappear once cell-type heterogeneity is resolved, while imputing or normalizing heterogeneous data can introduce unwanted noise. We propose a novel framework HIPPO (Heterogeneity-Inspired Pre-Processing tOol) that leverages zero proportions to explain cellular heterogeneity and integrates feature selection with iterative clustering. HIPPO leads to downstream analysis with greater flexibility and interpretability compared to alternatives.
Unramified affine Springer fibers and isospectral Hilbert schemes

For any connected reductive group G over $${{\mathbb {C}}}$$ , we revisit Goresky–Kottwitz–MacPherson’s description of the torus equivariant Borel–Moore homology of affine Springer fibers $${\mathrm {Sp}}_{\gamma }\subset {{\,\mathrm{Gr}\,}}_G$$ , where $$\gamma =zt^d$$ and z is a regular semisimple element in the Lie algebra of G. In the case $$G=GL_n$$ , we relate the equivariant cohomology of $${\mathrm {Sp}}_\gamma $$ to Haiman’s work on the isospectral Hilbert scheme of points on the plane. We also explain the connection to the HOMFLY homology of (n, dn)-torus links, and formulate a conjecture describing the homology of the Hilbert scheme of points on the curve $$\{x^n=y^{dn}\}$$ .
Climate gradients, and patterns of biodiversity and biotic homogenization in urban residential yards

Residential yards constitute a substantive biodiverse greenspace within urban areas. This biodiversity results from a combination of native and non-native species and can contribute to biotic homogenization. Geographical climatic patterns affect the distribution of native species and may differently affect non-native species. In this study, we examined biodiversity and biotic homogenization patterns of yard-dwelling land snails across 12 towns in Oklahoma and Kansas (USA). The 3 x 4 array of towns incorporated a N-S winter temperature gradient (mean low January temperature range = -8.4 to 0.1°C) and an E-W annual rainfall gradient (annual rainfall range = 113.8 to 61.3 cm/yr). Ten yards per town were surveyed. We hypothesized that mild winter temperatures and greater annual rainfall would be associated with greater snail abundance and richness, and that the presence of non-native species would contribute to biotic homogenization. Non-native snails were present and often abundant in all towns. Snail communities varied with both rainfall and cold temperature. Contrary to our prediction, snail abundance was inversely related to annual rainfall-likely because drier conditions resulted in greater yard watering that both augmented rainfall and maintained moist conditions. Sorensen similarity between towns for the entire land snail community and for only non-native species both showed distance-decay patterns, with snail composition becoming less similar with increasing distance-patterns resulting from species turnover. The biotic homogenization index also showed a distance-related pattern, such that closer towns were more likely to have biotic homogenization whereas more distant towns tended to have biotic differentiation. These results support the concept that biotic homogenization is more likely regionally and that climatic changes over distance result in species turnover and can reduce spatially broad biotic homogenization.
Neural network representation of the probability density function of diffusion processes.

Physics-informed neural networks are developed to characterize the state of dynamical systems in a random environment. The neural network approximates the probability density function (pdf) or the characteristic function (chf) of the state of these systems, which satisfy the Fokker–Planck equation or an integro-differential equation under Gaussian and/or Poisson white noises. We examine analytically and numerically the advantages and disadvantages of solving each type of differential equation to characterize the state. It is also demonstrated how prior information of the dynamical system can be exploited to design and simplify the neural network architecture. Numerical examples show that (1) the neural network solution can approximate the target solution even for partial integro-differential equations and a system of partial differential equations describing the time evolution of the pdf/chf, (2) solving either the Fokker–Planck equation or the chf differential equation using neural networks yields similar pdfs of the state, and (3) the solution to these differential equations can be used to study the behavior of the state for different types of random forcings.
Autonomously Navigating a Surgical Tool Inside the Eye by Learning from Demonstration

A fundamental challenge in retinal surgery is safely navigating a surgical tool to a desired goal position on the retinal surface while avoiding damage to surrounding tissues, a procedure that typically requires tens-of-microns accuracy. In practice, the surgeon relies on depth-estimation skills to localize the tool-tip with respect to the retina in order to perform the tool-navigation task, which can be prone to human error. To alleviate such uncertainty, prior work has introduced ways to assist the surgeon by estimating the tooltip distance to the retina and providing haptic or auditory feedback. However, automating the tool-navigation task itself remains unsolved and largely unexplored. Such a capability, if reliably automated, could serve as a building block to streamline complex procedures and reduce the chance for tissue damage. Towards this end, we propose to automate the tool-navigation task by learning to mimic expert demonstrations of the task. Specifically, a deep network is trained to imitate expert trajectories toward various locations on the retina based on recorded visual servoing to a given goal specified by the user. The proposed autonomous navigation system is evaluated in simulation and in physical experiments using a silicone eye phantom. We show that the network can reliably navigate a needle surgical tool to various desired locations within 137 µm accuracy in physical experiments and 94 µm in simulation on average, and generalizes well to unseen situations such as in the presence of auxiliary surgical tools, variable eye backgrounds, and brightness conditions.
PRMT5-mediated methylation of YBX1 regulates NF-κB activity in colorectal cancer

