cssi/SciSciGPT-SciSciNet huggingface dataset:
Aromatic motifs in the design of Ephedra ligands for application in the asymmetric addition of diethylzinc to aldehydes and diphenylphosphinoylimines

Using N-benzylephedrine as a model, a collection of N-arylmethylephedrine derivatives has been prepared. These derivatives were prepared by treatment of ephedrine with selected aldehydes to create oxazolidines 8a–e. Reduction of the oxazolidines with lithium aluminum hydride afforded the target β-amino alcohols 9a–e. When applied in the catalytic asymmetric addition of diethylzinc to aldehydes and diphenylphosphinoylimines, the derivatives yielded product enantioselectivities that were comparable to those of N-benzylephedrine. An N-cyclohexylmethylephedrine derivative was also prepared; this β-aminoalcohol did not perform well in the catalytic addition of diethylzinc to 2-naphthaldehyde, thus suggesting that the aromatic motif is important in terms of maintaining a reasonable level of asymmetric induction. Finally, N-benzyl-N-methyl-2-amino-1,2-diphenyl-1-ethanol, an analogue of the N-benzylephedrine derivative, was prepared. This compound yielded comparable enantioselectivities in the catalytic asymmetric addition when employed as a ligand.
Argosy: verifying layered storage systems with recovery refinement

Storage systems make persistence guarantees even if the system crashes at any time, which they achieve using recovery procedures that run after a crash. We present Argosy, a framework for machine-checked proofs of storage systems that supports layered recovery implementations with modular proofs. Reasoning about layered recovery procedures is especially challenging because the system can crash in the middle of a more abstract layer’s recovery procedure and must start over with the lowest-level recovery procedure. This paper introduces recovery refinement, a set of conditions that ensure proper implementation of an interface with a recovery procedure. Argosy includes a proof that recovery refinements compose, using Kleene algebra for concise definitions and metatheory. We implemented Crash Hoare Logic, the program logic used by FSCQ, to prove recovery refinement, and demonstrated the whole system by verifying an example of layered recovery featuring a write-ahead log running on top of a disk replication system. The metatheory of the framework, the soundness of the program logic, and these examples are all verified in the Coq proof assistant.
Rules for folding polyminoes from one level to two levels

Polyominoes have been the focus of many recreational and research investigations. In this article, the authors investigate whether a paper cutout of a polyomino can be folded to produce a second polyomino in the same shape as the original, but now with two layers of paper. For the folding, only "corner folds" and "half edge cuts" are allowed, unless the polyomino forms a closed loop, in which case one is allowed to completely cut two squares in the polyomino apart. With this set of allowable moves, the authors present algorithms for folding different types of polyominoes and prove that certain polyominoes can successfully be folded to two layers. The authors also establish that other polyominoes cannot be folded to two layers if only these moves are allowed.
Multiscale planar graph generation

The study of network representations of physical, biological, and social phenomena can help us better understand their structure and functional dynamics as well as formulate predictive models of these phenomena. However, due to the scarcity of real-world network data owing to factors such as cost and effort required in collection of network data and the sensitivity of this data towards theft and misuse, engineers and researchers often rely on synthetic data for simulations, hypothesis testing, decision making, and algorithm engineering. An important characteristic of infrastructure networks such as roads, water distribution and other utility systems is that they can be (almost fully) embedded in a plane, therefore to simulate these system we need realistic networks which are also planar. While the currently-available synthetic network generators can model networks that exhibit realism, they do not guarantee or achieve planarity. In this paper we present a flexible algorithm that can synthesize realistic networks that are planar. The method follows a multi-scale randomized editing approach generating a hierarchy of coarsened networks of a given planar graph and introducing edits at various levels in the hierarchy. The method preserves the structural properties with minimal bias including the planarity of the network, while introducing realistic variability at multiple scales. Reproducibility: All datasets and algorithm implementation presented in this work are available at https://bit.ly/2CjOUAS
Is Uncertainty Always Bad?: Effect of Topic Competence on Uncertain Opinions

