cssi/SciSciGPT-SciSciNet huggingface dataset:
The Incentive for Non-Price Discrimination by an Input Monopolist *

Abstract This paper considers the incentive for non-price discrimination of a monopolist in an input market who also sells in an oligopoly downstream market through a subsidiary. Such a monopolist can raise the costs of the rivals to its subsidiary though discriminatory quality degradation. I find that the monopolist always, even when it is cost-disadvantaged, has the incentive to raise the costs of the rivals to its subsidiary in a discriminatory fashion, but does not have the incentive to raise costs to the whole downstream industry including its subsidiary. Moreover, increasing rivals' costs nullifies the effects of traditional imputation floors, and prompts the creation of imputation floors that account for the artificial costs imposed on downstream rivals. The results of this paper raise concerns about the potentially anti-competitive effects of entry of local exchange carriers in long distance service. The results may also suggest the imposition of certain unbundling and technical specification disclosure requirements to monopolists in high technology industries.
Ultrathin Films of Pentacene on Ag(111): Charge-Transfer Bonding and Interadsorbate Interactions

Temperature-programmed desorption (TPD) was used to examine the surface binding and intermolecular interactions of mono- and multilayer thin films of the polycyclic aromatic acene, pentacene, depos...
Fundamental Analysis and Mean-Variance Optimal Portfolios

We integrate fundamental analysis with mean-variance portfolio optimization to form fully optimized fundamental portfolios. We find that fully optimized fundamental portfolios produce large out-of-sample factor alphas with high Sharpe ratios. They substantially outperform equal-weighted and value-weighted portfolios of stocks in the extreme decile of expected returns, an approach commonly used in fundamental analysis research. They also outperform the factor-based and parametric portfolio policy approaches used in the prior portfolio optimization literature. The relative performance gains from mean-variance optimized fundamental portfolios are persistent through time, robust to eliminating small capitalization firms from the investment set, and robust to incorporating estimated transactions costs. Our results suggest that future fundamental analysis research could implement this portfolio optimization approach to provide greater investment insights.
Single-top-quark production in the t-channel at NNLO

We present a calculation of t-channel single-top-quark production and decay in the five-flavor scheme at NNLO. Our results resolve a disagreement between two previous calculations of this process that found a difference in the inclusive cross section at the level of the NNLO coefficient itself. We compare in detail with the previous calculations at the inclusive, differential and fiducial level including b-quark tagging at a fixed scale μ = mt. In addition, we advocate the use of double deep inelastic scattering (DDIS) scales (μ2 = Q2 for the light-quark line and μ2 = Q2 + $$ {m}_t^2 $$ for the heavy-quark line) that maximize perturbative stability and allow for robust scale uncertainties. All NNLO and NLO⊗NLO contributions for production and decay are included in the on-shell and vertex-function approximation. We present fiducial and differential results for a variety of observables used in Standard Model and Beyond Standard Model analyses, and find an important difference between the NLO and NNLO predictions of exclusive t + n-jet cross sections. Overall we find that NNLO corrections are crucial for a precise identification of the t-channel process.
Leptin receptor expression in the dorsomedial hypothalamus stimulates breathing during NREM sleep in db/db mice.

Study objectives Obesity leads to obstructive sleep apnea (OSA), which is recurrent upper airway obstruction during sleep, and obesity hypoventilation syndrome (OHS), hypoventilation during sleep resulting in daytime hypercapnia. Impaired leptin signaling in the brain was implicated in both conditions, but mechanisms are unknown. We have previously shown that leptin stimulates breathing and treats OSA and OHS in leptin- deficient ob/ob mice and leptin-resistant diet-induced obese mice and that leptin's respiratory effects may occur in the dorsomedial hypothalamus (DMH). We hypothesized that leptin receptor LepR b-deficient db/db mice have obesity hypoventilation and that restoration of leptin signaling in the DMH will increase ventilation during sleep in these animals. Methods We measured arterial blood gas in unanesthetized awake db/db mice. We subsequently infected these animals with Ad-LepR b or control Ad-mCherry virus into the DMH and measured ventilation during sleep as well as CO2 production after intracerebroventricular (ICV) infusions of phosphate-buffered saline or leptin. Results Awake db/db mice had elevated CO2 levels in the arterial blood. Ad-LepR b infection resulted in LepR b expression in the DMH neurons in a similar fashion to wildtype mice. In LepR b-DMH db/db mice, ICV leptin shortened REM sleep and increased inspiratory flow, tidal volume and minute ventilation during NREM sleep without any effect on the quality of NREM sleep or CO2 production. Leptin had no effect on upper airway obstruction in these animals. Conclusion Leptin stimulates breathing and treats obesity hypoventilation acting on LepR b-positive neurons in the DMH.
Multi-Sparse Gaussian Process: Learning based Semi-Parametric Control