The multifunctional protein Y-box binding protein 1 (YBX1), is a critical regulator of transcription and translation, and is widely recognized as an oncogenic driver in several solid tumors, including colorectal cancer (CRC). However, very little is known about the upstream or downstream factors that underlie YBX1′s regulation and involvement in CRC. Previously, we demonstrated that YBX1 overexpression correlated with potent activation of nuclear factor κB (NF-κB), a well-known transcription factor believed to be crucial in CRC progression. Here, we report a novel interaction between NF-κB, YBX1 and protein arginine methyltransferase 5 (PRMT5). Our findings reveal for the first time that PRMT5 catalyzes methylation of YBX1 at arginine 205 (YBX1-R205me2), an event that is critical for YBX1-mediated NF-κB activation and its downstream target gene expression. Importantly, when WT-YBX1 is overexpressed, this methylation exists under basal (unstimulated) conditions and is further augmented upon interleukin-1β (IL-1β) stimulation. Mechanistically, co-immunoprecipitation studies reveal that the R205 to alanine (A) mutant of YBX1 (YBX1-R205A) interacted less well with the p65 subunit of NF-κB and attenuated the DNA binding ability of p65. Importantly, overexpression of YBX1-R205A significantly reduced cell growth, migration and anchorage-independent growth of CRC cells. Collectively, our findings shed important light on the regulation of a novel PRMT5/YBX1/NF-κB axis through PRMT5-mediated YBX1-R205 methylation. Given the fact that PRMT5, YBX1 and NF-κB are all among top crucial factors in cancer progression, pharmacological disruption of this pivotal axis could serve as the basis for new therapeutics for CRC and other PRMT5/YBX1/NF-κB-associated cancers.
INDRA: Intrusion Detection Using Recurrent Autoencoders in Automotive Embedded Systems

Today’s vehicles are complex distributed embedded systems that are increasingly being connected to various external systems. Unfortunately, this increased connectivity makes the vehicles vulnerable to security attacks that can be catastrophic. In this article, we present a novel intrusion detection system (IDS) called INDRA that utilizes a gated recurrent unit (GRU)-based recurrent autoencoder to detect anomalies in controller area network (CAN) bus-based automotive embedded systems. We evaluate our proposed framework under different attack scenarios and also compare it with the best known prior works in this area.
Simplified Neural Unsupervised Domain Adaptation.

Unsupervised domain adaptation (UDA) is the task of training a statistical model on labeled data from a source domain to achieve better performance on data from a target domain, with access to only unlabeled data in the target domain. Existing state-of-the-art UDA approaches use neural networks to learn representations that are trained to predict the values of subset of important features called “pivot features” on combined data from the source and target domains. In this work, we show that it is possible to improve on existing neural domain adaptation algorithms by 1) jointly training the representation learner with the task learner; and 2) removing the need for heuristically-selected “pivot features.” Our results show competitive performance with a simpler model.
Search@Home: A Commercial Off-the-Shelf Environment for Investigating Optimization Problems

Search heuristics, particularly those that are evaluation-driven (e.g., evolutionary computation), are often performed in simulation, enabling exploration of large solution spaces. Yet simulation may not truly replicate real-world conditions. However, search heuristics have been proven to be successful when executed in real-world constrained environments that limit searching ability even with broad solution spaces. Moreover, searching in situ provides the added benefit of exposing the search heuristic to the exact conditions and uncertainties that the deployed application will face. Software engineering problems can benefit from in situ search via instantiation and analysis in real-world environments. This paper introduces Search@Home, an environment comprising heterogeneous commercial off-the-shelf devices enabling rapid prototyping of optimization strategies for real-world problems.
Transfer learning in large-scale ocean bottom seismic wavefield reconstruction

Achieving desirable receiver sampling in ocean bottom acquisition is often not possible because of cost considerations. Assuming adequate source sampling is available, which is achievable by virtue of reciprocity and the use of modern randomized (simultaneous-source) marine acquisition technology, we are in a position to train convolutional neural networks (CNNs) to bring the receiver sampling to the same spatial grid as the dense source sampling. To accomplish this task, we form training pairs consisting of densely sampled data and artificially subsampled data using a reciprocity argument and the assumption that the source-site sampling is dense. While this approach has successfully been used on the recovery monochromatic frequency slices, its application in practice calls for wavefield reconstruction of time-domain data. Despite having the option to parallelize, the overall costs of this approach can become prohibitive if we decide to carry out the training and recovery independently for each frequency. Because different frequency slices share information, we propose the use the method of transfer training to make our approach computationally more efficient by warm starting the training with CNN weights obtained from a neighboring frequency slices. If the two neighboring frequency slices share information, we would expect the training to improve and converge faster. Our aim is to prove this principle by carrying a series of carefully selected experiments on a relatively large-scale five-dimensional data synthetic data volume associated with wide-azimuth 3D ocean bottom node acquisition. From these experiments, we observe that by transfer training we are able t significantly speedup in the training, specially at relatively higher frequencies where consecutive frequency slices are more correlated.
The logarithmic Sobolev inequality for a submanifold in Euclidean space

