cssi/SciSciGPT-SciSciNet huggingface dataset:
Representations of Lie superalgebras in prime characteristic II: The queer series

Abstract The modular representation theory of the queer Lie superalgebra q ( n ) over characteristic p > 2 is developed. We obtain a criterion for the irreducibility of baby Verma modules with semisimple p -characters χ and a criterion for the semisimplicity of the corresponding reduced enveloping algebras U χ ( q ( n ) ) . A ( 2 p ) -power divisibility of dimensions of q ( n ) -modules with nilpotent p -characters is established. The representation theory of q ( 2 ) is treated in detail. We formulate a Morita super-equivalence conjecture for q ( n ) with general p -characters which is verified for n = 2 .
Mitigating Bias in Adaptive Data Gathering via Differential Privacy

Data that is gathered adaptively --- via bandit algorithms, for example --- exhibits bias. This is true both when gathering simple numeric valued data --- the empirical means kept track of by stochastic bandit algorithms are biased downwards --- and when gathering more complicated data --- running hypothesis tests on complex data gathered via contextual bandit algorithms leads to false discovery. In this paper, we show that this problem is mitigated if the data collection procedure is differentially private. This lets us both bound the bias of simple numeric valued quantities (like the empirical means of stochastic bandit algorithms), and correct the p-values of hypothesis tests run on the adaptively gathered data. Moreover, there exist differentially private bandit algorithms with near optimal regret bounds: we apply existing theorems in the simple stochastic case, and give a new analysis for linear contextual bandits. We complement our theoretical results with experiments validating our theory.
ALGEBRAS OF ALMOST PERIODIC FUNCTIONS WITH BOHR-FOURIER SPECTRUM IN A SEMIGROUP: HERMITE PROPERTY AND ITS APPLICATIONS

Abstract It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr–Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr–Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener–Hopf type of rectangular matrix functions and the Toeplitz corona problem in the context of almost periodic functions of several variables.
The Iwasawa theoretic Gross–Zagier theorem

We prove Mazur and Rubin's Iwasawa-theoretic Gross-Zagier conjecture (under some restrictive hypotheses), which relates Heegner points in towers of number fields to the 2-variable p-adic L-function. The result generalizes Perrin-Riou's p-adic Gross-Zagier theorem.
Contact monoids and Stein cobordisms

Suppose S is a compact surface with boundary, and let g be a diffeomorphism of S which fixes the boundary pointwise. We denote by (M_{S,g},\xi_{S,g})$ the contact 3-manifold compatible with the open book (S,g). In this article, we construct a Stein cobordism from the contact connected sum (M_{S,h},\xi_{S,h}) # (M_{S,g},\xi_{S,g}) to (M_{S,hg},\xi_{S,hg}), for any two boundary-fixing diffeomorphisms h and g. This cobordism accounts for the comultiplication map on Heegaard Floer homology discovered in an earlier paper by the author, and it illuminates several geometrically interesting monoids in the mapping class group of S. We derive some consequences for the fillability of contact manifolds obtained as cyclic branched covers of transverse knots.
Symmetries and regularity for holomorphic maps between balls

Let $f:{\mathbb B}^n \to {\mathbb B}^N$ be a holomorphic map. We study subgroups $\Gamma_f \subseteq {\rm Aut}({\mathbb B}^n)$ and $T_f \subseteq {\rm Aut}({\mathbb B}^N)$. When $f$ is proper, we show both these groups are Lie subgroups. When $\Gamma_f$ contains the center of ${\bf U}(n)$, we show that $f$ is spherically equivalent to a polynomial. When $f$ is minimal we show that there is a homomorphism $\Phi:\Gamma_f \to T_f$ such that $f$ is equivariant with respect to $\Phi$. To do so, we characterize minimality via the triviality of a third group $H_f$. We relate properties of ${\rm Ker}(\Phi)$ to older results on invariant proper maps between balls. When $f$ is proper but completely non-rational, we show that either both $\Gamma_f$ and $T_f$ are finite or both are noncompact.
Fast and spectrally accurate evaluation of gyroaverages in non-periodic gyrokinetic-Poisson simulations

We present a fast and spectrally accurate numerical scheme for the evaluation of the gyroaveraged electrostatic potential in non-periodic gyrokinetic-Poisson simulations. Our method relies on a reformulation of the gyrokinetic-Poisson system in which the gyroaverage in Poisson’s equation is computed for the compactly supported charge density instead of the non-periodic, non-compactly supported potential itself. We calculate this gyroaverage with a combination of two Fourier transforms and a Hankel transform, which has the near optimal run-time complexity , where is the number of spatial grid points, the number of grid points in Fourier space and the number of grid points in velocity space. We present numerical examples illustrating the performance of our code and demonstrating geometric convergence of the error.
Simulation of unsteady blood flows in a patient-specific compliant pulmonary artery with a highly parallel monolithically coupled fluid-structure interaction algorithm.