A key challenge with controlling complex dynamical systems is to accurately model them. However, this requirement is very hard to satisfy in practice. Data-driven approaches such as Gaussian processes (GPs) have proved quite effective by employing regression based methods to capture the unmodeled dynamical effects. However, GPs scale cubically with number of data points n, and it is often a challenge to perform real-time regression. In this paper, we propose a semi-parametric framework exploiting sparsity for learning-based control. We combine the parametric model of the system with multiple sparse GP models to capture any unmodeled dynamics. Multi-Sparse Gaussian Process (MSGP) uses multiple sparse models with unique hyperparameters for each one, thereby, preserving the richness and uniqueness of each sparse model. For a query point, a weighted sparse posterior prediction is performed based on N neighboring sparse models. Hence, the prediction complexity is significantly reduced from $\mathcal{O}\left( {{n^3}} \right)$ to $\mathcal{O}\left( {Np{u^2}} \right)$, p and u are data points and pseudo-inputs respectively for each sparse model. We validate MSGP’s learning performance for a quadrotor using a geometric controller in simulation. Comparison with GP, sparse GP, and local GP shows that MSGP has higher prediction accuracy than sparse and local GP, with significantly lower time complexity than all three. We also validate MSGP on a real quadrotor setup for unmodeled mass, inertia, and disturbances. The experiment video can be seen at: https://youtu.be/zUk1ISux6ao.
Finding New Signature Effects on Galactic Dynamics to Constrain Bose-Einstein-Condensed Cold Dark Matter

If cosmological cold dark matter (CDM) consists of light enough bosonic particles that their phase–space density exceeds unity, they will comprise a Bose–Einstein condensate (BEC). The nature of this BEC-CDM as a quantum fluid may then distinguish it dynamically from the standard form of CDM involving a collisionless gas of non-relativistic particles that interact purely gravitationally. We summarize some of the dynamical properties of BEC-CDM that may lead to observable signatures in galactic halos and present some of the bounds on particle mass and self-interaction coupling strength that result from a comparison with observed galaxies.
Resolving the Disparate Impact of Uncertainty: Affirmative Action vs. Affirmative Information.

Algorithmic risk assessments hold the promise of greatly advancing accurate decision-making, but in practice, multiple real-world examples have been shown to distribute errors disproportionately across demographic groups. In this paper, we characterize why error disparities arise in the first place. We show that predictive uncertainty often leads classifiers to systematically disadvantage groups with lower-mean outcomes, assigning them smaller true and false positive rates than their higher-mean counterparts. This can occur even when prediction is group-blind. We prove that to avoid these error imbalances, individuals in lower-mean groups must either be over-represented among positive classifications or be assigned more accurate predictions than those in higher-mean groups. We focus on the latter condition as a solution to bridge error rate divides and show that data acquisition for low-mean groups can increase access to opportunity. We call the strategy "affirmative information" and compare it to traditional affirmative action in the classification task of identifying creditworthy borrowers.
Asymmetry underlies stability in power grids.

Behavioral homogeneity is often critical for the functioning of network systems of interacting entities. In power grids, whose stable operation requires generator frequencies to be synchronized—and thus homogeneous—across the network, previous work suggests that the stability of synchronous states can be improved by making the generators homogeneous. Here, we show that a substantial additional improvement is possible by instead making the generators suitably heterogeneous. We develop a general method for attributing this counterintuitive effect to converse symmetry breaking, a recently established phenomenon in which the system must be asymmetric to maintain a stable symmetric state. These findings constitute the first demonstration of converse symmetry breaking in real-world systems, and our method promises to enable identification of this phenomenon in other networks whose functions rely on behavioral homogeneity. Converse symmetry breaking is a counterintuitive phenomenon in which the system must have an asymmetry to stabilize a symmetric state. Molnar et al. demonstrate this effect in real power-grid networks and show that synchronous operation can be improved by inhomogeneities across power generators.
Anchor Distance for 3D Multi-Object Distance Estimation From 2D Single Shot

Visual perception of the objects in a 3D environment is a key to successful performance in autonomous driving and simultaneous localization and mapping (SLAM). In this letter, we present a real time approach for estimating the distances to multiple objects in a scene using only a single-shot image. Given a 2D Bounding Box (BBox) and object parameters, a 3D distance to the object can be calculated directly using 3D reprojection; however, such methods are prone to significant errors because an error from the 2D detection can be amplified in 3D. In addition, it is also challenging to apply such methods to a real-time system due to the computational burden. In the case of the traditional multi-object detection methods, existing works have been developed for specific tasks such as object segmentation or 2D BBox regression. These methods introduce the concept of anchor BBox for elaborate 2D BBox estimation, and predictors are specialized and trained for specific 2D BBoxes. In order to estimate the distances to the 3D objects from a single 2D image, we introduce the notion of anchor distance based on an object's location and propose a method that applies the anchor distance to the multi-object detector structure. We let the predictors catch the distance prior using anchor distance and train the network based on the distance. The predictors can be characterized to the objects located in a specific distance range. By propagating the distance prior using a distance anchor to the predictors, it is feasible to perform the precise distance estimation and real-time execution simultaneously. The proposed method achieves about 30 FPS speed, and shows the lowest RMSE compared to the existing methods.
Spatial factor modeling: A Bayesian matrix-normal approach for misaligned data