We prove a sharp logarithmic Sobolev inequality which holds for submanifolds in Euclidean space of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature.
COVID-19 and The Rise of Intimate Partner Violence

Stay-at-home policies have been implemented worldwide to reduce the spread of the SARS-CoV-2 virus. However, there is a growing concern that such policies could increase violence against women. We find evidence in support of this critical concern. We focus on Peru, a country that imposed a strict nationwide lockdown starting in mid-March and where nearly 60% of women already experienced violence before COVID-19. Using administrative data on phone calls to the helpline for domestic violence (Linea 100), we find that the incidence rate of the calls increased by 48 percent between April and July 2020, with effects increasing over time. The rise in calls is found across all states and it is not driven by baseline characteristics, including previous prevalence of violence against women. These findings create the need to identify policies to mitigate the negative impact of stay-at-home orders on women's safety.
Repairing deep neural networks: fix patterns and challenges

Significant interest in applying Deep Neural Network (DNN) has fueled the need to support engineering of software that uses DNNs. Repairing software that uses DNNs is one such unmistakable SE need where automated tools could be beneficial; however, we do not fully understand challenges to repairing and patterns that are utilized when manually repairing DNNs. What challenges should automated repair tools address? What are the repair patterns whose automation could help developers? Which repair patterns should be assigned a higher priority for building automated bug repair tools? This work presents a comprehensive study of bug fix patterns to address these questions. We have studied 415 repairs from Stack Overflow and 555 repairs from GitHub for five popular deep learning libraries Caffe, Keras, Tensorflow, Theano, and Torch to understand challenges in repairs and bug repair patterns. Our key findings reveal that DNN bug fix patterns are distinctive compared to traditional bug fix patterns; the most common bug fix patterns are fixing data dimension and neural network connectivity; DNN bug fixes have the potential to introduce adversarial vulnerabilities; DNN bug fixes frequently introduce new bugs; and DNN bug localization, reuse of trained model, and coping with frequent releases are major challenges faced by developers when fixing bugs. We also contribute a benchmark of 667 DNN (bug, repair) instances.
Synthesis runs counter to directional folding of a nascent protein domain.

Folding of individual domains in large proteins during translation helps to avoid otherwise prevalent inter-domain misfolding. How folding intermediates observed in vitro for the majority of proteins relate to co-translational folding remains unclear. Combining in vivo and single-molecule experiments, we followed the co-translational folding of the G-domain, encompassing the first 293 amino acids of elongation factor G. Surprisingly, the domain remains unfolded until it is fully synthesized, without collapsing into molten globule-like states or forming stable intermediates. Upon fully emerging from the ribosome, the G-domain transitions to its stable native structure via folding intermediates. Our results suggest a strictly sequential folding pathway initiating from the C-terminus. Folding and synthesis thus proceed in opposite directions. The folding mechanism is likely imposed by the final structure and might have evolved to ensure efficient, timely folding of a highly abundant and essential protein. In vivo experiments and optical tweezers force-spectroscopy measurements assessing the co-translational folding of the G-domain from bacterial elongation factor G reveal a sequential folding pathway initiating from the C-terminus. These results suggest that protein folding and synthesis proceed in opposite directions.
Sex Differences in Nociceptor Translatomes Contribute to Divergent Prostaglandin Signaling in Male and Female Mice

Abstract Background There are clinically relevant sex differences in acute and chronic pain mechanisms, but we are only beginning to understand their mechanistic basis. Transcriptome analyses of rodent whole dorsal root ganglion (DRG) have revealed sex differences, mostly in immune cells. We examined the transcriptome and translatome of the mouse DRG with the goal of identifying sex differences. Methods We used translating ribosome affinity purification sequencing and behavioral pharmacology to test the hypothesis that in Nav1.8-positive neurons, most of which are nociceptors, translatomes would differ by sex. Results We found 80 genes with sex differential expression in the whole DRG transcriptome and 66 genes whose messenger RNAs were sex differentially actively translated (translatome). We also identified different motifs in the 3′ untranslated region of messenger RNAs that were sex differentially translated. In further validation studies, we focused on Ptgds, which was increased in the translatome of female mice. The messenger RNA encodes the prostaglandin PGD2 synthesizing enzyme. We observed increased PTGDS protein and PGD2 in female mouse DRG. The PTGDS inhibitor AT-56 caused intense pain behaviors in male mice but was only effective at high doses in female mice. Conversely, female mice responded more robustly to another major prostaglandin, PGE2, than did male mice. PTGDS protein expression was also higher in female cortical neurons, suggesting that DRG findings may be generalizable to other nervous system structures. Conclusions Our results demonstrate sex differences in nociceptor-enriched translatomes and reveal unexpected sex differences in one of the oldest known nociceptive signaling molecule families, the prostaglandins.
Maternal Experience of Multiple Hardships and Fetal Growth: Extending Environmental Mixtures Methodology to Social Exposures.