Computational fluid dynamics (CFD) is increasingly used to study blood flows in patient-specific arteries for understanding certain cardiovascular diseases. The techniques work quite well for relatively simple problems but need improvements when the problems become harder when (a) the geometry becomes complex (eg, a few branches to a full pulmonary artery), (b) the model becomes more complex (eg, fluid-only to coupled fluid-structure interaction), (c) both the fluid and wall models become highly nonlinear, and (d) the computer on which we run the simulation is a supercomputer with tens of thousands of processor cores. To push the limit of CFD in all four fronts, in this paper, we develop and study a highly parallel algorithm for solving a monolithically coupled fluid-structure system for the modeling of the interaction of the blood flow and the arterial wall. As a case study, we consider a patient-specific, full size pulmonary artery obtained from computed tomography (CT) images, with an artificially added layer of wall with a fixed thickness. The fluid is modeled with a system of incompressible Navier-Stokes equations, and the wall is modeled by a geometrically nonlinear elasticity equation. As far as we know, this is the first time the unsteady blood flow in a full pulmonary artery is simulated without assuming a rigid wall. The proposed numerical algorithm and software scale well beyond 10 000 processor cores on a supercomputer for solving the fluid-structure interaction problem discretized with a stabilized finite element method in space and an implicit scheme in time involving hundreds of millions of unknowns.
A Cheeger-type inequality on simplicial complexes

Abstract In this paper, we consider a variation on Cheeger numbers related to the coboundary expanders recently defined by Dotterrer and Kahle. A Cheeger-type inequality is proved, which is similar to a result on graphs due to Fan Chung. This inequality is then used to study the relationship between coboundary expanders on simplicial complexes and their corresponding eigenvalues, complementing and extending results found by Gundert and Wagner. In particular, we find these coboundary expanders do not satisfy natural Buser or Cheeger inequalities.
Hyponormal Toeplitz operators with non-harmonic algebraic symbol

Given a bounded function $$\varphi $$ on the unit disk in the complex plane, we consider the operator $$T_{\varphi }$$, defined on the Bergman space of the disk and given by $$T_{\varphi }(f)=P(\varphi f)$$, where P denotes the orthogonal projection to the Bergman space in $$L^2({\mathbb {D}},dA)$$. For algebraic symbols $$\varphi $$, we provide new necessary conditions on $$\varphi $$ for $$T_{\varphi }$$ to be hyponormal, extending recent results of Fleeman and Liaw. Our approach is perturbative and aims to understand how small changes to a symbol preserve or destroy hyponormality of the corresponding operator. We consider both additive and multiplicative perturbations of a variety of algebraic symbols. One of our main results provides a necessary condition on the complex constant C for the operator $$T_{z^n+C|z|^s}$$ to be hyponormal. This condition is also sufficient if $$s\ge 2n$$.
Umklapp Scattering and Heat Conductivity of Superlattices

The mean free path of phonons in superlattices is estimated. It is shown to be strongly dependent on the superlattice period due to the Umklapp scattering in subbands. It first falls with increasing the superlattice period until it becomes comparable with the latter after what it rises back to the bulk value. Similar behavior is expected of heat conductivity, which is proportional to the mean free path.
Strain induced slowdown of front propagation in random shear flow via analysis of G-equations

It is proved that for the 2-dimensional case with random shear flow of the G-equation model with strain term, the strain term reduces the front propagation. Also an improvement of the main result by Armstrong-Souganidis is provided.
Monitoring voltage collapse margin with synchrophasors across transmission corridors with multiple lines and multiple contingencies

We use synchrophasor measurements of the complex voltage and current at both ends of multiple transmission lines that connect areas of a power system to monitor the online voltage collapse margin. A new reduction is used to reduce the multiple transmission lines to a single line equivalent and determine how to combine the synchrophasor measurements. Generator reactive power limits can be accommodated. The results show that this methodology can capture the effect of multiple contingencies inside the transmission corridors, giving awareness to the operators about the severity of contingencies with respect to voltage stability.
Bounded Composition Operators and Multipliers of Some Reproducing Kernel Hilbert Spaces on the Bidisk

We study the boundedness of composition operators on the bidisk using reproducing kernels. We show that a composition operator is bounded on the Hardy space $$H^2(\mathbb {D}^2)$$ if some associated function is a positive kernel. This positivity condition naturally leads to the study of the sub-Hardy Hilbert spaces of the bidisk, which are analogs of de Branges–Rovnyak spaces on the unit disk. We discuss multipliers of those spaces and obtain some classes of bounded composition operators on the bidisk.
Euclidean signature semi-classical methods for bosonic field theories: interacting scalar fields