Author(s): Zhang, Lu; Banerjee, Sudipto | Abstract: Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences.Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture anyunderlying spatial association for each variable and associations among the different dependent variables.Multivariate latent spatial process models have proved effective in driving statistical inference andrendering better predictive inference at arbitrary locations for the spatial process. High-dimensionalmultivariate spatial data, which is the theme of this article, refers to data sets where the number of spatiallocations and the number of spatially dependent variables is very large. The field has witnessed substantialdevelopments in scalable models for univariate spatial processes, but such methods for multivariate spatialprocesses, especially when the number of outcomes is moderately large, are limited in comparison. Here,we extend scalable modeling strategies for a single process to multivariate processes. We pursue Bayesianinference which is attractive for full uncertainty quantification of the latent spatial process. Our approachexploits distribution theory for the Matrix-Normal distribution, which we use to construct scalableversions of a hierarchical linear model of coregionalization (LMC) and spatial factor models that deliverinference over a high-dimensional parameter space including the latent spatial process. We illustrate thecomputational and inferential benefits of our algorithms over competing methods using simulation studiesand an analysis of a massive vegetation index dataset.
Rolling contact fatigue deformation mechanisms of nickel-rich nickel-titanium-hafnium alloys

Abstract The deformation mechanisms that dictate the tribological performances of heat treated Ni55Ti45, Ni54Ti45Hf1 and Ni56Ti36Hf8 alloys are revealed through rolling contact fatigue (RCF) testing and transmission electron microscopy (TEM) analyses. Analysis of worn samples that passed a 5×108 cycle RCF runout condition shows that damage is primarily confined to deformation bands that propagate several hundred nanometers – to – several microns beneath the surface. These bands nucleate via localization of dislocation slip within the B2 austenite phase of the alloys. For the Ni55Ti45 and Ni54Ti45Hf1 samples, further damage and eventual spall failures occur by shearing and dissolution of the strengthening Ni4Ti3 nanoprecipitates within the deformation bands, followed by nanocrystallization that sometimes includes stress-induced nucleation of B19′ nanocrystals. Eventually, complete amorphization occurs prior to fracture. The relative 15 – 25% increase in RCF contact stress performance of the Ni56Ti36Hf8 alloy correlates with a more limited depth of damaged material beneath the wear surface; heavily damaged material beneath spall failure sites only extends 1.5 µm into the sample, compared to > 6 µm for Ni55Ti45 and Ni54Ti45Hf1 alloys. This superior RCF damage resistance of the Ni56Ti36Hf8 alloy results from a lower fraction of B2 matrix phase (≤ 13 %) that is highly confined by both cubic Ni-rich NiTiHf and H-phase nanoprecipitates. Specifically, this microstructure limits the widths of deformation bands within the B2 austenite phase to less than the size of the strengthening nanoprecipitates, which in turn inhibits precipitate shearing and dissolution processes that precede nanocrystallization and amorphization.
Regularity and Expansion for Steady Prandtl Equations

Due to degeneracy near the boundary, the question of high regularity for solutions to the steady Prandtl equations has been a longstanding open question since the celebrated work of Oleinik. We settle this open question in affirmative in the absence of an external pressure. Our method is based on energy estimates for the quotient, $$q = \frac{v}{\bar{u}}$$ , $$\bar{u}$$ being the classical Prandtl solution, via the linear derivative Prandtl (LDP) equation. As a consequence, our regularity result leads to the construction of Prandtl layer expansion up to any order.
Models to inform neutralizing antibody therapy strategies during pandemics: the case of SARS-CoV-2

Background Neutralizing antibodies (nAbs) against SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) can play an important role in reducing impacts of the COVID-19 pandemic, complementing ongoing public health efforts such as diagnostics and vaccination. Rapidly designing, manufacturing and distributing nAbs requires significant planning across the product value chain and an understanding of the opportunities, challenges and risks throughout. Methods A systems framework comprised of four critical components is presented to aid in developing effective end-to-end nAbs strategies in the context of a pandemic: (1) product design and optimization, (2) epidemiology, (3) demand and (4) supply. Quantitative models are used to estimate product demand using available epidemiological data, simulate biomanufacturing operations from typical bioprocess parameters and calculate antibody production costs to meet clinical needs under various realistic scenarios. Results In a US-based case study during the 9-month period from March 15 to December 15, 2020, the projected number of SARS-CoV-2 infections was 15.73 million. The estimated product volume needed to meet therapeutic demand for the maximum number of clinically eligible patients ranged between 6.3 and 31.5 tons for 0.5 and 2.5 g dose sizes, respectively. The relative production scale and cost needed to meet demand are calculated for different centralized and distributed manufacturing scenarios. Conclusions Meeting demand for anti-SARS-CoV-2 nAbs requires significant manufacturing capacity and planning for appropriate administration in clinical settings. MIT Center for Biomedical Innovation's data-driven tools presented can help inform time-critical decisions by providing insight into important operational and policy considerations for making nAbs broadly accessible, while considering time and resource constraints.
Determinants of Pre-Pandemic Demand for the IMF's Concessional Financing