The proliferation of information disseminated by public/social media has made decision-making highly challenging due to the wide availability of noisy, uncertain, or unverified information. Although the issue of uncertainty in information has been studied for several decades, little work has investigated how noisy (or uncertain) or valuable (or credible) information can be formulated into people's opinions, modeling uncertainty both in the quantity and quality of evidence leading to a specific opinion. In this work, we model and analyze an opinion and information model by using Subjective Logic where the initial set of evidence is mixed with different types of evidence (i.e., pro vs. con or noisy vs. valuable) which is incorporated into the opinions of original propagators, who propagate information over a network. With the help of an extensive simulation study, we examine how the different ratios of information types or agents' prior belief or topic competence affect the overall information diffusion. Based on our findings, agents' high uncertainty is not necessarily always bad in making a right decision as long as they are competent enough not to be at least biased towards false information (e.g., neutral between two extremes).
Word Representations via Gaussian Embedding

Abstract: Current work in lexical distributed representations maps each word to a point vector in low-dimensional space. Mapping instead to a density provides many interesting advantages, including better capturing uncertainty about a representation and its relationships, expressing asymmetries more naturally than dot product or cosine similarity, and enabling more expressive parameterization of decision boundaries. This paper advocates for density-based distributed embeddings and presents a method for learning representations in the space of Gaussian distributions. We compare performance on various word embedding benchmarks, investigate the ability of these embeddings to model entailment and other asymmetric relationships, and explore novel properties of the representation.
Learning Self-Imitating Diverse Policies

The success of popular algorithms for deep reinforcement learning, such as policy-gradients and Q-learning, relies heavily on the availability of an informative reward signal at each timestep of the sequential decision-making process. When rewards are only sparsely available during an episode, or a rewarding feedback is provided only after episode termination, these algorithms perform sub-optimally due to the difficultly in credit assignment. Alternatively, trajectory-based policy optimization methods, such as cross-entropy method and evolution strategies, do not require per-timestep rewards, but have been found to suffer from high sample complexity by completing forgoing the temporal nature of the problem. Improving the efficiency of RL algorithms in real-world problems with sparse or episodic rewards is therefore a pressing need. In this work, we introduce a self-imitation learning algorithm that exploits and explores well in the sparse and episodic reward settings. We view each policy as a state-action visitation distribution and formulate policy optimization as a divergence minimization problem. We show that with Jensen-Shannon divergence, this divergence minimization problem can be reduced into a policy-gradient algorithm with shaped rewards learned from experience replays. Experimental results indicate that our algorithm works comparable to existing algorithms in environments with dense rewards, and significantly better in environments with sparse and episodic rewards. We then discuss limitations of self-imitation learning, and propose to solve them by using Stein variational policy gradient descent with the Jensen-Shannon kernel to learn multiple diverse policies. We demonstrate its effectiveness on a challenging variant of continuous-control MuJoCo locomotion tasks.
A Statistical Recurrent Model on the Manifold of Symmetric Positive Definite Matrices

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several recent papers have shown how convolutional neural networks (CNNs) can be extended to learn with graph-based data. In this work, we study the setting where the data (or measurements) are ordered, longitudinal or temporal in nature and live on a Riemannian manifold -- this setting is common in a variety of problems in statistical machine learning, vision and medical imaging. We show how recurrent statistical recurrent network models can be defined in such spaces. We give an efficient algorithm and conduct a rigorous analysis of its statistical properties. We perform extensive numerical experiments demonstrating competitive performance with state of the art methods but with significantly less number of parameters. We also show applications to a statistical analysis task in brain imaging, a regime where deep neural network models have only been utilized in limited ways.
One-Level density for holomorphic cusp forms of arbitrary level

In 2000 Iwaniec, Luo, and Sarnak proved for certain families of L-functions associated to holomorphic newforms of square-free level that, under the Generalized Riemann Hypothesis, as the conductors tend to infinity the one-level density of their zeros matches the one-level density of eigenvalues of large random matrices from certain classical compact groups in the appropriate scaling limit. We remove the square-free restriction by obtaining a trace formula for arbitrary level by using a basis developed by Blomer and Milicevic, which is of use for other problems as well.
2D Euler equation on the strip: Stability of a rectangular patch

We consider the 2D Euler equation of incompressible fluids on a strip ℝ×&#x1d54b; and prove the stability of the rectangular stationary state χ|x|<L for large enough L.
Discriminants of Taft Algebra Smash Products and Applications