Author(s): Goin, Dana E; Izano, Monika A; Eick, Stephanie M; Padula, Amy M; DeMicco, Erin; Woodruff, Tracey J; Morello-Frosch, Rachel | Abstract: BackgroundWomen can be exposed to a multitude of hardships before and during pregnancy that may affect fetal growth, but previous approaches have not analyzed them jointly as social exposure mixtures.MethodsWe evaluated the independent, mutually adjusted, and pairwise joint associations between self-reported hardships and birthweight for gestational age z-scores in the Chemicals in Our Bodies-2 prospective birth cohort (N = 510) using G-computation. We examined financial hardship, food insecurity, job strain, poor neighborhood environment, low community standing, caregiving, high burden of stressful life events, and unplanned pregnancy collected via questionnaire administered in the second trimester of pregnancy. We used propensity scores to ensure our analyses had sufficient data support and estimated absolute differences in outcomes.ResultsFood insecurity was most strongly associated with reduced birthweight for gestational age z-scores individually, with an absolute difference of -0.16, 95% confidence interval (CI) -0.45, 0.14. We observed an unexpected increase in z-scores associated with poor perceived neighborhood environment (0.18, 95% CI -0.04, 0.41). Accounting for coexposures resulted in similar findings. The pairwise joint effects were strongest for food insecurity in combination with unplanned pregnancy (-0.45, 95% CI -0.93, 0.02) and stressful life events (-0.42, 95% CI -0.90, 0.05). Poor neighborhood environment in combination with caregiving was associated with an increase in z-scores (0.47, 95% CI -0.01, 0.95).ConclusionsOur results are consistent with the hypothesis that experiencing food insecurity during pregnancy, alone and in combination with stressful life events and unplanned pregnancy, may affect fetal growth.
Data Augmentation and Loss Normalization for Deep Noise Suppression

Speech enhancement using neural networks is recently receiving large attention in research and being integrated in commercial devices and applications. In this work, we investigate data augmentation techniques for supervised deep learning-based speech enhancement. We show that not only augmenting SNR values to a broader range and a continuous distribution helps to regularize training, but also augmenting the spectral and dynamic level diversity. However, to not degrade training by level augmentation, we propose a modification to signal-based loss functions by applying sequence level normalization. We show in experiments that this normalization overcomes the degradation caused by training on sequences with imbalanced signal levels, when using a level-dependent loss function.
DEEP LEARNING OF PARAMETERIZED EQUATIONS WITH APPLICATIONS TO UNCERTAINTY QUANTIFICATION

We propose a numerical method for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the recent work of discovering unknown dynamical systems, in particular those using deep neural network (DNN). We propose a DNN structure, largely based upon the residual network (ResNet), to not only learn the unknown form of the governing equation but also take into account the random effect embedded in the system, which is generated by the random parameters. Once the DNN model is successfully constructed, it is able to produce system prediction over longer term and for arbitrary parameter values. For uncertainty quantification, it allows us to conduct uncertainty analysis by evaluating solution statistics over the parameter space.
The cosmic x-ray background

Abstract As the sky in the microwave band is dominated by a cosmic background, so too is the X-ray sky. In this report, the experimental approach used for measuring the X-ray background is explained and evaluated. The Compton-Getting interpretation of the dipole anisotropy in the microwave background is presented as a diagnostic of the weak asymmetry exhibited by the cosmic X-ray background. Spectral characteristics and spatial fluctuations of this X-ray background are described and then discussed within the context of what is known about individual extragalactic sources. It is concluded that the bulk of the cosmic X-ray background is yet to be understood. The critical apparatus of modern cosmology is reviewed and applied to this problem, providing constraints and indicating possible avenues for achieving a solution. The outlook for obtaining the new data called for is examined in terms of experiments now in preparation.
Worst-case Satisfaction of STL Specifications Using Feedforward Neural Network Controllers: A Lagrange Multipliers Approach

In this paper, a reinforcement learning approach for designing feedback neural network controllers for nonlinear systems is proposed. Given a Signal Temporal Logic (STL) specification which needs to be satisfied by the system over a set of initial conditions, the neural network parameters are tuned in order to maximize the satisfaction of the STL formula. The framework is based on a max-min formulation of the robustness of the STL formula. The maximization is solved through a Lagrange multipliers method, while the minimization corresponds to a falsification problem. We present our results on a vehicle and a quadrotor model and demonstrate that our approach reduces the training time more than 50 percent compared to the baseline approach.
H3DNet: 3D Object Detection Using Hybrid Geometric Primitives