This study focuses on identifying the main factors that influenced country-specific and aggregate demand for IMF concessional financing between 1986 and 2018 and makes within-period and out-of-period forecasts. We find that the external debt level, inflation, and real effective exchange rate are the main economic variables influencing concessional borrowing for most eligible countries. Finally, our approach is able to provide quite accurate country-level and aggregate forecasts for historical financing events prior to the COVID-19 pandemic.
Sample size and power analysis for stepped wedge cluster randomised trials with binary outcomes

In stepped wedge cluster randomised trials (SW-CRTs), clusters of subjects are randomly assigned to sequences, where they receive a specific order of treatments. Compared to conventional cluster ra...
Metrics for aerial, urban lidar point clouds

Abstract This paper introduces five new density and accuracy metrics for aerial point clouds that address the complexity and objectives of modern, dense laser scans of urban scenes. The five metrics describe (1) vertical surface density (points per area on vertical surfaces); (2) vertical density as a function of horizontal density; (3) vertical surface accuracy; and a decomposition of error into (4) within-pass and (5) cross-pass components. Specifically considered is vertical surface coverage and the practice of overlapping flight passes to reduce the occlusions and achieve the vertical density needed for twenty-first-century use cases (e.g. curb and window detection). The application of these metrics to a quartet of recent urban flyovers demonstrates their relevance by establishing (1) the efficacy of considering sensor position and wall height when predicting point density on vertical surfaces; (2) that cross-pass registration accounts for a disproportionate amount of the vertical surface error (but not horizontal) and provides a meaningful parameter to compare high-density, urban point clouds; and (3) that compared to horizontal density and accuracy, the vertical counterparts are disproportionately impacted (positively for density and negatively for accuracy) by modern, optimized flight missions.
Symmetry in stationary and uniformly rotating solutions of active scalar equations

We study the radial symmetry properties of stationary and uniformly rotating solutions of the 2D Euler and gSQG equations, both in the smooth setting and the patch setting. For the 2D Euler equation, we show that any smooth stationary solution with compactly supported and nonnegative vorticity must be radial, without any assumptions on the connectedness of the support or the level sets. For the 2D Euler equation in the patch setting, we show that every uniformly rotating patch D with angular velocity Ω≤0 or Ω≥1 2 must be radial, where both bounds are sharp. For the gSQG equation, we obtain a similar symmetry result for Ω≤0 or Ω≥Ωα (with the bounds being sharp), under the additional assumption that the patch is simply connected. These results settle several open questions posed by Hmidi, de la Hoz, Hassainia, and Mateu on uniformly rotating patches. Along the way, we close a question by Choksi, Neumayer, and Topaloglu on overdetermined problems for the fractional Laplacian, which may be of independent interest. The main new ideas come from a calculus-of-variations point of view.
Extensive Entropy from Unitary Evolution

In quantum many-body systems, a Hamiltonian is called an ``extensive entropy generator'' if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any Hamiltonian whose spectrum has non-degenerate gaps is an extensive entropy generator; (ii) in the space of (geometrically) local Hamiltonians, the non-degenerate gap condition is satisfied almost everywhere. Specializing to many-body localized systems, these results imply the observation stated in the title of Bardarson et al. [PRL 109, 017202 (2012)].
High-throughput kinase inhibitor screening reveals roles for Aurora and Nuak kinases in neurite initiation and dendritic branching

Kinases are essential regulators of a variety of cellular signaling processes, including neurite formation-a foundational step in neurodevelopment. Aberrant axonal sprouting and failed regeneration of injured axons are associated with conditions like traumatic injury, neurodegenerative disease, and seizures. Investigating the mechanisms underlying neurite formation will allow for identification of potential therapeutics. We used a kinase inhibitor library to screen 493 kinase inhibitors and observed that 45% impacted neuritogenesis in Neuro2a (N-2a) cells. Based on the screening, we further investigated the roles of Aurora kinases A, B, and C and Nuak kinases 1 and 2. The roles of Aurora and Nuak kinases have not been thoroughly studied in the nervous system. Inhibition or overexpression of Aurora and Nuak kinases in primary cortical neurons resulted in various neuromorphological defects, with Aurora A regulating neurite initiation, Aurora B and C regulating neurite initiation and elongation, all Aurora kinases regulating arborization, and all Nuak kinases regulating neurite initiation and elongation and arborization. Our high-throughput screening and analysis of Aurora and Nuak kinases revealed their functions and may contribute to the identification of therapeutics.
Moral Decisions in the Age of COVID-19: Your Choices Really Matter

