cssi/SciSciGPT-SciSciNet huggingface dataset:
Can hot temperatures limit disease transmission? A test of mechanisms in a zooplankton–fungus system

Thermal ecology theory predicts that transmission of infectious diseases should respond unimodally to temperature, that is be maximized at intermediate temperatures and constrained at extreme low and high temperatures. However, empirical evidence linking hot temperatures to decreased transmission in nature remains limited. We tested the hypothesis that hot temperatures constrain transmission in a zooplankton–fungus (Daphnia dentifera–Metschnikowia bicuspidata) disease system where autumnal epidemics typically start after lakes cool from their peak summer temperatures. This pattern suggested that maximally hot summer temperatures could be inhibiting disease spread. Using a series of laboratory experiments, we examined the effects of high temperatures on five mechanistic components of transmission. We found that (a) high temperatures increased exposure to parasites by speeding up foraging rate but (b) did not alter infection success post‐exposure. (c) High temperatures lowered parasite production (due to faster host death and an inferred delay in parasite growth). (d) Parasites made in hot conditions were less infectious to the next host (instilling a parasite ‘rearing’ or 'trans‐host' effect of temperature during the prior infection). (e) High temperatures in the free‐living stage also reduce parasite infectivity, either by killing or harming parasites. We then assembled the five mechanisms into an index of disease spread. The resulting unimodal thermal response was most strongly driven by the rearing effect. Transmission peaked at intermediate hot temperatures (25–26°C) and then decreased at maximally hot temperatures (30–32°C). However, transmission at these maximally hot temperatures only trended slightly lower than the baseline control (20°C), which easily sustains epidemics in laboratory conditions and in nature. Overall, we conclude that while exposure to hot epilimnetic temperatures does somewhat constrain disease, we lack evidence that this effect fully explains the lack of summer epidemics in this natural system. This work demonstrates the importance of experimentally testing hypothesized mechanisms of thermal constraints on disease transmission. Furthermore, it cautions against drawing conclusions based on field patterns and theory alone. A free Plain Language Summary can be found within the Supporting Information of this article.
Parabolic equations with variably partially VMO coefficients

We prove the $W^{1,2}_{p}$-solvability of second order parabolic equations in nondivergence form in the whole space for $p\in (1,\infty)$. The leading coefficients are assumed to be measurable in one spatial direction and have vanishing mean oscillation (VMO) in the orthogonal directions and the time variable in each small parabolic cylinder with the direction depending on the cylinder. This extends a recent result by Krylov [17] for elliptic equations and removes the restriction that $p>2$.
Generalized Hilbert coefficients and Northcott's inequality

Abstract Let R be a Cohen–Macaulay local ring of dimension d with infinite residue field. Let I be an R-ideal that has analytic spread l ( I ) = d , satisfies the G d condition and the weak Artin–Nagata property A N d − 2 − . We provide a formula relating the length λ ( I n + 1 / J I n ) to the difference P I ( n ) − H I ( n ) , where J is a general minimal reduction of I, P I ( n ) and H I ( n ) are respectively the generalized Hilbert–Samuel polynomial and the generalized Hilbert–Samuel function. We then use it to establish formulas to compute the generalized Hilbert coefficients of I. As an application, we extend Northcott's inequality to non- m -primary ideals. Furthermore, when equality holds, we prove that the ideal I enjoys nice properties. Indeed, if this is the case, then the reduction number of I is at most one and the associated graded ring of I is Cohen–Macaulay. We also recover results of G. Colome-Nin, C. Polini, B. Ulrich and Y. Xie on the positivity of the generalized first Hilbert coefficient j 1 ( I ) . Our work extends that of S. Huckaba, C. Huneke and A. Ooishi to ideals that are not necessarily m -primary.
Subcomplete forcing principles and definable well-orders

It is shown that the boldface maximality principle for subcomplete forcing, together with the assumption that the universe has only set-many grounds, implies the existence of a (parameter-free) definable well-ordering of $\mathcal{P}(\omega_1)$. The same conclusion follows from the boldface maximality for subcomplete forcing, assuming there is no inner model with an inaccessible limit of measurable cardinals. Similarly, the bounded subcomplete forcing axiom, together with the assumption that $x^\#$ does not exist, for some $x\subseteq\omega_1$, implies the existence of a well-order of $\mathcal{P}(\omega_1)$ which is $\Delta_1$-definable without parameters, and $\Delta_1(H_{\omega_2})$-definable using a subset of $\omega_1$ as a parameter. This well-order is in $L(\mathcal{P}(\omega_1))$. Enhanced version of bounded forcing axioms are introduced that are strong enough to have the implications of the maximality principles mentioned above.
Linear differential equations and Hurwitz series

In this article, we study the set of all solutions of linear differential equations using Hurwitz series. We first obtain explicit recursive expressions for solutions of such equations and study the group of differential automorphisms of the set of all solutions. Moreover, we give explicit formulas that compute the group of differential automorphisms. We require neither that the underlying field be algebraically closed nor that the characteristic of the field be zero.
A Computational Approach to Steady State Correspondence of Regular and Generalized Mass Action Systems.