A general criterion is given for when the center of a Taft algebra smash product is the fixed ring. This is applied to the study of the noncommutative discriminant. Our method relies on the Poisson methods of Nguyen, Trampel, and Yakimov, but also makes use of Poisson Ore extensions. Specifically, we fully determine the inner faithful actions of Taft algebras on quantum planes and quantum Weyl algebras. We compute the discriminant of the corresponding smash product and apply it to compute the Azumaya locus and restricted automorphism group.
A note on Grothendieck’s standard conjectures of type C⁺ and D

Grothendieck conjectured in the sixties that the even Kunneth projector (with respect to a Weil cohomology theory) is algebraic and that the homological equivalence relation on algebraic cycles coincides with the numerical equivalence relation. In this note we extend these celebrated conjectures from smooth projective schemes to the broad setting of smooth proper dg categories. As an application, we prove that Grothendieck's original conjectures are invariant under homological projective duality. This leads to a proof of Grothendieck's conjectures in the case of intersections of quadrics, linear sections of determinantal varieties, and intersections of bilinear divisors. Along the way, we prove also the case of quadric fibrations.
Adversarial Classification on Social Networks

The spread of unwanted or malicious content through social media has become a major challenge. Traditional examples of this include social network spam, but an important new concern is the propagation of fake news through social media. A common approach for mitigating this problem is by using standard statistical classification to distinguish malicious (e.g., fake news) instances from benign (e.g., actual news stories). However, such an approach ignores the fact that malicious instances propagate through the network, which is consequential both in quantifying consequences (e.g., fake news diffusing through the network), and capturing detection redundancy (bad content can be detected at different nodes). An additional concern is evasion attacks, whereby the generators of malicious instances modify the nature of these to escape detection. We model this problem as a Stackelberg game between the defender who is choosing parameters of the detection model, and an attacker, who is choosing both the node at which to initiate malicious spread, and the nature of malicious entities. We develop a novel bi-level programming approach for this problem, as well as a novel solution approach based on implicit function gradients, and experimentally demonstrate the advantage of our approach over alternatives which ignore network structure.
Convergence Time of Quantized Metropolis Consensus Over Time-Varying Networks

We consider the quantized consensus problem on undirected time-varying connected graphs with $n$ nodes, and devise a protocol with fast convergence time to the set of consensus points. Specifically, we show that when the edges of each network in a sequence of connected time-varying networks are activated based on Poisson processes with Metropolis rates, the expected convergence time to the set of consensus points is at most $O(n^{2}\log^{2}n)$ , where each node performs a constant number of updates per unit time.
50 Years of First-Passage Percolation

We celebrate the 50th anniversary of one the most classical models in probability theory. In this survey, we describe the main results of first passage percolation, paying special attention to the recent burst of advances of the past 5 years. The purpose of these notes is twofold. In the first chapters, we give self-contained proofs of seminal results obtained in the '80s and '90s on limit shapes and geodesics, while covering the state of the art of these questions. Second, aside from these classical results, we discuss recent perspectives and directions including (1) the connection between Busemann functions and geodesics, (2) the proof of sublinear variance under 2+log moments of passage times and (3) the role of growth and competition models. We also provide a collection of (old and new) open questions, hoping to solve them before the 100th birthday.
Searching for Activation Functions

The choice of activation functions in deep networks has a significant effect on the training dynamics and task performance. Currently, the most successful and widely-used activation function is the Rectified Linear Unit (ReLU). Although various hand-designed alternatives to ReLU have been proposed, none have managed to replace it due to inconsistent gains. In this work, we propose to leverage automatic search techniques to discover new activation functions. Using a combination of exhaustive and reinforcement learning-based search, we discover multiple novel activation functions. We verify the effectiveness of the searches by conducting an empirical evaluation with the best discovered activation function. Our experiments show that the best discovered activation function, $f(x) = x \cdot \text{sigmoid}(\beta x)$, which we name Swish, tends to work better than ReLU on deeper models across a number of challenging datasets. For example, simply replacing ReLUs with Swish units improves top-1 classification accuracy on ImageNet by 0.9\% for Mobile NASNet-A and 0.6\% for Inception-ResNet-v2. The simplicity of Swish and its similarity to ReLU make it easy for practitioners to replace ReLUs with Swish units in any neural network.
Space functions of groups