The moral decisions we make during this period, such as deciding whether to comply with quarantine rules, have unprecedented societal effects We simulate the “escape from Milan” that occurred on March 7th-8th 2020, when many travelers moved from a high-risk zone (Milan) to southern regions of Italy (Campania and Lazio) immediately after an imminent lockdown was announced Our simulations show that fewer than 50 active cases might have caused the sudden spread of the virus observed afterwards in these regions The surprising influence of the actions of few individuals on societal dynamics challenges our cognitive expectations – as in normal conditions, collective dynamics are rather robust to the decisions of few “cheaters” This situation therefore requires novel educational strategies that increase our awareness and understanding of the unprecedented effects of our individual moral decisions
Nano-confinement effects on liquid pressure

In this study, molecular dynamics simulations are performed to estimate the equilibrium pressure of liquid confined in nanopores. The simulations show that pressure is highly sensitive to the pore size and can significantly change from absolute positive to absolute negative values for a very small (0.1 nm) change in the pore size. The contribution from the solid–liquid interaction always dominates the pressure in the first liquid layer adjacent to the surface and the sensitiveness of pressure on the pore size is dependent on the atom distribution in the liquid layers. A surface influence number S is introduced to quantitatively characterize the degree of the confinement. At constant system temperature, the S number decreases with increasing pore size based on a power-law function. In nanopores with large S number, the pore liquid pressure is found to be independent of bulk liquid pressure, whereas in nanopores with small S number, the pore pressure is dependent and increases with bulk pressure.
Reducing travel-related SARS-CoV-2 transmission with layered mitigation measures: symptom monitoring, quarantine, and testing.

Balancing the control of SARS-CoV-2 transmission with the resumption of travel is a global priority. Current recommendations include mitigation measures before, during, and after travel. Pre- and post-travel strategies including symptom monitoring, antigen or nucleic acid amplification testing, and quarantine can be combined in multiple ways considering different trade-offs in feasibility, adherence, effectiveness, cost, and adverse consequences. We used a mathematical model to analyze the expected effectiveness of symptom monitoring, testing, and quarantine under different estimates of the infectious period, test-positivity relative to time of infection, and test sensitivity to reduce the risk of transmission from infected travelers during and after travel. If infection occurs 0–7 days prior to travel, immediate isolation following symptom onset prior to or during travel reduces risk of transmission while traveling by 30–35%. Pre-departure testing can further reduce risk, with testing closer to the time of travel being optimal even if test sensitivity is lower than an earlier test. For example, testing on the day of departure can reduce risk while traveling by 44–72%. For transmission risk after travel with infection time up to 7 days prior to arrival at the destination, isolation based on symptom monitoring reduced introduction risk at the destination by 42–56%. A 14-day quarantine after arrival, without symptom monitoring or testing, can reduce post-travel risk by 96–100% on its own. However, a shorter quarantine of 7 days combined with symptom monitoring and a test on day 5–6 after arrival is also effective (97--100%) at reducing introduction risk and is less burdensome, which may improve adherence. Quarantine is an effective measure to reduce SARS-CoV-2 transmission risk from travelers and can be enhanced by the addition of symptom monitoring and testing. Optimal test timing depends on the effectiveness of quarantine: with low adherence or no quarantine, optimal test timing is close to the time of arrival; with effective quarantine, testing a few days later optimizes sensitivity to detect those infected immediately before or while traveling. These measures can complement recommendations such as social distancing, using masks, and hand hygiene, to further reduce risk during and after travel.
Mayer–Vietoris property for relative symplectic cohomology

We construct a Hamiltonian Floer theory-based invariant called relative symplectic cohomology, which assigns a module over the Novikov ring to compact subsets of closed symplectic manifolds. We show the existence of restriction maps, and prove some basic properties. Our main contribution is to identify natural geometric conditions in which relative symplectic cohomology of two subsets satisfies the Mayer–Vietoris property. These conditions involve certain integrability assumptions involving geometric objects called barriers — roughly, a 1–parameter family of rank 2 coisotropic submanifolds. The proof uses a deformation argument in which the topological energy zero (ie constant) Floer solutions are the main actors.
Decentralized Frequency Alignment for Collaborative Beamforming in Distributed Phased Arrays