It has been recently observed that the dynamical properties of mass action systems arising from many models of biochemical reaction networks can be characterized by considering the corresponding properties of a related generalized mass action system. The correspondence process known as network translation in particular has been shown to be useful in characterizing a system’s steady states. In this paper, we further develop the theory of network translation with particular focus on a subclass of translations known as improper translations. For these translations, we derive conditions on the network topology of the translated network which are sufficient to guarantee the original and translated systems share the same steady states. We then present a mixed-integer linear programming algorithm capable of determining whether a mass action system can be corresponded to a generalized system through the process of network translation.
SUPC: SDN enabled Universal Policy Checking in Cloud Network

Multi-tenant cloud networks have various security and monitoring service functions (SFs) that constitute a service function chain (SFC) between two endpoints. SF rule ordering overlaps and policy conflicts can cause increased latency, service disruption and security breaches in cloud networks. Software Defined Network (SDN) based Network Function Virtualization (NFV) has emerged as a solution that allows dynamic SFC composition and traffic steering in a cloud network. We propose an SDN enabled Universal Policy Checking (SUPC) framework, to provide 1) Flow Composition and Ordering by translating various SF rules into the OpenFlow format. This ensures elimination of redundant rules and policy compliance in SFC. 2) Flow conflict analysis to identify conflicts in header space and actions between various SF rules. Our results show a significant reduction in SF rules on composition. Additionally, our conflict checking mechanism was able to identify several rule conflicts that pose security, efficiency, and service availability issues in the cloud network.
Learning Approximately Objective Priors

Informative Bayesian priors are often difficult to elicit, and when this is the case, modelers usually turn to noninformative or objective priors. However, objective priors such as the Jeffreys and reference priors are not tractable to derive for many models of interest. We address this issue by proposing techniques for learning reference prior approximations: we select a parametric family and optimize a black-box lower bound on the reference prior objective to find the member of the family that serves as a good approximation. We experimentally demonstrate the method's effectiveness by recovering Jeffreys priors and learning the Variational Autoencoder's reference prior.
Improving End-of-Turn Detection in Spoken Dialogues by Detecting Speaker Intentions as a Secondary Task

This work focuses on the use of acoustic cues for modeling turn-taking in dyadic spoken dialogues. Previous work has shown that speaker intentions (e.g., asking a question, uttering a backchannel, etc.) can influence turn-taking behavior and are good predictors of turn-transitions in spoken dialogues. However, speaker intentions are not readily available for use by automated systems at run-time; making it difficult to use this information to anticipate a turn-transition. To this end, we propose a multi-task neural approach for predicting turn-transitions and speaker intentions simultaneously. Our results show that adding the auxiliary task of speaker intention prediction improves the performance of turn-transition prediction in spoken dialogues, without relying on additional input features during run-time.
Punctured spheres in complex hyperbolic surfaces and bielliptic ball quotient compactifications

In this paper, we study punctured spheres in two dimensional ball quotient compactifications $(X, D)$. For example, we show that smooth toroidal compactifications of ball quotients cannot contain properly holomorphically embedded $3$-punctured spheres. We also use totally geodesic punctured spheres to prove ampleness of $K_X + \alpha D$ for $\alpha \in (\frac{1}{4}, 1)$, giving a sharp version of a theorem of the first author with G. Di Cerbo. Finally, we produce the first examples of bielliptic ball quotient compactifications modeled on the Gaussian integers.
A surgical system for automatic registration, stiffness mapping and dynamic image overlay

In this paper we develop a surgical system using the da Vinci research kit (dVRK) that is capable of autonomously searching for tumors and dynamically displaying the tumor location using augmented reality. Such a system has the potential to quickly reveal the location and shape of tumors and visually overlay that information to reduce the cognitive overload of the surgeon. To the best of our knowledge, our approach is one of the first to incorporate state-of-the-art methods in registration, force sensing and tumor localization into a unified surgical system. First, the preoperative model is registered to the intra-operative scene using a Bingham distribution-based filtering approach. An active level set estimation is then used to find the location and the shape of the tumors. We use a recently developed miniature force sensor to perform the palpation. The estimated stiffness map is then dynamically overlaid onto the registered preoperative model of the organ. We demonstrate the efficacy of our system by performing experiments on phantom prostate models with embedded stiff inclusions.
Spectral radius of {0,1}-tensor with prescribed number of ones

Abstract For any r-order { 0 , 1 } -tensor A with e ones, we prove that the spectral radius of A is at most e r − 1 r with the equality holds if and only if e = k r for some integer k and all ones forms a principal sub-tensor 1 k × ⋯ × k . We also prove a stability result for general tensor A with e ones where e = k r + l with relatively small l. Using the stability result, we completely characterized the tensors achieving the maximum spectral radius among all r-order { 0 , 1 } -tensor A with k r + l ones, for − r − 1 ≤ l ≤ r , and k sufficiently large.
Characterization of Si hybrid CMOS detectors for use in the soft x-ray band