Elegant 'microlocal' methods have long since been extensively developed for the analysis of conventional Schroedinger eigenvalue problems. For technical reasons though these methods have not heretofore been applicable to quantum field theories. In this article however we initiate a 'Euclidean signature semi-classical' program to extend the scope of these analytical techniques to encompass the study of self-interacting scalar fields in 1 + 1, 2 + 1 and 3 + 1 dimensions. The basic microlocal approach entails, first of all, the solution of a single, nonlinear equation of Hamilton-Jacobi type followed by the integration (for both ground and excited states) of a sequence of linear 'transport' equations along the 'flow' generated by the 'fundamental solution' to the aforementioned Hamilton-Jacobi equation. Using a combination of the direct method of the calculus of variations, elliptic regularity theory and the Banach space version of the implicit function theorem we establish, in a suitable function space setting, the existence, uniqueness and global regularity of this needed 'fundamental solution' to the relevant, Euclidean signature Hamilton-Jacobi equation for the systems under study. Our methods are applicable to (massive) scalar fields with polynomial self-interactions of renormalizable type. They can, as we shall show elsewhere, also be applied to Yang-Mills fields in 2 + 1 and 3 + 1 dimensions.
Reconstructing Speech Stimuli From Human Auditory Cortex Activity Using a WaveNet Approach

The superior temporal gyrus (STG) region of cortex critically contributes to speech recognition. In this work, we show that a proposed WaveNet, with limited available data, is able to reconstruct speech stimuli from STG intracranial recordings. We further investigate the impulse response of the fitted model for each recording electrode and observe phoneme level temporospectral tuning properties for the recorded area of cortex. This discovery is consistent with previous studies implicating the posterior STG (pSTG) in a phonetic representation of speech and provides detailed acoustic features that certain electrode sites possibly extract during speech recognition.
Near-Optimal Sample Complexity Bounds for Maximum Likelihood Estimation of Multivariate Log-concave Densities

We study the problem of learning multivariate log-concave densities with respect to a global loss function. We obtain the first upper bound on the sample complexity of the maximum likelihood estimator (MLE) for a log-concave density on $\mathbb{R}^d$, for all $d \geq 4$. Prior to this work, no finite sample upper bound was known for this estimator in more than $3$ dimensions. In more detail, we prove that for any $d \geq 1$ and $\epsilon>0$, given $\tilde{O}_d((1/\epsilon)^{(d+3)/2})$ samples drawn from an unknown log-concave density $f_0$ on $\mathbb{R}^d$, the MLE outputs a hypothesis $h$ that with high probability is $\epsilon$-close to $f_0$, in squared Hellinger loss. A sample complexity lower bound of $\Omega_d((1/\epsilon)^{(d+1)/2})$ was previously known for any learning algorithm that achieves this guarantee. We thus establish that the sample complexity of the log-concave MLE is near-optimal, up to an $\tilde{O}(1/\epsilon)$ factor.
Centralizers of Camina $p$-groups of nilpotence class $3$

Let $G$ be a Camina $p$-group of nilpotence class $3$. We prove that if $G' < C_G (G')$, then $|Z(G)| \le |G':G_3|^{1/2}$. We also prove that if $G/G_3$ has only one or two abelian subgroups of order $|G:G'|$, then $G' < C_G (G')$. If $G/G_3$ has $p^a + 1$ abelian subgroups of order $|G:G'|$, then either $G' < C_G (G')$ or $|Z(G)| \le p^{2a}$.
Brouwer's fixed-point theorem in real-cohesive homotopy type theory

We combine homotopy type theory with axiomatic cohesion, expressing the latter internally with a version of ‘adjoint logic’ in which the discretization and codiscretization modalities are characterized using a judgemental formalism of ‘crisp variables.’ This yields type theories that we call ‘spatial’ and ‘cohesive,’ in which the types can be viewed as having independent topological and homotopical structure. These type theories can then be used to study formally the process by which topology gives rise to homotopy theory (the ‘fundamental ∞-groupoid’ or ‘shape’), disentangling the ‘identifications’ of homotopy type theory from the ‘continuous paths’ of topology. In a further refinement called ‘real-cohesion,’ the shape is determined by continuous maps from the real numbers, as in classical algebraic topology. This enables us to reproduce formally some of the classical applications of homotopy theory to topology. As an example, we prove Brouwer's fixed-point theorem.
NONALTERNATING KNOTS AND JONES POLYNOMIALS

We consider here nonalternating knots and their properties. Specifically, we show certain classes of knots have nontrivial Jones polynomials.
Metacognitive and motivation deficits, exposure to trauma, and high parental demands characterize adolescents with late-onset ADHD

The objective of this study is to evaluate support for three hypotheses about the etiology of adolescent-onset ADHD symptoms: (1) a “cool” cognitive load hypothesis, (2) a “hot” rewards processing hypothesis, and (3) a trauma exposure hypothesis. Participants (N = 50) were drawn from two public high schools in a culturally diverse metropolitan area. A detailed procedure for identifying and confirming late-onset ADHD cases is described. Adolescents with late-onset ADHD (n = 15) were identified and compared to childhood-onset (n = 17) and non-ADHD classmates (n = 18). Adolescents and parents completed measures of neurocognition, rewards’ processing, clinical profile, and environmental demands. Late-onset cases were clinically and neurocognitively indistinguishable from childhood-onset cases; however, they experienced higher demands from parents (d = 1.09). Compared to the non-ADHD group, late-onset cases showed significant deficits in metacognition (d = 1.25) and academic motivation (d = 0.80), as well as a pronounced history of multiple trauma exposure (OR 11.82). At 1-year follow-up, ADHD persisted in 67.7% of late-onset cases. Late-onset cases (26.7%) were more likely than childhood-onset cases (0.0%) to transfer to alternative schools by 1-year follow-up. Multiple factors may contribute to adolescent-onset ADHD. Adolescents with metacognition and motivation deficits may be at greatest risk for the late-onset ADHD phenotype, particularly in highly demanding environments. Exposure to traumatic stress may play a key role in the exacerbation of existing deficits or onset of new symptoms. Late-onset ADHD was persistent in most cases and associated with higher risk for school disengagement than childhood-onset ADHD. Further work is needed to better understand the etiologies of late-onset ADHD symptoms.
Safe Adaptive Switching among Dynamical Movement Primitives: Application to 3D Limit-Cycle Walkers