A new approach to distributed synchronization (frequency alignment) for the coordination of nodes in open loop coherent distributed antenna arrays to enable distributed beamforming is presented. This approach makes use of the concept of consensus optimization among nodes without requiring centralized control. Decentralized frequency consensus can be achieved through iterative frequency exchange among nodes. We derive a model of the signal received from a coherent distributed array and analyze the effects on beamforming of phase errors induced by oscillator frequency drift. We introduce and discuss the average consensus protocol for frequency transfer in undirected networks where each node transmits and receives frequency information from other nodes. We analyze the following cases: 1) undirected networks with a static topology; 2) undirected networks with a dynamic topology, where connections between nodes are made and lost dynamically; and 3) undirected networks with oscillator frequency drift. We show that all the nodes in a given network achieve average consensus and the number of iterations needed to achieve consensus can be minimized for a given cluster of nodes. We derive the theoretical phase error resulting from both processing noise and measurement noise, and derive an optimal update interval that minimizes the error. Numerical simulations demonstrate that the consensus algorithm enables tolerable errors to obtain high coherent gain of greater than 90% of the ideal gain in an error-free distributed phased array.
Spectral methods for nonlinear functionals and functional differential equations

We present a rigorous convergence analysis for cylindrical approximations of nonlinear functionals, functional derivatives, and functional differential equations (FDEs). The purpose of this analysis is twofold: First, we prove that continuous nonlinear functionals, functional derivatives, and FDEs can be approximated uniformly on any compact subset of a real Banach space admitting a basis by high-dimensional multivariate functions and high-dimensional partial differential equations (PDEs), respectively. Second, we show that the convergence rate of such functional approximations can be exponential, depending on the regularity of the functional (in particular its Frechet differentiability), and its domain. We also provide necessary and sufficient conditions for consistency, stability and convergence of cylindrical approximations to linear FDEs. These results open the possibility to utilize numerical techniques for high-dimensional systems such as deep neural networks and numerical tensor methods to approximate nonlinear functionals in terms of high-dimensional functions, and compute approximate solutions to FDEs by solving high-dimensional PDEs. Numerical examples are presented and discussed for prototype nonlinear functionals and for an initial value problem involving a linear FDE.
Police-Generated Killings: The Gap between Ethics and Law:

This article offers a normative analysis of some of the most controversial incidents involving police—what I call police-generated killings. In these cases, bad police tactics create a situation wh...
Deterministic ill-posedness and probabilistic well-posedness of the viscous nonlinear wave equation describing fluid-structure interaction

We study low regularity behavior of the nonlinear wave equation in $\mathbb{R}^2$ augmented by the viscous dissipative effects described by the Dirichlet-Neumann operator. Problems of this type arise in fluid-structure interaction where the Dirichlet-Neumann operator models the coupling between a viscous, incompressible fluid and an elastic structure. We show that despite the viscous regularization, the Cauchy problem with initial data $(u,u_t)$ in $H^s(\mathbb{R}^2)\times H^{s-1}(\mathbb{R}^2)$, is ill-posed whenever ${0 < s < s_{cr}}$, where the critical exponent $s_{cr}$ depends on the degree of nonlinearity. In particular, for the quintic nonlinearity $u^5$, the critical exponent in $\mathbb{R}^2$ is $s_{cr} = 1/2$, which is the same as the critical exponent for the associated nonlinear wave equation without the viscous term. We then show that if the initial data is perturbed using a Wiener randomization, which perturbs initial data in the frequency space, then the Cauchy problem for the quintic nonlinear viscous wave equation is well-posed almost surely for the supercritical exponents $s$ such that $-1/6 < s \le s_{cr} = 1/2$. To the best of our knowledge, this is the first result showing ill-posedness and probabilistic well-posedness for the nonlinear viscous wave equation arising in fluid-structure interaction.
Dispersion formulas in QFTs, CFTs and holography

We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At n-points, the QFT dispersion formula depends on a sum of nested advanced commutators. For CFT four-point functions, we show that the momentum space dispersion formula is equivalent to the CFT dispersion formula, up to possible semi-local terms. We also show that the Polyakov-Regge expansions associated to the momentum space and CFT dispersion formulas are related by a Fourier transform. In the process, we prove that the momentum space conformal blocks of the causal double-commutator are equal to cut Witten diagrams. Finally, by combining the momentum space dispersion formulas with the AdS Cutkosky rules, we find a complete, bulk unitarity method for AdS/CFT correlators in momentum space.
Cautious Reinforcement Learning via Distributional Risk in the Dual Domain

We study the estimation of risk-sensitive policies in reinforcement learning (RL) problems defined by a Markov Decision Process (MDPs) whose state and action spaces are countably finite. Prior efforts are predominately afflicted by computational challenges associated with the fact that risk-sensitive MDPs are time-inconsistent, and hence modifications of Bellman’s equations are required, which often do not permit efficient fixed point schemes. To ameliorate this issue, we propose a new definition of risk, which we call caution , as a penalty function added to the dual of the linear programming (LP) formulation of tabular RL. Caution quantifies the distributional risk of a policy, and is a function of the policy’s long-term state occupancy measure. When the risk is a convex function of the occupancy measure, we propose to solve this problem in an online model-free manner with a stochastic variant of primal-dual method that uses Kullback-Lieber (KL) divergence as its proximal term. We establish that the sample complexity required to attain near-optimal solutions matches tight dependencies on the cardinality of the spaces, but also depends on the infinity norm of the risk measure’s gradient. Moreover, when the risk is non-convex, we propose a block-coordinate augmentation of the aforementioned approach, and establish its convergence to KKT points. Experiments demonstrate that this approach improves the reliability of reward accumulation without additional computation as compared to risk-neutral LP solvers, both for convex and non-convex risks, respectively, for the cases of KL divergence to a prior, and the variance.
MSR-GAN: Multi-Segment Reconstruction via Adversarial Learning