We report on the characterization of four HAWAII Hybrid Si CMOS detectors (HCD) developed for use as X-ray detectors as part of a joint program between Penn State University and Teledyne Imaging Sensors (TIS). Interpixel capacitive crosstalk (IPC) has been measured for standard H1RG detectors as well as a specially developed H2RG that uses a unique bonding structure. The H2RG shows significant reduction in IPC, as reported by Griffith et al. 2012. Energy resolution at 1.5 & 5.9 keV was measured as well as read noise for each detector. Dark current as a function of temperature is reported from 150 – 210 K and dark current figures of merit are estimated for each detector. We also discuss upcoming projects including testing of a new HCD called the Speedster-EXD. This prototype detector will have a low noise, high gain CTIA to reduce IPC and read noise as well as in-pixel CDS and event flagging. In the coming year PSU and TIS will begin work on a project to incorporate CTIA and CDS circuitry into the ROIC of a HAWAII HCD like detector to satisfy the small pixel and high rate needs of future X-ray observatories.
A rigidity result for effective Hamiltonians with 3-mode periodic potentials

Abstract We continue studying an inverse problem in the theory of periodic homogenization of Hamilton–Jacobi equations proposed in [14] . Let V 1 , V 2 ∈ C ( R n ) be two given potentials which are Z n -periodic, and H ‾ 1 , H ‾ 2 be the effective Hamiltonians associated with the Hamiltonians 1 2 | p | 2 + V 1 , 1 2 | p | 2 + V 2 , respectively. A main result in this paper is that, if the dimension n = 2 , and each of V 1 , V 2 contains exactly 3 mutually non-parallel Fourier modes, then H ‾ 1 ≡ H ‾ 2 ⇔ V 1 ( x ) = V 2 ( x c + x 0 ) for all x ∈ T 2 = R 2 / Z 2 , for some c ∈ Q ∖ { 0 } and x 0 ∈ T 2 . When n ≥ 3 , the scenario is slightly more subtle, and a complete description is provided for any dimension. These resolve partially a conjecture stated in [14] . Some other related results and open problems are also discussed.
Higher rho invariants and the moduli space of positive scalar curvature metrics

Abstract Given a closed smooth manifold M which carries a positive scalar curvature metric, one can associate an abelian group P ( M ) to the space of positive scalar curvature metrics on this manifold. The group of all diffeomorphisms of the manifold naturally acts on P ( M ) . The moduli group P ˜ ( M ) of positive scalar curvature metrics is defined to be the quotient abelian group of this action, i.e. the coinvariant of the action. P ˜ ( M ) measures the size of the moduli space of positive scalar curvature metrics on M. In this paper, we use the higher rho invariant and the finite part of the K-theory of the group C ⁎ -algebra of π 1 ( M ) to give a lower bound of the rank of the moduli group P ˜ ( M ) . The key idea of our proof is the use of higher rho invariant; this is a secondary invariant associated to Dirac operators and in particular depends on the choice of Riemannian metric. We show that the higher rho invariant remains unchanged in a certain K-theory group under the action of the diffeomorphism group, allowing us to distinguish elements in P ˜ ( M ) .
A functorial Dowker theorem and persistent homology of asymmetric networks

We study two methods for computing network features with topological underpinnings: the Rips and Dowker persistent homology diagrams. Our formulations work for general networks, which may be asymmetric and may have any real number as an edge weight. We study the sensitivity of Dowker persistence diagrams to asymmetry via numerous theoretical examples, including a family of highly asymmetric cycle networks that have interesting connections to the existing literature. In particular, we characterize the Dowker persistence diagrams arising from asymmetric cycle networks. We investigate the stability properties of both the Dowker and Rips persistence diagrams, and use these observations to run a classification task on a dataset comprising simulated hippocampal networks. Our theoretical and experimental results suggest that Dowker persistence diagrams are particularly suitable for studying asymmetric networks. As a stepping stone for our constructions, we prove a functorial generalization of a theorem of Dowker, after whom our constructions are named.
Fully Decentralized Policies for Multi-Agent Systems: An Information Theoretic Approach

Learning cooperative policies for multi-agent systems is often challenged by partial observability and a lack of coordination. In some settings, the structure of a problem allows a distributed solution with limited communication. Here, we consider a scenario where no communication is available, and instead we learn local policies for all agents that collectively mimic the solution to a centralized multi-agent static optimization problem. Our main contribution is an information theoretic framework based on rate distortion theory which facilitates analysis of how well the resulting fully decentralized policies are able to reconstruct the optimal solution. Moreover, this framework provides a natural extension that addresses which nodes an agent should communicate with to improve the performance of its individual policy.
A mechanism of failure in shear bands

Abstract We have carried out dilatant plasticity simulations to investigate the process of void-mediated failure inside a shear band. The constitutive model accounts for possibly inhomogeneous flow within the band, void rotation and void elongation. We found that the material in the band may soften with no increase in the void volume fraction. For a given matrix hardening capacity, the rate of softening was found to depend strongly on the ratio of shear band width to in-plane void spacing. The emergent softening led to complete loss of load bearing capacity thereby providing a physical mechanism of failure in shear bands. The mechanism is consistent with essential features of shear-fractured specimens in terms of surface roughness, porosity and dimple shape.
Integers divisible by a large shifted prime