We consider space functions $s(n)$ of finitely presented groups $G = .$ (These functions have a natural geometric analog.) To define $s(n)$ we start with a word $w$ over $A$ of length at most $n$ equal to 1 in $G$ and use relations from $R$ for elementary transformations to obtain the empty word; $s(n)$ bounds from above the tape space (or computer memory) one needs to transform any word of length at most $n$ vanishing in $G$ to the empty word. One of the main obtained results is the following criterion: A finitely generated group $H$ has decidable word problem of polynomial space complexity if and only if $H$ is a subgroup of a finitely presented group $G$ with a polynomial space function.
A Hierarchical Latent Vector Model for Learning Long-Term Structure in Music

The Variational Autoencoder (VAE) has proven to be an effective model for producing semantically meaningful latent representations for natural data. However, it has thus far seen limited application to sequential data, and, as we demonstrate, existing recurrent VAE models have difficulty modeling sequences with long-term structure. To address this issue, we propose the use of a hierarchical decoder, which first outputs embeddings for subsequences of the input and then uses these embeddings to generate each subsequence independently. This structure encourages the model to utilize its latent code, thereby avoiding the "posterior collapse" problem, which remains an issue for recurrent VAEs. We apply this architecture to modeling sequences of musical notes and find that it exhibits dramatically better sampling, interpolation, and reconstruction performance than a "flat" baseline model. An implementation of our "MusicVAE" is available online at this http URL.
A Multivariate Hawkes Process With Gaps in Observations

Given a collection of entities (or nodes) in a network and our intermittent observations of activities from each entity, an important problem is to learn the hidden edges depicting directional relationships among these entities. Here, we study causal relationships (excitations) that are realized by a multivariate Hawkes process (MHP). The MHP and its variations (spatio-temporal point processes) have been used to study contagion in earthquakes, crimes, neural spiking activities, the stock and foreign exchange markets, and so on. In this paper, we consider the MHP with gaps (MHPG) in observations. We propose a variational problem for detecting sparsely hidden relationships with an MHP that takes into account the gaps from each entity. We bypass the problem of dealing with a large amount of missing events by introducing a small number of unknown boundary conditions. In the case where our observations are sparse (e.g., from 10% to 30%), we show through numerical simulations that robust recovery with MHPG is still possible even if the lengths of the observed intervals are small but they are chosen accordingly. The numerical results also show that the knowledge of gaps and imposing the right boundary conditions are very crucial in discovering the underlying patterns and hidden relationships.
Probabilistic Typology: Deep Generative Models of Vowel Inventories

Linguistic typology studies the range of structures present in human language. The main goal of the field is to discover which sets of possible phenomena are universal, and which are merely frequent. For example, all languages have vowels, while most—but not all—languages have an /u/ sound. In this paper we present the first probabilistic treatment of a basic question in phonological typology: What makes a natural vowel inventory? We introduce a series of deep stochastic point processes, and contrast them with previous computational, simulation-based approaches. We provide a comprehensive suite of experiments on over 200 distinct languages.
A primal-dual type algorithm with the O(1/t) convergence rate for large scale constrained convex programs

This paper considers large scale constrained convex programs. These are often difficult to solve by interior point methods or other Newton-type methods due to the prohibitive computation and storage complexity for Hessians or matrix inversions. Instead, large scale constrained convex programs are often solved by gradient based methods or decomposition based methods. The conventional primal-dual subgradient method, also known as the Arrow-Hurwicz-Uzawa subgradient method, is a low complexity algorithm with the O(1/√t) convergence rate, where t is the number of iterations. If the objective and constraint functions are separable, the Lagrangian dual type method can decompose a large scale convex program into multiple parallel small scale convex programs. The classical dual gradient algorithm is an example of Lagrangian dual type methods and has convergence rate O(1/√t). Recently, the authors of the current paper proposed a new Lagrangian dual type algorithm with faster O(1/t) convergence. However, if the objective or constraint functions are not separable, each iteration requires to solve a large scale unconstrained convex program, which can have huge complexity. This paper proposes a new primal-dual type algorithm, which only involves simple gradient updates at each iteration and has O(1/t) convergence.
Efficient Convex Optimization with Membership Oracles