We introduce H3DNet, which takes a colorless 3D point cloud as input and outputs a collection of oriented object bounding boxes (or BB) and their semantic labels. The critical idea of H3DNet is to predict a hybrid set of geometric primitives, i.e., BB centers, BB face centers, and BB edge centers. We show how to convert the predicted geometric primitives into object proposals by defining a distance function between an object and the geometric primitives. This distance function enables continuous optimization of object proposals, and its local minimums provide high-fidelity object proposals. H3DNet then utilizes a matching and refinement module to classify object proposals into detected objects and fine-tune the geometric parameters of the detected objects. The hybrid set of geometric primitives not only provides more accurate signals for object detection than using a single type of geometric primitives, but it also provides an overcomplete set of constraints on the resulting 3D layout. Therefore, H3DNet can tolerate outliers in predicted geometric primitives. Our model achieves state-of-the-art 3D detection results on two large datasets with real 3D scans, ScanNet and SUN RGB-D. Our code is open-sourced at here.
Gait modeling and optimization for the perturbed Stokes regime

Many forms of locomotion, both natural and artificial, are dominated by viscous friction in the sense that without power expenditure they quickly come to a standstill. From geometric mechanics, it is known that for swimming at the “Stokesian” (viscous; zero Reynolds number) limit, the motion is governed by a reduced-order “connection” model that describes how body shape change produces motion for the body frame with respect to the world. In the “perturbed Stokes regime” where inertial forces are still dominated by viscosity, but are not negligible (low Reynolds number), we show that motion is still governed by a functional relationship between shape velocity and body velocity, but this function is no longer linear in shape change rate. We derive this model using results from singular perturbation theory and the theory of noncompact normally hyperbolic invariant manifolds. Using the theoretical properties of this reduced-order model, we develop an algorithm that estimates an approximation to the dynamics near a cyclic body shape change (a “gait”) directly from observational data of shape and body motion. This extends our previous work which assumed kinematic “connection” models. To compare the old and new algorithms, we analyze simulated swimmers over a range of inertia-to-damping ratios. Our new class of models performs well on the Stokesian regime and over several orders of magnitude outside it into the perturbed Stokes regime, where it gives significantly improved prediction accuracy compared to previous work. In addition to algorithmic improvements, we thereby present a new class of models that is of independent interest. Their application to data-driven modeling improves our ability to study the optimality of animal gaits and our ability to use hardware-in-the-loop optimization to produce gaits for robots.
Small BGK Waves and Nonlinear Landau Damping

Consider a 1D Vlasov-poisson system with a fixed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space $${W^{s,p}\left( p >1 ,s <1 +\frac{1}{p}\right)}$$ of the steady distribution function, there exist nontrivial travelling wave solutions (BGK waves) with arbitrary minimal period and traveling speed. This implies that nonlinear Landau damping is not true in $${W^{s,p}\left( s <1 +\frac{1}{p}\right)}$$ space for any homogeneous equilibria and any spatial period. Indeed, in a $${W^{s,p}\left(s <1 +\frac{1}{p}\right)}$$ neighborhood of any homogeneous state, the long time dynamics is very rich, including travelling BGK waves, unstable homogeneous states and their possible invariant manifolds. Second, it is shown that for homogeneous equilibria satisfying Penrose’s linear stability condition, there exist no nontrivial travelling BGK waves and unstable homogeneous states in some $${W^{s,p}\left( p >1 ,s >1 +\frac{1}{p}\right)}$$ neighborhood. Furthermore, when p = 2, we prove that there exist no nontrivial invariant structures in the $${H^{s}\left( s > \frac{3}{2}\right) }$$ neighborhood of stable homogeneous states. These results suggest the long time dynamics in the $${W^{s,p}\left( s >1 +\frac{1}{p}\right) }$$ and particularly, in the $${H^{s}\left( s > \frac{3}{2}\right) }$$ neighborhoods of a stable homogeneous state might be relatively simple. We also demonstrate that linear damping holds for initial perturbations in very rough spaces, for a linearly stable homogeneous state. This suggests that the contrasting dynamics in W s, p spaces with the critical power $${s=1+\frac{1}{p}}$$ is a truly nonlinear phenomena which can not be traced back to the linear level.
Social Learning and Diffusion of Pervasive Goods: An Empirical Study of an African App Store

In this study, the authors develop a structural model that combines a macro diffusion model with a micro choice model to control for the effect of social influence on the mobile app choices of customers over app stores. Social influence refers to the density of adopters within the proximity of other customers. Using a large data set from an African app store and Bayesian estimation methods, the authors quantify the effect of social influence and investigate the impact of ignoring this process in estimating customer choices. The findings show that customer choices in the app store are explained better by offline than online density of adopters and that ignoring social influence in estimations results in biased estimates. Furthermore, the findings show that the mobile app adoption process is similar to adoption of music CDs, among all other classic economy goods. A counterfactual analysis shows that the app store can increase its revenue by 13.6% through a viral marketing policy (e.g., a sharing with friends and family button).
Intrinsic Alignment of Cluster Galaxies: The Redshift Evolution