Complex robot motions are frequently generated by composing simpler primitive movements. We use this approach to formulate robot motion plans as sequences of primitives to be executed one after the other. When dealing with dynamical movement primitives, besides accomplishing the high-level objective, planners must also reason about the effect of the plan’s execution on the safety of the platform. This task is exacerbated by the presence of disturbances, such as non-vanishing external forces. To address this issue, we present a framework that builds on rigorous control-theoretic tools to generate safely executable motion plans for externally excited robotic systems. We illustrate the proposed framework on adapting the motion of a 3D bipedal robot model to persistent external forcing by switching among dynamic movement primitives, each corresponding to a limit-cycle walking gait.
Mosquito and primate ecology predict human risk of yellow fever virus spillover in Brazil

Many (re)emerging infectious diseases in humans arise from pathogen spillover from wildlife or livestock, and accurately predicting pathogen spillover is an important public health goal. In the Americas, yellow fever in humans primarily occurs following spillover from non-human primates via mosquitoes. Predicting yellow fever spillover can improve public health responses through vector control and mass vaccination. Here, we develop and test a mechanistic model of pathogen spillover to predict human risk for yellow fever in Brazil. This environmental risk model, based on the ecology of mosquito vectors and non-human primate hosts, distinguished municipality-months with yellow fever spillover from 2001 to 2016 with high accuracy (AUC = 0.72). Incorporating hypothesized cyclical dynamics of infected primates improved accuracy (AUC = 0.79). Using boosted regression trees to identify gaps in the mechanistic model, we found that important predictors include current and one-month lagged environmental risk, vaccine coverage, population density, temperature and precipitation. More broadly, we show that for a widespread human viral pathogen, the ecological interactions between environment, vectors, reservoir hosts and humans can predict spillover with surprising accuracy, suggesting the potential to improve preventive action to reduce yellow fever spillover and avert onward epidemics in humans. This article is part of the theme issue 'Dynamic and integrative approaches to understanding pathogen spillover'.
Joint RElaxation-Diffusion Imaging Moments to Probe Neurite Microstructure

Joint relaxation-diffusion measurements can provide new insight about the tissue microstructural properties. Most recent methods have focused on inverting the Laplace transform to recover the joint distribution of relaxation-diffusion. However, as is well-known, this problem is notoriously ill-posed and numerically unstable. In this work, we address this issue by directly computing the joint moments of transverse relaxation rate and diffusivity, which can be robustly estimated. To zoom into different parts of the joint distribution, we further enhance our method by applying multiplicative filters to the joint probability density function of relaxation and diffusion and compute the corresponding moments. We propose an approach to use these moments to compute several novel scalar indices to characterize specific properties of the underlying tissue microstructure. Furthermore, for the first time, we propose an algorithm to estimate diffusion signals that are independent of echo time based on the moments of the marginal probability density function of diffusion. We demonstrate its utility in extracting tissue information not contaminated with multiple intra-voxel relaxation rates. We compare the performance of four types of filters that zoom into tissue components with different relaxation and diffusion properties and demonstrate it on an in-vivo human dataset. Experimental results show that these filters are able to characterize heterogeneous tissue microstructure. Moreover, the filtered diffusion signals are also able to distinguish fiber bundles with similar orientations but different relaxation rates. The proposed method thus allows to characterize the neural microstructure information in a robust and unique manner not possible using existing techniques.
A Local Maximum in the Superconducting Transition Temperature of Nb-Doped Strontium Titanate Under Uniaxial Compressive Stress

Superconducting strontium titanate (STO) is in the spotlight as a low carrier concentration semiconductor in proximity to polar order. Its superconducting pairing mechanism poses an open fundamental challenge, which may be resolved by controlling how strongly the superconducting and polar orders interact. Here, we show for the first time that non-monotonic superconducting transition temperature behavior in uniaxially compressed STO can occur, revealing a reduction followed by a peak in the superconducting transition temperature. The corresponding displacements in the lattice are extremely small, in the sub picometer range, indicating that this material approaches a singularity in electron-phonon coupling, consistent with STO transforming to the polar (ferroelectric) phase that influences the superconductivity.
Geometric coupling of helicoidal ramps and curvature-inducing proteins in organelle membranes