Let $N(x,y)$ denote the number of integers $n\le x$ which are divisible by a shifted prime $p-1$ with $p>y$, $p$ prime. Improving upon recent bounds of McNew, Pollack and Pomerance, we establish the exact order of growth of $N(x,y)$ for all $x\ge 2y\ge 4$.
Subgradient Methods for Sharp Weakly Convex Functions

Subgradient methods converge linearly on a convex function that grows sharply away from its solution set. In this work, we show that the same is true for sharp functions that are only weakly convex, provided that the subgradient methods are initialized within a fixed tube around the solution set. A variety of statistical and signal processing tasks come equipped with good initialization and provably lead to formulations that are both weakly convex and sharp. Therefore, in such settings, subgradient methods can serve as inexpensive local search procedures. We illustrate the proposed techniques on phase retrieval and covariance estimation problems.
Foundational aspects of singular integrals

Abstract We investigate integration of classes of real-valued continuous functions on ( 0 , 1 ] . Of course difficulties arise if there is a non- L 1 element in the class, and the Hadamard finite part integral (p.f.) does not apply. Such singular integrals arise naturally in many contexts including PDEs and singular ODEs. The Lebesgue integral as well as p.f., starting at zero, obey two fundamental conditions: (i) they act as antiderivatives and, (ii) if f = g on ( 0 , a ) , then their integrals from 0 to x coincide for any x ∈ ( 0 , a ) . We find that integrals from zero with the essential properties of p.f., plus positivity, exist by virtue of the Axiom of Choice (AC) on all functions on ( 0 , 1 ] which are L 1 ( ( e , 1 ] ) for all e > 0 . However, this existence proof does not provide a satisfactory construction. Without some regularity at 0, the existence of general antiderivatives which satisfy only (i) and (ii) above on classes with a non- L 1 element is independent of ZF (the usual ZFC axioms for mathematics without AC), and even of ZFDC (ZF with the Axiom of Dependent Choice). Moreover we show that there is no mathematical description that can be proved (within ZFC or even extensions of ZFC with large cardinal hypotheses) to uniquely define such an antiderivative operator. Such results are precisely formulated for a variety of sets of functions, and proved using methods from mathematical logic, descriptive set theory and analysis. We also analyze p.f. on analytic functions in the punctured unit disk, and make the connection to singular initial value problems.
Scattering above energy norm of solutions of a loglog energy-supercritical Schrodinger equation with radial data

Abstract We prove global well-posedness and scattering of H ˜ k : = H ˙ k ( R n ) ∩ H ˙ 1 ( R n ) -solutions of the loglog energy-supercritical Schrodinger equation i ∂ t u + Δ u = | u | 4 n − 2 u log c ( log ( 10 + | u | 2 ) ) , 0 c c n , n = { 3 , 4 } , with radial data u ( 0 ) = u 0 ∈ H ˜ k : = H ˙ k ( R n ) ∩ H ˙ 1 ( R n ) , k > n 2 . This is achieved, roughly speaking, by extending Bourgain's argument in Bourgain (1999) [1] (see also Grillakis, 2000 [5] ) and Tao's argument in Tao (2005) [10] in high dimensions.
Efficient Numerical Analysis of Stability of High-Order Systems with a Time Delay

Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative results. While more exact methods exist, these become inefficient for large systems. This paper provides a methodology for analyzing the stability of time-delayed systems that is derived from exact methods but is efficient for high-order systems. The computational and memory cost of this new technique is compared to the costs of existing techniques, and its efficiency is shown using a distributed system with over four hundred states.
Overcrowding and hole probabilities for random zeros on complex manifolds

We give asymptotic large deviations estimates for the volume inside a domain U of the zero set of a random polynomial of degree N, or more generally, of a random holomorphic section of the N-th power of a positive line bundle on a compact Kahler manifold. In particular, we show that for all δ > 0, the probability that this volume differs by more than δN from its average value is less than exp(-C δ,U N m+1 ), for some constant C δ,U > 0. As a consequence, the "hole probability" that a random section does not vanish in U has an upper bound of the form exp(-C U N m+1 ).
Safe sequential path planning under disturbances and imperfect information

Multi-UAV systems are safety-critical, and guarantees must be made to ensure no unsafe configurations occur. Hamilton-Jacobi (HJ) reachability is ideal for analyzing such safety-critical systems; however, its direct application is limited to small-scale systems of no more than two vehicles due to an exponentially-scaling computational complexity. Previously, the sequential path planning (SPP) method, which assigns strict priorities to vehicles, was proposed; SPP allows multi-vehicle path planning to be done with a linearly-scaling computational complexity. However, the previous formulation assumed that there are no disturbances, and that every vehicle has perfect knowledge of higher-priority vehicles' positions. In this paper, we make SPP more practical by providing three different methods to account for disturbances in dynamics and imperfect knowledge of higher-priority vehicles' states. Each method has different assumptions about information sharing. We demonstrate our proposed methods in simulations.
Network anomaly detection: A survey and comparative analysis of stochastic and deterministic methods

We present five methods to the problem of network anomaly detection. These methods cover most of the common techniques in the anomaly detection field, including Statistical Hypothesis Tests (SHT), Support Vector Machines (SVM) and clustering analysis. We evaluate all methods in a simulated network that consists of nominal data, three flow-level anomalies and one packet-level attack. Through analyzing the results, we point out the advantages and disadvantages of each method and conclude that combining the results of the individual methods can yield improved anomaly detection results.
Super-Isolated Elliptic Curves and Abelian Surfaces in Cryptography

We call a simple abelian variety over Fp super-isolated if its (Fp-rational) isogeny class contains no other varieties. The motivation for considering these varieties comes from concerns about isog...
Bernoulli Embeddings for Graphs.