We present measurements of two types of cluster galaxy alignments based on a volume limited and highly pure (≥90%) sample of clusters from the GMBCG catalog derived from Data Release 7 of the Sloan Digital Sky Survey (SDSS DR7). We detect a clear brightest cluster galaxy (BCG) alignment (the alignment of major axis of the BCG toward the distribution of cluster satellite galaxies). We find that the BCG alignment signal becomes stronger as the redshift and BCG absolute magnitude decrease and becomes weaker as BCG stellar mass decreases. No dependence of the BCG alignment on cluster richness is found. We can detect a statistically significant (≥3σ) satellite alignment (the alignment of the major axes of the cluster satellite galaxies toward the BCG) only when we use the isophotal fit position angles (P.A.s), and the satellite alignment depends on the apparent magnitudes rather than the absolute magnitudes of the BCGs. This suggests that the detected satellite alignment based on isophotal P.A.s from the SDSS pipeline is possibly due to the contamination from the diffuse light of nearby BCGs. We caution that this should not be simply interpreted as non-existence of the satellite alignment, but rather that we cannot detect them with our current photometric SDSS data. We perform our measurements on both SDSS r-band and i-band data, but do not observe a passband dependence of the alignments.
Impurity Effects of Aerogel in Superfluid (3)He

The discovery of superfluid 3 He in high porosity silica aerogels, and subsequent experimental and theoretical work, have led to a better general understanding of quasiparticle scattering from impurities in unconventional pairing systems. It is immensely helpful for understanding impurity effects in the case of superfluid 3 He that the structure of its order parameter is well-established. An overview of impurity effects is presented with emphasis on those experiments which have a quantitative interpretation in terms of theoretical models for homogeneous and inhomogeneous scattering. The latter can account successfully for most experimental results.
PRESBURGER ARITHMETIC, RATIONAL GENERATING FUNCTIONS, AND QUASI-POLYNOMIALS

Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose characteristic functions can be represented by rational generating functions; a geometric characterization of such sets is also given. In addition, if p = (p1, . . . , pn) are a subset of the free variables in a Presburger formula, we can define a counting function g(p) to be the number of solutions to the formula, for a given p. We show that every counting function obtained in this way may be represented as, equivalently, either a piecewise quasi-polynomial or a rational generating function. Finally, we translate known computational complexity results into this setting and discuss open directions.
An Analysis of SVD for Deep Rotation Estimation

Symmetric orthogonalization via SVD, and closely related procedures, are well-known techniques for projecting matrices onto $O(n)$ or $SO(n)$. These tools have long been used for applications in computer vision, for example optimal 3D alignment problems solved by orthogonal Procrustes, rotation averaging, or Essential matrix decomposition. Despite its utility in different settings, SVD orthogonalization as a procedure for producing rotation matrices is typically overlooked in deep learning models, where the preferences tend toward classic representations like unit quaternions, Euler angles, and axis-angle, or more recently-introduced methods. Despite the importance of 3D rotations in computer vision and robotics, a single universally effective representation is still missing. Here, we explore the viability of SVD orthogonalization for 3D rotations in neural networks. We present a theoretical analysis that shows SVD is the natural choice for projecting onto the rotation group. Our extensive quantitative analysis shows simply replacing existing representations with the SVD orthogonalization procedure obtains state of the art performance in many deep learning applications covering both supervised and unsupervised training.
CONSTRAINING SATURN'S CORE PROPERTIES BY A MEASUREMENT OF ITS MOMENT OF INERTIA—IMPLICATIONS TO THE CASSINI SOLSTICE MISSION

Knowledge of Saturn's axial moment of inertia can provide valuable information on its internal structure. We suggest that Saturn's angular momentum may be determined by the Solstice Mission (Cassini XXM) by measuring Saturn's pole precession rate and the Lense-Thirring acceleration on the spacecraft, and therefore put constraints on Saturn's moment of inertia. It is shown that Saturn's moment of inertia can change up to ~2% due to different core properties. However, a determination of Saturn's rotation rate is required to constrain its axial moment of inertia. A change of about seven minutes in rotation period leads to a similar uncertainty in the moment of inertia value as different core properties (mass, radius). A determination of Saturn's angular momentum and rotation period by the Solstice Mission could reveal important information on Saturn's internal structure, in particular, its core properties.
An Operator-Valued Kantorovich Metric on Complete Metric Spaces