Cellular membranes display an incredibly diverse range of shapes, both in the plasma membrane and at membrane bound organelles. These morphologies are intricately related to cellular functions, enabling and regulating fundamental membrane processes. However, the biophysical mechanisms at the origin of these complex geometries are not fully understood from the standpoint of membrane-protein coupling. In this study, we focused on a minimal model of helicoidal ramps representative of specialized endoplasmic reticulum compartments. Given a helicoidal membrane geometry, we asked what is the distribution of spontaneous curvature required to maintain this shape at mechanical equilibrium? Based on the Helfrich energy of elastic membranes with spontaneous curvature, we derived the shape equation for minimal surfaces, and applied it to helicoids. We showed the existence of switches in the sign of the spontaneous curvature associated with geometric variations of the membrane structures. Furthermore, for a prescribed gradient of spontaneous curvature along the exterior boundaries, we identified configurations of the helicoidal ramps that are confined between two infinitely large energy barriers. Overall our results suggest possible mechanisms for geometric control of helicoidal ramps in membrane organelles based on curvature-inducing proteins.
Fragmentation of postoperative care after surgical management of ovarian cancer at 30-days and 90-days

Abstract Background Fragmentation of care, wherein a patient is discharged from an index hospital and undergoes an unexpected readmission to a non-index hospital, is associated with increased risk of adverse outcomes. Fragmentation is not well characterized in ovarian cancer. Objective The objective of this study was to assess risk factors and outcomes associated with fragmentation of care among women who undergo surgical treatment of ovarian cancer. Study Design The Nationwide Readmission Database was used to identify all-cause 30-day and 90-day postoperative readmissions following surgical management of ovarian cancer between 2010-2014. Postoperative fragmentation was defined as readmission to a hospital other than the index hospital of the initial surgery. Multivariable regression analyses were used to identify predictors of fragmentation in both 30-day and 90-day readmissions. Similarly, multivariable models were developed to determine the association between fragmentation and mortality among women who were readmitted. Results A total of 10,445 patients (13.3%) were readmitted at 30-days and 14,124 patients (18.0%) were readmitted at 90-days. Of these, there was a 20.8% and 25.7% rate of postoperative care fragmentation for 30-day and 90-day readmissions, respectively. Patient risk factors associated with fragmented postoperative care included Medicare insurance, lower income quartiles, and non-routine discharge to facility. Hospital factors associated with decreased risk of fragmentation included operation at a metropolitan teaching hospital, and performance of extended procedures. Cost and length of stay for the readmission were similar among those who had fragmented and non-fragmented readmissions at both 30 and 90-days. While there was no association between mortality and fragmentation for patients readmitted within 30-days (OR=1.19; 95% CI, 0.93-1.51), patients who had a fragmented readmission at 90-days were 22% more likely to die than those readmitted at 90-days to their index hospital (OR=1.22; 95% CI, 1.00-1.49) Conclusion Fragmentation of care is common in women with ovarian cancer who require postoperative readmission. Fragmented postoperative care is associated with an increased risk of mortality among women readmitted within 90-days of surgery.
An Exploratory Study of Live-Streamed Programming

In live-streamed programming, developers broadcast their development work on open source projects using streaming media such as YouTube or Twitch. Sessions are first announced by a developer acting as the streamer, inviting other developers to join and interact as watchers using chat. To better understand the characteristics, motivations, and challenges in live-streamed programming, we analyzed 20 hours of live-streamed programming videos and surveyed 7 streamers about their experiences. The results reveal that live-streamed programming shares some of the characteristics and benefits of pair programming, but differs in the nature of the relationship between the streamer and watchers. We also found that streamers are motivated by knowledge sharing, socializing, and building an online identity, but face challenges with tool limitations and maintaining engagement with watchers. We discuss the implications of these findings, identify limitations with current tools, and propose design recommendations for new forms of tools to better supporting live-streamed programming.
Hippocampal connectivity with sensorimotor cortex during volitional finger movements: Laterality and relationship to motor learning

Hippocampal interactions with the motor system are often assumed to reflect the role of memory in motor learning. Here, we examine hippocampal connectivity with sensorimotor cortex during two tasks requiring paced movements, one with a mnemonic component (sequence learning) and one without (repetitive tapping). Functional magnetic resonance imaging activity was recorded from thirteen right-handed subjects; connectivity was identified from sensorimotor cortex correlations with psychophysiological interactions in hippocampal activity between motor and passive visual tasks. Finger movements in both motor tasks anticipated the timing of the metronome, reflecting cognitive control, yet evidence of motor learning was limited to the sequence learning task; nonetheless, hippocampal connectivity was observed during both tasks. Connectivity from corresponding regions in the left and right hippocampus overlapped extensively, with improved sensitivity resulting from their conjunctive (global) analysis. Positive and negative connectivity were both evident, with positive connectivity in sensorimotor cortex ipsilateral to the moving hand during unilateral movements, whereas negative connectivity was prominent in whichever hemisphere was most active during movements. Results implicate the hippocampus in volitional finger movements even in the absence of motor learning or recall.
The “quantum” Turán problem for operator systems