Just as semantic hashing can accelerate information retrieval, binary valued embeddings can significantly reduce latency in the retrieval of graphical data. We introduce a simple but effective model for learning such binary vectors for nodes in a graph. By imagining the embeddings as independent coin flips of varying bias, continuous optimization techniques can be applied to the approximate expected loss. Embeddings optimized in this fashion consistently outperform the quantization of both spectral graph embeddings and various learned real-valued embeddings, on both ranking and pre-ranking tasks for a variety of datasets.
A probabilistic approach to knowledge translation

In this paper, we focus on a novel knowledge reuse scenario where the knowledge in the source schema needs to be translated to a semantically heterogeneous target schema. We refer to this task as "knowledge translation" (KT). Unlike data translation and transfer learning, KT does not require any data from the source or target schema. We adopt a probabilistic approach to KT by representing the knowledge in the source schema, the mapping between the source and target schemas, and the resulting knowledge in the target schema all as probability distributions, specially using Markov random fields and Markov logic networks. Given the source knowledge and mappings, we use standard learning and inference algorithms for probabilistic graphical models to find an explicit probability distribution in the target schema that minimizes the Kullback-Leibler divergence from the implicit distribution. This gives us a compact probabilistic model that represents knowledge from the source schema as well as possible, respecting the uncertainty in both the source knowledge and the mapping. In experiments on both propositional and relational domains, we find that the knowledge obtained by KT is comparable to other approaches that require data, demonstrating that knowledge can be reused without data.
Infinite-Dimensional Measure Spaces and Frame Analysis

We study certain infinite-dimensional probability measures in connection with frame analysis. Earlier work on frame-measures has so far focused on the case of finite-dimensional frames. We point out that there are good reasons for a sharp distinction between stochastic analysis involving frames in finite vs. infinite dimensions. For the case of infinite-dimensional Hilbert space ℋ, we study three cases of measures. We first show that, for ℋ infinite dimensional, one must resort to infinite dimensional measure spaces which properly contain ℋ. The three cases we consider are: (i) Gaussian frame measures, (ii) Markov path-space measures, and (iii) determinantal measures.
Optimum Linear Codes with Support Constraints over Small Fields

The problem of designing a linear code with the largest possible minimum distance, subject to support constraints on the generator matrix, has recently found several applications. These include multiple access networks [3], [5] as well as weakly secure data exchange [4], [8]. A simple upper bound on the maximum minimum distance can be obtained from a sequence of Singleton bounds (see (3) below) and can further be achieved by randomly choosing the nonzero elements of the generator matrix from a field of a large enough size.
A dataset and architecture for visual reasoning with a working memory

A vexing problem in artificial intelligence is reasoning about events that occur in complex, changing visual stimuli such as in video analysis or game play. Inspired by a rich tradition of visual reasoning and memory in cognitive psychology and neuroscience, we developed an artificial, configurable visual question and answer dataset (COG) to parallel experiments in humans and animals. COG is much simpler than the general problem of video analysis, yet it addresses many of the problems relating to visual and logical reasoning and memory – problems that remain challenging for modern deep learning architectures. We additionally propose a deep learning architecture that performs competitively on other diagnostic VQA datasets (i.e. CLEVR) as well as easy settings of the COG dataset. However, several settings of COG result in datasets that are progressively more challenging to learn. After training, the network can zero-shot generalize to many new tasks. Preliminary analyses of the network architectures trained on COG demonstrate that the network accomplishes the task in a manner interpretable to humans.
Disjoint Borel Functions

Abstract For each a ∈ ω ω , we define a Baire class one function f a : ω ω → ω ω which encodes a in a certain sense. We show that for each Borel g : ω ω → ω ω , f a ∩ g = ∅ implies a ∈ Δ 1 1 ( c ) where c is any code for g. We generalize this theorem for g in a larger pointclass Γ. Specifically, when Γ = Δ 2 1 , a ∈ L [ c ] . Also for all n ∈ ω , when Γ = Δ 3 + n 1 , a ∈ M 1 + n ( c ) .
Relaxation of functionals in the space of vector-valued functions of bounded Hessian