The Kantorovich metric provides a way of measuring the distance between two Borel probability measures on a metric space. This metric has a broad range of applications from bioinformatics to image processing, and is commonly linked to the optimal transport problem in computer science (Deng and Du in Electron. Notes Theor. Comput. Sci. 253: 73–82, 2009; Villani in Optimal Transport: Old and New, Grundlehren der mathematischen Wissenschaften, vol. 338, 2009). Noteworthy to this paper will be the role of the Kantorovich metric in the study of iterated function systems, which are families of contractive mappings on a complete metric space. When the underlying metric space is compact, it is well known that the space of Borel probability measures on this metric space, equipped with the Kantorovich metric, constitutes a compact, and thus complete metric space. In previous work, we generalized the Kantorovich metric to operator-valued measures for a compact underlying metric space, and applied this generalized metric to the setting of iterated function systems (Davison in Acta Appl. Math., 2014, https://doi.org/10.1007/s10440-014-9976-y ; Generalizing the Kantorovich Metric to Projection-Valued Measures: With an Application to Iterated Function Systems, 2015; Acta Appl. Math., 2018, https://doi.org/10.1007/s10440-018-0161-6 ). We note that the work of P. Jorgensen, K. Shuman, and K. Kornelson provided the framework for our application to this setting (Jorgensen in Adv. Appl. Math. 34(3):561–590, 2005; Jorgenson et al. in J. Math. Phys. 48(8):083511, 2007; Jorgensen in Operator Theory, Operator Algebras, and Applications, Contemp. Math., vol. 414, pp. 13–26, 2006). The situation when the underlying metric space is complete, but not necessarily compact, has been studied by A. Kravchenko (Sib. Math. J. 47(1), 68–76, 2006). In this paper, we extend the results of Kravchenko to the generalized Kantorovich metric on operator-valued measures.
Deformations of Galois representations and exceptional monodromy

For any simple algebraic group G of exceptional type, we construct geometric \(\ell \)-adic Galois representations with algebraic monodromy group equal to G, in particular producing the first such examples in types \(\mathrm {F}_4\) and \(\mathrm {E}_6\). To do this, we extend to general reductive groups Ravi Ramakrishna’s techniques for lifting odd two-dimensional Galois representations to geometric \(\ell \)-adic representations.
Non-Iterative Rigid 2D/3D Point-Set Registration Using Semidefinite Programming

We describe a convex programming framework for pose estimation in 2D/3D point-set registration with unknown point correspondences. We give two mixed-integer nonlinear program (MINLP) formulations of the 2D/3D registration problem when there are multiple 2D images, and propose convex relaxations for both the MINLPs to semidefinite programs that can be solved efficiently by interior point methods. Our approach to the 2D/3D registration problem is non-iterative in nature as we jointly solve for pose and correspondence. Furthermore, these convex programs can readily incorporate feature descriptors of points to enhance registration results. We prove that the convex programs exactly recover the solution to the MINLPs under certain noiseless condition. We apply these formulations to the registration of 3D models of coronary vessels to their 2D projections obtained from multiple intra-operative fluoroscopic images. For this application, we experimentally corroborate the exact recovery property in the absence of noise and further demonstrate robustness of the convex programs in the presence of noise.
Spectral Neural Network Potentials for Binary Alloys

In this work, we present a numerical implementation to compute the atom-centered descriptors introduced by Bartok et al. [Phys. Rev. B 87, 184115 (2013)] based on the harmonic analysis of the atomic neighbor density function. Specifically, we focus on two types of descriptors, the smooth SO(3) power spectrum with the explicit inclusion of a radial basis and the SO(4) bispectrum obtained through mapping the radial component onto a polar angle of a four dimensional hypersphere. With these descriptors, various interatomic potentials for binary Ni–Mo alloys are obtained based on linear and neural network regression models. Numerical experiments suggest that both descriptors produce similar results in terms of accuracy. For linear regression, the smooth SO(3) power spectrum is superior to the SO(4) bispectrum when a large band limit is used. In neural network regression, better accuracy can be achieved with even less number of expansion components for both descriptors. As such, we demonstrate that spectral neural network potentials are feasible choices for large scale atomistic simulations.
Affine Hecke Algebras via DAHA

A method is suggested for obtaining the Plancherel measure for Affine Hecke Algebras as a limit of integral-type formulas for inner products in the polynomial and related modules of Double Affine Hecke Algebras. The analytic continuation necessary here is a generalization of “picking up residues” due to Arthur, Heckman, Opdam and others, which can be traced back to Hermann Weyl. Generally, it is a finite sum of integrals over double affine residual subtori; a complete formula is presented for $$A_1$$ in the spherical case.
Why Holes are not like Electrons Iii:. how Holes in the Normal State Turn Into Electrons in the Superconducting State

In recent work, we discussed the difference between electrons and holes in energy band in solids from a many-particle point of view, originating in the electron–electron interaction,1 and from a single particle point of view, originating in the electron–ion interaction.2 We proposed that superconductivity in solids only occurs when the Fermi level is close to the top of a band (hole carriers), that it originates in "undressing" of carriers from both the electron–electron and the electron–ion interaction, and that as a consequence holes in the normal state behave like electrons in the superconducting state.3 However, the connection between both undressing effects was left unclear, as was left unclear how the transformation from hole behavior to electron behavior occurs. Here, we clarify these questions by showing that the same electron–electron interaction physics that promotes pairing of hole carriers and undressing of carriers from the electron–electron interaction leads to undressing of carriers from the electron–ion interaction and transforms the behavior of carriers from hole-like to electron-like. A complete reorganization of the occupation of single-particle energy levels occurs. Furthermore this phenomenon is connected with the expulsion of negative charge that we predict to occur in superconductors. These unexpected connections support the validity of our theoretical framework, the theory of hole superconductivity, to explain superconductivity in solids.
Grid diagrams and Manolescu's unoriented skein exact triangle for knot Floer homology