Multi-segment reconstruction (MSR) is the problem of estimating a signal given noisy partial observations. Here each observation corresponds to a randomly located segment of the signal. While previous works address this problem using template or moment-matching, in this paper we address MSR from an unsupervised adversarial learning standpoint, named MSR-GAN. We formulate MSR as a distribution matching problem where the goal is to recover the signal and the probability distribution of the segments such that the distribution of the generated measurements following a known forward model is close to the real observations. This is achieved once a min-max optimization involving a generator-discriminator pair is solved. MSR-GAN is mainly inspired by CryoGAN [1]. However, in MSR-GAN we no longer assume the probability distribution of the latent variables, i.e. segment locations, is given and seek to recover it alongside the unknown signal. For this purpose, we show that the loss at the generator side originally is non-differentiable with respect to the segment distribution. Thus, we propose to approximate it using Gumbel-Softmax reparametrization trick. Our proposed solution is generalizable to a wide range of inverse problems. Our simulation results and comparison with various baselines verify the potential of our approach in different settings.
Fake $13$-projective spaces with cohomogeneity one actions

We show that some embedded standard $13$-spheres in Shimada's exotic $15$-spheres have $\mathbb{Z}_2$ quotient spaces, $P^{13}$s, that are fake real $13$-dimensional projective spaces, i.e., they are homotopy equivalent, but not diffeomorphic to the standard $\mathbb{R}\mathrm{P}^{13}$. As observed by F. Wilhelm and the second named author in [RW], the Davis $\mathsf{SO}(2)\times \mathsf{G}_2$ actions on Shimada's exotic $15$-spheres descend to the cohomogeneity one actions on the $P^{13}$s. We prove that the $P^{13}$s are diffeomorphic to well-known $\mathbb{Z}_2$ quotients of certain Brieskorn varieties, and that the Davis $\mathsf{SO}(2)\times \mathsf{G}_2$ actions on the $P^{13}$s are equivariantly diffeomorphic to well-known actions on these Brieskorn quotients. The $P^{13}$s are octonionic analogues of the Hirsch-Milnor fake $5$-dimensional projective spaces, $P^{5}$s. K. Grove and W. Ziller showed that the $P^{5}$s admit metrics of non-negative curvature that are invariant with respect to the Davis $\mathsf{SO}(2)\times \mathsf{SO}(3)$-cohomogeneity one actions. In contrast, we show that the $P^{13}$s do not support $\mathsf{SO}(2)\times \mathsf{G}_2$-invariant metrics with non-negative sectional curvature.
Comparison of radiomic feature aggregation methods for patients with multiple tumors

Radiomic feature analysis has been shown to be effective at analyzing diagnostic images to model cancer outcomes. It has not yet been established how to best combine radiomic features in cancer patients with multifocal tumors. As the number of patients with multifocal metastatic cancer continues to rise, there is a need for improving personalized patient-level prognosis to better inform treatment. We compared six mathematical methods of combining radiomic features of 3,596 tumors in 831 patients with multiple brain metastases and evaluated the performance of these aggregation methods using three survival models: a standard Cox proportional hazards model, a Cox proportional hazards model with LASSO regression, and a random survival forest. Across all three survival models, the weighted average of the largest three metastases had the highest concordance index (95% confidence interval) of 0.627 (0.595–0.661) for the Cox proportional hazards model, 0.628 (0.591–0.666) for the Cox proportional hazards model with LASSO regression, and 0.652 (0.565–0.727) for the random survival forest model. This finding was consistent when evaluating patients with different numbers of brain metastases and different tumor volumes. Radiomic features can be effectively combined to estimate patient-level outcomes in patients with multifocal brain metastases. Future studies are needed to confirm that the volume-weighted average of the largest three tumors is an effective method for combining radiomic features across other imaging modalities and tumor types.
Fly seizure EEG: field potential activity in the Drosophila brain