In this paper it is shown that if $$\varOmega \subset \mathbb {R}^N$$ is an open, bounded Lipschitz set, and if $$f: \varOmega \times \mathbb {R}^{d \times N \times N} \rightarrow [0, \infty )$$ is a continuous function with $$f(x, \cdot )$$ of linear growth for all $$x \in \varOmega $$ , then the relaxed functional in the space of functions of Bounded Hessian of the energy $$\begin{aligned} F[u] = \int _{\varOmega } f(x, \nabla ^2u(x)) dx \end{aligned}$$ for bounded sequences in $$W^{2,1}$$ is given by $$\begin{aligned} {{\mathcal {F}}}[u] = \int _\varOmega {{\mathcal {Q}}}_2f(x, \nabla ^2u) dx + \int _\varOmega ({{\mathcal {Q}}}_2f)^{\infty }\bigg (x, \frac{d D_s(\nabla u)}{d |D_s(\nabla u)|} \bigg ) d |D_s(\nabla u) |. \end{aligned}$$ This result is obtained using blow-up techniques and establishes a second order version of the BV relaxation theorems of Ambrosio and Dal Maso (J Funct Anal 109:76–97, 1992) and Fonseca and Muller (Arch Ration Mech Anal 123:1–49, 1993). The use of the blow-up method is intended to facilitate future study of integrands which include lower order terms and applications in the field of second order structured deformations.
Controlling electric, magnetic, and chiral dipolar emission with PT-symmetric potentials

We investigate the effect of parity-time (PT)-symmetric optical potentials on the radiation of achiral and chiral emitters. Mode coalescence and the appearance of exceptional points lead to orders-of-magnitude enhancements in the emitted dipole power. Further, the emitter can be tuned to behave as a strong optical source or absorber based on the non-Hermiticity parameter. Chiral enantiomers radiating near PT metamaterials exhibit a 4.5-fold difference in their decay rate. The results of this work could enable new atom-cavity interactions for quantum optics, as well as all- optical enantio-specific separation.
Yin and Yang: Balancing and Answering Binary Visual Questions

The complex compositional structure of language makes problems at the intersection of vision and language challenging. But language also provides a strong prior that can result in good superficial performance, without the underlying models truly understanding the visual content. This can hinder progress in pushing state of art in the computer vision aspects of multi-modal AI. In this paper, we address binary Visual Question Answering (VQA) on abstract scenes. We formulate this problem as visual verification of concepts inquired in the questions. Specifically, we convert the question to a tuple that concisely summarizes the visual concept to be detected in the image. If the concept can be found in the image, the answer to the question is "yes", and otherwise "no". Abstract scenes play two roles (1) They allow us to focus on the highlevel semantics of the VQA task as opposed to the low-level recognition problems, and perhaps more importantly, (2) They provide us the modality to balance the dataset such that language priors are controlled, and the role of vision is essential. In particular, we collect fine-grained pairs of scenes for every question, such that the answer to the question is "yes" for one scene, and "no" for the other for the exact same question. Indeed, language priors alone do not perform better than chance on our balanced dataset. Moreover, our proposed approach matches the performance of a state-of-the-art VQA approach on the unbalanced dataset, and outperforms it on the balanced dataset.
Combining uncertain estimates

In an expert system, it is necessary to supply the values of various parameters. Ideally, an absolutely reliable source is available to supply an exact value for any parameter. In reality, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. This paper is a consideration of how to represent and combine imperfect estimates. It is assumed that the knowledge from each source takes the form of an estimate of the parameter value, paired with an associated measure of uncertainty. This uncertainty may arise from lack of confidence on the part of a human source, from some appraisal of the (un)reliability of a source, or both. Functions are proposed that combine several such value-and-uncertainty pairs to produce a resultant of the same form, that is, a resultant value and a resultant uncertainty. The proposed combination functions are most comfortably understood in terms of a parameter with values on the reals, but there is some consideration of alternative scales. The functions are developed in terms of an analogy to statistical sampling. They conform with various intuitions about the way estimates should combine. Three related matters are worth mentioning, though space constraints preclude proper discussion. First, in addition to representing uncertain values it is also necessary to be able to compute with them, to determine both values and appropriate uncertainties for related, derived parameters in the system. (On this point, see [Garv81], and [Quin83]). Next, if there is sharp disagreement among confident and ostensibly reliable sources, one may think of reevaluating their degree of reliability. Last, there is the possibility of using information about uncertainty for deciding when it is worthwhile to seek more information that might reduce uncertainty. (Ideas related to this point are present in [Slag84] and [Duda79]).
Asymptotic Delsarte cliques in distance-regular graphs

We give a new bound on the parameter $$\lambda $$? (number of common neighbors of a pair of adjacent vertices) in a distance-regular graph G, improving and generalizing bounds for strongly regular graphs by Spielman (1996) and Pyber (2014. arXiv:1409.3041). The new bound is one of the ingredients of recent progress on the complexity of testing isomorphism of strongly regular graphs (Babai et al. 2013). The proof is based on a clique geometry found by Metsch (Des Codes Cryptogr 1(2):99---116, 1991) under certain constraints on the parameters. We also give a simplified proof of the following asymptotic consequence of Metsch's result: If $$k\mu = o(\lambda ^2)$$kμ=o(?2), then each edge of G belongs to a unique maximal clique of size asymptotically equal to $$\lambda $$?, and all other cliques have size $$o(\lambda )$$o(?). Here k denotes the degree and $$\mu $$μ the number of common neighbors of a pair of vertices at distance 2. We point out that Metsch's cliques are "asymptotically Delsarte" when $$k\mu = o(\lambda ^2)$$kμ=o(?2), so families of distance-regular graphs with parameters satisfying $$k\mu = o(\lambda ^2)$$kμ=o(?2) are "asymptotically Delsarte-geometric."
Stability Conditions Under the Fourier-Mukai Transforms on Abelian Threefolds