We rederive Manolescu’s unoriented skein exact triangle for knot Floer homology over F2 combinatorially using grid diagrams, and extend it to the case with ℤ coefficients by sign refinements. Iteration of the triangle gives a cube of resolutions that converges to the knot Floer homology of an oriented link. Finally, we reestablish the homological σ–thinness of quasialternating links.
A Comprehensive Archival Chandra Search for X-ray Emission from Ultracompact Dwarf Galaxies

We present the first comprehensive archival study of the X-ray properties of ultracompact dwarf (UCD) galaxies, with the goal of identifying weakly-accreting central black holes in UCDs. Our study spans 578 UCDs distributed across thirteen different host systems, including clusters, groups, fossil groups, and isolated galaxies. Of the 336 spectroscopically-confirmed UCDs with usable archival Chandra imaging observations, 21 are X-ray-detected. Imposing a completeness limit of $L_X>2\times10^{38}$ erg s$^{-1}$, the global X-ray detection fraction for the UCD population is $\sim3\%$. Of the 21 X-ray-detected UCDs, seven show evidence of long-term X-ray time variability on the order of months to years. X-ray-detected UCDs tend to be more compact than non-X-ray-detected UCDs, and we find tentative evidence that the X-ray detection fraction increases with surface luminosity density and global stellar velocity dispersion. The X-ray emission of UCDs is fully consistent with arising from a population of low-mass X-ray binaries (LMXBs). In fact, there are fewer X-ray sources than expected using a naive extrapolation from globular clusters. Invoking the fundamental plane of black hole activity for SUCD1 near the Sombrero galaxy, for which archival Jansky Very Large Array imaging at 5 GHz is publicly available, we set an upper limit on the mass of a hypothetical central black hole in that UCD to be $\lesssim10^5M_{\odot}$. While the majority of our sources are likely LMXBs, we cannot rule out central black holes in some UCDs based on X-rays alone, and so we address the utility of follow-up radio observations to find weakly-accreting central black holes.
WHAT LIES BENEATH: USING p(z) TO REDUCE SYSTEMATIC PHOTOMETRIC REDSHIFT ERRORS

We use simulations to demonstrate that photometric redshift "errors" can be greatly reduced by using the photometric redshift probability distribution p(z) rather than a one-point estimate such as the most likely redshift. In principle, this involves tracking a large array of numbers rather than a single number for each galaxy. We introduce a very simple estimator that requires tracking only a single number for each galaxy, while retaining the systematic-error-reducing properties of using the full p(z) and requiring only very minor modifications to existing photometric redshift codes. We find that using this redshift estimator (or using the full p(z)) can substantially reduce systematics in dark energy parameter estimation from weak lensing, at no cost to the survey.
Einstein-Hilbert action on the brane for the bulk graviton

We find new closed string couplings on Dp-branes for the bosonic string. These couplings are quadratic in derivatives and therefore take the form of induced kinetic terms on the brane. For the graviton in particular we find the induced Einstein-Hilbert term as well as terms quadratic in the second fundamental tensor. We comment on tachyon dependences of these brane-localized couplings.
Soft Hair as a Soft Wig

We consider large gauge transformations of gravity and electromagnetism in $D=4$ asymptotically flat spacetime. Already at the classical level, we identify a canonical transformation that decouples the soft variables from the hard dynamics. We find that only the soft dynamics is constrained by BMS or large $U(1)$ charge conservation. Physically this corresponds to the fact that sufficiently long-wavelength photons or gravitons that are added to the in-state will simply pass through the interaction region, they scatter trivially in their own sector. This implies in particular that the large gauge symmetries bear no relevance to the black hole information paradox. We also present the quantum version of soft decoupling. As a consistency check, we show that the apparent mixing of soft and hard modes in the original variables arises entirely from the long range field of the hard charges, which is fixed by gauge invariance and so contains no additional information.
Bulk Locality and Entanglement Swapping in AdS/CFT

Localized bulk excitations in AdS/CFT are produced by operators which modify the pattern of entanglement in the boundary state. We show that simple models — consisting of entanglement swapping operators acting on a qubit system or a free field theory — capture qualitative features of gravitational backreaction and reproduce predictions of the Ryu-Takayanagi formula. These entanglement swapping operators naturally admit multiple representations associated with different degrees of freedom, thereby reproducing the code subspace structure emphasized by Almheiri, Dong, and Harlow. We also show that the boundary Reeh-Schlieder theorem implies that equivalence of certain operators on a code subspace necessarily breaks down when non-perturbative effects are taken into account (as is expected based on bulk arguments).