Let V be a linear subspace of M_n(C) which contains the identity matrix and is stable under Hermitian transpose. A "quantum k-clique" for V is a rank k orthogonal projection P in M_n(C) for which dim(PVP) = k^2, and a "quantum k-anticlique" is a rank k orthogonal projection for which dim(PVP) = 1. We give upper and lower bounds both for the largest dimension of V which would ensure the existence of a quantum k-anticlique, and for the smallest dimension of V which would ensure the existence of a quantum k-clique.
Bayesian Modeling and Computation for Analyte Quantification in Complex Mixtures Using Raman Spectroscopy

Abstract A two-stage algorithm based on Bayesian modeling and computation for quantifying analyte concentration in complex mixtures with Raman spectroscopy is proposed. A hierarchical Bayesian model is constructed for spectral signal analysis, and reversible-jump Markov chain Monte Carlo (RJMCMC) computation is carried out for model selection and spectral variable estimation. Processing is performed in two stages. In the first stage, the peak representation for a target analyte spectrum is learned. In the second, the peak variables learned from the first stage are used to estimate the concentration of the target analyte in a mixture. Numerical experiments validated the performance over a wide range of simulation conditions and established the algorithm accuracy over conventional multivariate regression algorithms for analyte quantification (when constrained to a small training sample size). In addition, the algorithm was applied to analyze experimental spontaneous Raman spectroscopy data collected for glucose concentration estimation in a biopharmaceutical process monitoring application. The results show that this algorithm can be a promising complementary tool alongside conventional multivariate regression algorithms in Raman spectroscopy-based mixture quantification studies, especially when collection of a large training dataset is challenging or resource-intensive.
RedMed: Extending drug lexicons for social media applications

Abstract Social media has been identified as a promising potential source of information for pharmacovigilance. The adoption of social media data has been hindered by the massive and noisy nature of the data. Initial attempts to use social media data have relied on exact text matches to drugs of interest, and therefore suffer from the gap between formal drug lexicons and the informal nature of social media. The Reddit comment archive represents an ideal corpus for bridging this gap. We trained a word embedding model, RedMed, to facilitate the identification and retrieval of health entities from Reddit data. We compare the performance of our model trained on a consumer-generated corpus against publicly available models trained on expert-generated corpora. Our automated classification pipeline achieves an accuracy of 0.88 and a specificity of >0.9 across four different term classes. Of all drug mentions, an average of 79% ( ± 0.5%) were exact matches to a generic or trademark drug name, 14% ( ± 0.5%) were misspellings, 6.4% ( ± 0.3%) were synonyms, and 0.13% ( ± 0.05%) were pill marks. We find that our system captures an additional 20% of mentions; these would have been missed by approaches that rely solely on exact string matches. We provide a lexicon of misspellings and synonyms for 2978 drugs and a word embedding model trained on a health-oriented subset of Reddit.
Private Information Retrieval With Side Information

We study the problem of Private Information Retrieval (PIR) in the presence of prior side information. The problem setup includes a database of $K$ independent messages possibly replicated on several servers, and a user that needs to retrieve one of these messages. In addition, the user has some prior side information in the form of a subset of $M$ messages, not containing the desired message and unknown to the servers. This problem is motivated by practical settings in which the user can obtain side information opportunistically from other users or has previously downloaded some messages using classical PIR schemes. The objective of the user is to retrieve the required message with downloading minimum amount of data from the servers while achieving information-theoretic privacy in one of the following two scenarios: (i) the user wants to protect jointly the identities of the demand and the side information; (ii) the user wants to protect only the identity of the demand, but not necessarily the side information. To highlight the role of side information, we focus first on the case of a single server (single database). In the first scenario, we prove that the minimum download cost is $K-M$ messages, and in the second scenario it is $\lceil K/(M+1)\rceil $ messages, which should be compared to $K$ messages—the minimum download cost in the case of no side information. Then, we extend some of our results to the case of the database replicated on multiple servers. Our proof techniques relate PIR with side information to the index coding problem. We leverage this connection to prove converse results, as well as to design achievability schemes.
Single-boundary control of the two-phase Stefan system

Abstract This paper presents the control design of the two-phase Stefan problem. The two-phase Stefan problem is a representative model of liquid–solid phase transition by describing the time evolutions of the temperature profile, which is divided by subdomains of liquid and solid phases as the liquid–solid moving interface position. The mathematical formulation is given by two diffusion partial differential equations (PDEs) defined on a time-varying spatial domain described by an ordinary differential equation (ODE) driven by the Neumann boundary values of both PDE states, resulting in a nonlinear coupled PDE–ODE–PDE system. We design a state feedback control law by means of energy-shaping to stabilize the interface position to a desired setpoint by using single boundary heat input. We prove that the closed-loop system under the control law ensures some conditions for model validity, and the global exponential stability estimate is shown in the spatial L 2 norm. Furthermore, the robustness of the closed-loop stability with respect to the uncertainties of the physical parameters is shown. Numerical simulation is provided to illustrate the desired performance of the proposed control law in comparison to the control design for the one-phase Stefan problem.
Analysis of RF Energy Harvesting in Uplink-NOMA IoT-Based Network