We realize explicit symmetries of Bridgeland stability conditions on any abelian threefold given by Fourier-Mukai transforms. In particular, we extend the previous joint work with Maciocia to study the slope and tilt stabilities of sheaves and complexes under the Fourier-Mukai transforms, and then to show that certain Fourier-Mukai transforms give equivalences of the stability condition hearts of bounded t-structures which are double tilts of coherent sheaves. Consequently, we show that the conjectural construction proposed by Bayer, Macri and Toda gives rise to Bridgeland stability conditions on any abelian threefold by proving that tilt stable objects satisfy the Bogomolov-Gieseker type inequality. Our proof of the Bogomolov-Gieseker type inequality conjecture for any abelian threefold is a generalization of the previous joint work with Maciocia for a principally polarized abelian threefold with Picard rank one case, and also this gives an alternative proof of the same result in full generality due to Bayer, Macri and Stellari. Moreover, we realize the induced cohomological Fourier-Mukai transform explicitly in anti-diagonal form, and consequently, we describe a polarization on the derived equivalent abelian variety by using Fourier-Mukai theory.
Estimates for Dirichlet-to-Neumann Maps as Integro-differential Operators

Some linear integro-differential operators have old and classical representations as the Dirichlet-to-Neumann operators for linear elliptic equations, such as the 1/2-Laplacian or the generator of the boundary process of a reflected diffusion. In this work, we make some extensions of this theory to the case of a nonlinear Dirichlet-to-Neumann mapping that is constructed using a solution to a fully nonlinear elliptic equation in a given domain, mapping Dirichlet data to its normal derivative of the resulting solution. Here we begin the process of giving detailed information about the Levy measures that will result from the integro-differential representation of the Dirichlet-to-Neumann mapping. We provide new results about both linear and nonlinear Dirichlet-to-Neumann mappings. Information about the Levy measures is important if one hopes to use recent advancements of the integro-differential theory to study problems involving Dirichlet-to-Neumann mappings.
A remark on asymptotic enumeration of highest weights in tensor powers of a representation

We consider the semigroup S of highest weights appearing in tensor powers V k of a nite dimensional representation V of a connected reductive group. We describe the cone generated by S as the cone over the weight polytope of V intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in V k in terms of the volume of this polytope.
Modules induced from polynomial subalgebras of the Virasoso algebra

Abstract The Virasoro Lie algebra is a one-dimensional central extension of the Witt algebra, which can be realized as the Lie algebra of derivations on the algebra C [ t ± ] of Laurent polynomials. Using this fact, we define a natural family of subalgebras of the Virasoro algebra, which we call polynomial subalgebras. We describe the one-dimensional modules for polynomial subalgebras, and we use this description to study the corresponding induced modules for the Virasoro algebra. We show that these induced modules are frequently simple and generalize a family of recently discovered simple modules. Additionally, we explore tensor products involving these induced modules. This allows us to describe new simple modules and also recover results on recently discovered simple modules for the Virasoro algebra.
From quantum Ore extensions to quantum tori via noncommutative UFDs

Abstract All iterated skew polynomial extensions arising from quantized universal enveloping algebras of Kac–Moody algebras are special examples of a very large, axiomatically defined class of algebras, called CGL extensions. For the purposes of constructing initial clusters for quantum cluster algebra structures on an algebra R , and classification of the automorphisms of R , one needs embeddings of R into quantum tori T which have the property that R contains the corresponding quantum affine space algebra A . We explicitly construct such an embedding A ⊆ R ⊂ T for each CGL extension R using the methods of noncommutative noetherian unique factorization domains and running a Gelfand–Tsetlin type procedure with normal, instead of central elements. Along the way we classify the homogeneous prime elements of all CGL extensions and we prove that each CGL extension R has an associated maximal torus which covers the automorphisms of R corresponding to all normal elements. For symmetric CGL extensions, we describe the relationship between our quantum affine space algebra A and Cauchon's quantum affine space algebra generated by elements obtained via deleting derivations.
The Influence of the Aortic Root Geometry on Flow Characteristics of a Bileaflet Mechanical Heart Valve