Hypersynchronous neural activity is a characteristic feature of seizures. Although many Drosophila mutants of epilepsy-related genes display clear behavioral spasms and motor unit hyperexcitability, field potential measurements of aberrant hypersynchronous activity across brain regions during seizures have yet to be described. Here, we report a straightforward method to observe local field potentials (LFPs) from the Drosophila brain to monitor ensemble neural activity during seizures in behaving tethered flies. High frequency stimulation across the brain reliably triggers a stereotypic sequence of electroconvulsive seizure (ECS) spike discharges readily detectable in the dorsal longitudinal muscle (DLM) and coupled with behavioral spasms. During seizure episodes, the LFP signal displayed characteristic large-amplitude oscillations with a stereotypic temporal correlation to DLM flight muscle spiking. ECS-related LFP events were clearly distinct from rest- and flight-associated LFP patterns. We further characterized the LFP activity during different types of seizures originating from genetic and pharmacological manipulations. In the 'bang-sensitive' sodium channel mutant bangsenseless (bss), the LFP pattern was prolonged, and the temporal correlation between LFP oscillations and DLM discharges was altered. Following administration of the pro-convulsant GABAA blocker picrotoxin, we uncovered a qualitatively different LFP activity pattern, which consisted of a slow (1-Hz), repetitive, waveform, closely coupled with DLM bursting and behavioral spasms. Our approach to record brain LFPs presents an initial framework for electrophysiological analysis of the complex brain-wide activity patterns in the large collection of Drosophila excitability mutants.
Structure and Mechanistic Analyses of the Gating Mechanism of Elongating Ketosynthases

Abstract Ketosynthases (KSs) catalyze carbon-carbon bond forming reactions in fatty acid synthases (FASs) and polyketide synthases (PKSs). KSs utilize a two-step ping pong kinetic mechanism to carry out an overall decarboxylative thio-Claisen condensation that can be separated into the transacylation and condensation reactions. In both steps, an acyl carrier protein (ACP) delivers thioester tethered substrates to the active sites of KSs. Therefore, protein-protein interactions (PPIs) and KS-mediated substrate recognition events are required for catalysis. Recently, crystal structures of Escherichia coli elongating type II FAS KSs, FabF and FabB, in complex with E. coli ACP, AcpP, revealed distinct conformational states of two active site KS loops. These loops were proposed to operate via a gating mechanism to coordinate substrate recognition and delivery followed by catalysis. Here we interrogate this proposed gating mechanism by solving two additional high-resolution structures of substrate engaged AcpP-FabF complexes, one of which provides the missing AcpP-FabF gate-closed conformation. Clearly defined interactions of one of these active site loops with AcpP are present in both the open and closed conformations, suggesting AcpP binding triggers or stabilizes gating transitions, further implicating PPIs in carrier protein-dependent catalysis. We functionally demonstrate the importance of gating in the overall KS condensation reaction and provide experimental evidence for its role in the transacylation reaction. Furthermore, we evaluate the catalytic importance of these loops using alanine scanning mutagenesis and also investigate chimeric FabF constructs carrying elements found in type I PKS KS domains. These findings broaden our understanding of the KS mechanism which advances future engineering efforts in both FASs and evolutionarily related PKSs.
Designing temporal networks that synchronize under resource constraints

Being fundamentally a non-equilibrium process, synchronization comes with unavoidable energy costs and has to be maintained under the constraint of limited resources. Such resource constraints are often reflected as a finite coupling budget available in a network to facilitate interaction and communication. Here, we show that introducing temporal variation in the network structure can lead to efficient synchronization even when stable synchrony is impossible in any static network under the given budget, thereby demonstrating a fundamental advantage of temporal networks. The temporal networks generated by our open-loop design are versatile in the sense of promoting synchronization for systems with vastly different dynamics, including periodic and chaotic dynamics in both discrete-time and continuous-time models. Furthermore, we link the dynamic stabilization effect of the changing topology to the curvature of the master stability function, which provides analytical insights into synchronization on temporal networks in general. In particular, our results shed light on the effect of network switching rate and explain why certain temporal networks synchronize only for intermediate switching rate. The ability of complex networks to synchronize themselves is limited by available coupling resources. Zhang and Strogatz show that allowing temporal variation in the network structure can lead to synchronization even when stable synchrony is impossible in any static network under the fixed budget.
Assessment of the relativistic rotational transformations

Rotational transformations describe relativistic effects in rotating frames. There are four major kinematic rotational transformations: the Langevin metric; Post transformation; Franklin transforma...
Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds

To recover the topology of a manifold in the presence of heavy tailed or exponentially decaying noise, one must understand the behavior of geometric complexes whose points lie in the tail of these noise distributions. This study advances this line of inquiry, and demonstrates functional strong laws of large numbers for the Euler characteristic process of random geometric complexes formed by random points outside of an expanding ball in $\mathbb {R}^{d}$ . When the points are drawn from a heavy tailed distribution with a regularly varying tail, the Euler characteristic process grows at a regularly varying rate, and the scaled process converges uniformly and almost surely to a smooth function. When the points are drawn from a distribution with an exponentially decaying tail, the Euler characteristic process grows logarithmically, and the scaled process converges to another smooth function in the same sense. All of the limit theorems take place when the points inside the expanding ball are densely distributed, so that the simplex counts outside of the ball of all dimensions contribute to the Euler characteristic process.