Internet of Things (IoT) systems in general consist of a lot of devices with massive connectivity. Those devices are usually constrained with limited energy supply and can only operate at low power and low rate. One solution to limited energy is to use energy harvesting to provide sustainable energy. The set of technologies adopted in next-generation wireless communication systems, such as massive MIMO and Non-Orthogonal Multiple Access (NOMA), can provide solutions to increase the throughput of IoT systems. In this paper we investigate a cellular- based IoT system combined with energy harvesting and NOMA. We consider all base stations (BS) and IoT devices follow the Poisson Point Process (PPP) distribution in a given area. The unit time slot is divided into two phases, energy harvesting phase in downlink (DL) and data transmission phase in uplink (UL). That is, IoT devices will first harvest energy from all BS transmissions and then use the harvested energy to do the NOMA information transmission. We define an energy harvesting circle within which all IoT devices can harvest enough energy for NOMA transmission. The design objective is to maximize the total throughput in UL within the circle by varying the duration T of energy harvesting phase. In our work, we also consider the inter-cell interference in the throughput calculation. The analysis of Probability Mass Function (PMF) for IoT devices in the energy harvesting circle is also compared with simulation results. It is shown that the BS density needs to be carefully set so that the IoT devices in the energy harvesting circle receive relatively smaller interference and energy circles overlap only with small probability. Our simulations show that there exists an optimal T to achieve maximum throughput. When the BSs are densely deployed consequently the total throughput will decrease because of the interference.
Dimension independent bounds for general shallow networks

Abstract This paper proves an abstract theorem addressing in a unified manner two important problems in function approximation: avoiding curse of dimensionality and estimating the degree of approximation for out-of-sample extension in manifold learning. We consider an abstract (shallow) network that includes, for example, neural networks, radial basis function networks, and kernels on data defined manifolds used for function approximation in various settings. A deep network is obtained by a composition of the shallow networks according to a directed acyclic graph, representing the architecture of the deep network. In this paper, we prove dimension independent bounds for approximation by shallow networks in the very general setting of what we have called G -networks on a compact metric measure space, where the notion of dimension is defined in terms of the cardinality of maximal distinguishable sets, generalizing the notion of dimension of a cube or a manifold. Our techniques give bounds that improve without saturation with the smoothness of the kernel involved in an integral representation of the target function. In the context of manifold learning, our bounds provide estimates on the degree of approximation for an out-of-sample extension of the target function to the ambient space. One consequence of our theorem is that without the requirement of robust parameter selection, deep networks using a non-smooth activation function such as the ReLU, do not provide any significant advantage over shallow networks in terms of the degree of approximation alone.
A Unified Formula For Light-adapted Pupil Size

The size of the pupil has a large effect on visual function, and pupil size depends mainly on the adapting luminance, modulated by other factors. Over the last century, a number of formulas have been proposed to describe this dependence. Here we review seven published formulas and develop a new unified formula that incorporates the effects of luminance, size of the adapting field, age of the observer, and whether one or both eyes are adapted. We provide interactive demonstrations and software implementations of the unified formula.
Design and analysis considerations for cohort stepped wedge cluster randomized trials with a decay correlation structure

A stepped wedge cluster randomized trial is a type of longitudinal cluster design that sequentially switches clusters to intervention over time until all clusters are treated. While the traditional posttest-only parallel design requires adjustment for a single intraclass correlation coefficient, the stepped wedge design allows multiple outcome measurements from the same cluster and so additional correlation parameters are necessary to characterize the within-cluster correlation structure. Although a number of studies have differentiated between the concepts of within-period and between-period correlations, only a few studies have allowed the between-period correlation to decay over time. In this article, we consider the proportional decay correlation structure for a cohort stepped wedge design, and provide a matrix-adjusted quasi-least squares approach to accurately estimate the correlation parameters along with the marginal intervention effect. We further develop the sample size and power procedures accounting for the correlation decay, and investigate the accuracy of the power procedure with continuous outcomes in a simulation study. We show that the empirical power agrees well with the prediction even with as few as nine clusters, when data are analyzed with matrix-adjusted quasi-least squares concurrently with a suitable bias-corrected sandwich variance. Two trial examples are provided to illustrate the new sample size procedure.
Optimization of Structural Flood Mitigation Strategies