Bileaflet mechanical heart valves have one of the most successful valve designs for more than 30 years. These valves are often used for aortic valve replacement, where the geometry of the aortic root sinuses may vary due to valvular disease and affect valve performance. Common geometrical sinus changes may be due to valve stenosis and insufficiency. In the current study, the effect of these geometrical changes on the mean flow and velocity fluctuations downstream of the valve and aortic sinuses were investigated. The study focused on the fully-open leaflet position where blood velocities are close to their maximum. Simulation results were validated using previous experimental laser Doppler anemometry (LDA) measurements. Results showed that as the stenosis and insufficiency increased there were more flow separation and increased local mean velocity downstream of the leaflets. In addition, the detected elevated velocity fluctuations were associated with higher Reynolds shear stresses levels, which may increase the chances of blood damage and platelet activation and may lead to increased risk of blood clot formation.
Non-parametric regression for spatially dependent data with wavelets

We study non-parametric regression estimates for random fields. The data satisfies certain strong mixing conditions and is defined on the regular N-dimensional lattice structure. We show consistenc...
A Control-Theoretic Approach to Analysis and Parameter Selection of Douglas–Rachford Splitting

Douglas–Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on the choice of step size parameters, for which the optimal values are known in some specific cases, and otherwise are set heuristically. We provide a new unified method of convergence analysis and parameter selection by interpreting the algorithm as a linear dynamical system with nonlinear feedback. This approach allows us to derive a dimensionally independent matrix inequality whose feasibility is sufficient for the algorithm to converge at a specified rate. By analyzing this inequality, we are able to give performance guarantees and parameter settings of the algorithm under a variety of assumptions regarding the convexity and smoothness of the objective function. In particular, our framework enables us to obtain a new and simple proof of the ${O}$ (1/ ${k}$ ) convergence rate of the algorithm when the objective function is not strongly convex.
A mixed finite element approximation for Darcy–Forchheimer flows of slightly compressible fluids

Abstract In this paper, we consider the generalized Forchheimer flows for slightly compressible fluids in porous media. Using Muskat's and Ward's general form of Forchheimer equations, we describe the flow of a single-phase fluid in R d , d ≥ 2 by a nonlinear degenerate system of density and momentum. A mixed finite element method is proposed for the approximation of the solution of the above system. The stability of the approximations are proved; the error estimates are derived for the numerical approximations for both continuous and discrete time procedures. The continuous dependence of numerical solutions on physical parameters are demonstrated. Experimental studies are presented regarding convergence rates and showing the dependence of the solution on the physical parameters.
On the Cohen–Macaulayness of the conormal module of an ideal

Abstract In the present paper we investigate a question stemming from a long-standing conjecture of Vasconcelos: given a generically complete intersection perfect ideal I in a regular local ring R, when is it true that the Cohen–Macaulayness of I / I 2 (or R / I 2 ) implies that R / I is Gorenstein? This property is known to hold for licci ideals and, essentially, squarefree monomial ideals. We show that a positive answer actually holds for every monomial ideal. We then give a positive answer for several special classes of ideals and provide application to algebroid curves with low multiplicity. We also exhibit prime ideals in regular local rings and homogeneous level ideals in polynomial rings for which the answer is negative and use them to show the sharpness of our main result, as they lie in the first class of ideals not covered by it. The homogeneous examples have been found thanks to the help of J.C. Migliore. As a by-product, we exhibit several classes of Cohen–Macaulay ideals whose square is not Cohen–Macaulay. Our methods work both in the homogeneous and in the local settings.
Perfect Numbers in ACL2.

A perfect number is a positive integer n such that n equals the sum of all positive integer divisors of n that are less than n. That is, although n is a divisor of n, n is excluded from this sum. Thus 6 = 1 + 2 + 3 is perfect, but 12 < 1 + 2 + 3 + 4 + 6 is not perfect. An ACL2 theory of perfect numbers is developed and used to prove, in ACL2(r), this bit of mathematical folklore: Even if there are infinitely many perfect numbers the series of the reciprocals of all perfect numbers converges.
Weak capacity and modulus comparability in Ahlfors regular metric spaces

Let $(Z,d,\mu)$ be a compact, connected, Ahlfors $Q$-regular metric space with $Q>1$. Using a hyperbolic filling of $Z$, we define the notions of the $p$-capacity between certain subsets of $Z$ and of the weak covering $p$-capacity of path families $\Gamma$ in $Z$. We show comparability results and quasisymmetric invariance. As an application of our methods we deduce a result due to Tyson on the geometric quasiconformality of quasisymmetric maps between compact, connected Ahlfors $Q$-regular metric spaces.
Fundamental limits of ultrathin metasurfaces

We present a set of universal relations which relate the local transmission, reflection, and polarization conversion coefficients of a general class of non-magnetic passive ultrathin metasurfaces. We show that these relations are a result of equal forward and backward scattering by single layer ultrathin metasurfaces, and they lead to confinement of the transmission, reflection, and polarization conversion coefficients to limited regions of the complex plane. Using these relations, we investigate the effect of the presence of a substrate, and show that the maximum polarization conversion efficiency for a transmissive metasurface decreases as the refractive index contrast between the substrate and cladding layer increases. Furthermore, we demonstrate that a single layer reflective metasurface can achieve full 2π phase shift coverage without altering the polarization if it is illuminated from the higher refractive index material. We also discuss two approaches for achieving asymmetric scattering from metasurfaces, and realizing metasurfaces which overcome the performance limitations of single layer ultrathin metasurfaces.