The dynamics of flooding are primarily influenced by the shape, height, and roughness (friction) of the underlying topography. For this reason, mechanisms to mitigate floods frequently employ structural measures that either modify topographic elevation, e.g., through the placement of levees and sandbags, or increase roughness, e.g., through revegetation projects. However, the configuration of these measures is typically decided in an ad hoc manner, limiting their overall effectiveness. The advent of high-performance surface water modeling software and improvements in black-box optimization suggest that a more principled design methodology may be possible. This paper proposes a new computational approach to the problem of designing structural mitigation strategies under physical and budgetary constraints. It presents the development of a problem discretization amenable to simulation-based, derivative-free optimization. However, meta-heuristics alone are found to be insufficient for obtaining quality solutions in a reasonable amount of time. As a result, this paper proposes novel numerical and physics-based procedures to improve convergence to a high-quality mitigation. The efficiency of the approach is demonstrated on hypothetical dam break scenarios of varying complexity under various mitigation budget constraints. In particular, experimental results show that, on average, the final proposed algorithm results in a 65% improvement in solution quality compared to a direct implementation.
Depth and Stanley depth of the edge ideals of the powers of paths and cycles

Let $k$ be a positive integer. We compute depth and Stanley depth of the quotient ring of the edge ideal associated to the $k^{th}$ power of a path on $n$ vertices. We show that both depth and Stanley depth have the same values and can be given in terms of $k$ and $n$. For $n\geq 2k+1$, let $n\equiv 0,k+1,k+2,\dots, n-1(\mod(2k+1))$. Then we give values of depth and Stanley depth of the quotient ring of the edge ideal associated to the $k^{th}$ power of a cycle on $n$ vertices and tight bounds otherwise, in terms of $n$ and $k$. We also compute lower bounds for the Stanley depth of the edge ideals associated to the $k^{th}$ power of a path and a cycle and prove a conjecture of Herzog presented in \cite{HS} for these ideals.
Multiple Linear Regression Haze-Removal Model Based on Dark Channel Prior

Dark Channel Prior (DCP) is a widely recognized traditional dehazing algorithm. However, it may fail in bright region and the brightness of the restored image is darker than hazy image. In this paper, we propose an effective method to optimize DCP. We build a multiple linear regression haze-removal model based on DCP atmospheric scattering model and train this model with RESIDE dataset, which aims to reduce the unexpected errors caused by the rough estimations of transmission map t(x) and atmospheric light A. The RESIDE dataset provides enough synthetic hazy images and their corresponding groundtruth images to train and test. We compare the performances of different dehazing algorithms in terms of two important full-reference metrics, the peak-signal-to-noise ratio (PSNR) as well as the structural similarity index measure (SSIM). The experiment results show that our model gets highest SSIM value and its PSNR value is also higher than most of state-of-the-art dehazing algorithms. Our results also overcome the weakness of DCP on real-world hazy images.
Quantifying and engineering mucus adhesion of probiotics

Mucus in the gastrointestinal (GI) tract is the primary point-of-interaction between humans and their gut microbiota. This intimates that mucus not only ensures protection against endogenous and exogenous opportunists but also provisions for the human microbiota to reside and flourish. With the emergence of living therapeutics, engineered microbes can deliver and produce increasingly complex medicine, and controlling the mucoadhesive properties of different microbial chassis can dictate dose-response in a patient. Here we present a redesigned, in vitro, plate-based assay to measure the mucus adhesion of various probiotics. Cell-mucus interactions were isolated by immobilizing mucus to the plate surface. Binding parameters were derived for each probiotic strain by measuring cell adhesion over a wide range of cell concentrations, providing dose-dependent adhesion metrics. Surface proteins and cell components known to influence mucoadhesion were then heterologously expressed or altered in Lactococcus lactis MG1363 and Escherichia coli Nissle 1917 to control mucus-binding capacity, avidity, and cooperativity.
High-NA achromatic metalenses by inverse design

We use inverse design to discover metalens structures that exhibit broadband, achromatic focusing across low, moderate, and high numerical apertures. We show that standard unit-cell approaches cannot achieve high-efficiency high-NA focusing, even at a single frequency, due to the incompleteness of the unit-cell basis, and we provide computational upper bounds on their maximum efficiencies. At low NA, our devices exhibit the highest theoretical efficiencies to date. At high NA—of 0.9 with translation-invariant films and of 0.99 with “freeform” structures—our designs are the first to exhibit achromatic high-NA focusing.
A hybrid model for the effects of treatment and demography on malaria superinfection.

Abstract As standard mathematical models for the transmission of vector-borne pathogens with weak or no apparent sterilizing immunity, Susceptible-Infected-Susceptible (SIS) systems such as the Ross-Macdonald equations are a useful starting point for modeling the impacts of interventions on prevalence for diseases that cannot superinfect their hosts. In particular, they are parameterizable from quantities we can estimate such as the force of infection (FOI), the rate of natural recovery from a single infection, the treatment rate, and the rate of demographic turnover. However, malaria parasites can superinfect their host which has the effect of increasing the duration of infection before total recovery. Queueing theory has been applied to capture this behavior, but a problem with current queueing models is the exclusion of factors such as demographic turnover and treatment. These factors in particular can affect the entire shape of the distribution of the multiplicity of infection (MOI) generated by the superinfection process, its transient dynamics, and the population mean recovery rate. Here we show the distribution of MOI can be described by an alternative hyper-Poisson distribution. We then couple our resulting equations to a simple vector transmission model, extending previous Ross-Macdonald theory.