We consider the problem of minimizing a convex function over a convex set given access only to an evaluation oracle for the function and a membership oracle for the set. We give a simple algorithm which solves this problem with $\tilde{O}(n^2)$ oracle calls and $\tilde{O}(n^3)$ additional arithmetic operations. Using this result, we obtain more efficient reductions among the five basic oracles for convex sets and functions defined by Grotschel, Lovasz and Schrijver.
On the Gaussian Z-interference channel with processing energy cost

This work considers a Gaussian interference channel with processing energy cost, which explicitly takes into account the energy expended for processing when each transmitter is on. With processing overhead, bursty transmission at each transmitter generally becomes more advantageous. Assuming on-off states do not carry information, for a two-user Z-interference channel, the new regime of very strong interference is identified and shown to be enlarged compared with the conventional one. With the interfered receiver listening when its own transmitter is silent, for a wide range of cross-link power gains, one can either achieve or get close to the interference-free upper bound on sum rate.
Improved Semantic-Aware Network Embedding with Fine-Grained Word Alignment

Network embeddings, which learns low-dimensional representations for each vertex in a large-scale network, have received considerable attention in recent years. For a wide range of applications, vertices in a network are typically accompanied by rich textual information such as user profiles, paper abstracts, etc. In this paper, we propose to incorporate semantic features into network embeddings by matching important words between text sequences for all pairs of vertices. We introduce an word-by-word alignment framework that measures the compatibility of embeddings between word pairs, and then adaptively accumulates these alignment features with a simple yet effective aggregation function. In experiments, we evaluate the proposed framework on three real-world benchmarks for downstream tasks, including link prediction and multi-label vertex classification. The experimental results demonstrate that our model outperforms state-of-the-art network embedding methods by a large margin.
Combating Adversarial Attacks Using Sparse Representations.

It is by now well-known that small adversarial perturbations can induce classification errors in deep neural networks (DNNs). In this paper, we make the case that sparse representations of the input data are a crucial tool for combating such attacks. For linear classifiers, we show that a sparsifying front end is provably effective against $\ell_{\infty}$-bounded attacks, reducing output distortion due to the attack by a factor of roughly $K / N$ where $N$ is the data dimension and $K$ is the sparsity level. We then extend this concept to DNNs, showing that a "locally linear" model can be used to develop a theoretical foundation for crafting attacks and defenses. Experimental results for the MNIST dataset show the efficacy of the proposed sparsifying front end.
Learning long term dependencies via Fourier recurrent units

It is a known fact that training recurrent neural networks for tasks that have long term dependencies is challenging. One of the main reasons is the vanishing or exploding gradient problem, which prevents gradient information from propagating to early layers. In this paper we propose a simple recurrent architecture, the Fourier Recurrent Unit (FRU), that stabilizes the gradients that arise in its training while giving us stronger expressive power. Specifically, FRU summarizes the hidden states $h^{(t)}$ along the temporal dimension with Fourier basis functions. This allows gradients to easily reach any layer due to FRU's residual learning structure and the global support of trigonometric functions. We show that FRU has gradient lower and upper bounds independent of temporal dimension. We also show the strong expressivity of sparse Fourier basis, from which FRU obtains its strong expressive power. Our experimental study also demonstrates that with fewer parameters the proposed architecture outperforms other recurrent architectures on many tasks.
Four factorization formulas for plane partitions

All ten symmetry classes of plane partitions that fit in a given box are known to be enumerated by simple product formulas, but there is still no unified proof for all of them. Progress towards this goal can be made by establishing identities connecting the various symmetry classes. We present in this paper four such identities, involving all ten symmetry classes. We discuss their proofs and generalizations. The main result of this paper is to give a generalization of one of them, in the style of the identity presented in "A factorization theorem for rhombus tilings," M. Ciucu and C. Krattenthaler, arXiv:1403.3323.
Geometric limits of Mandelbrot and Julia sets under degree growth

First, for the family Pn,c(z) = zn + c, we show that the geometric limit of the Mandelbrot sets Mn(P) as n → ∞ exists and is the closed unit disk, and that the geometric limit of the Julia sets J(Pn,c) as n tends to infinity is the unit circle, at least when |c| ≠ 1. Then, we establish similar results for some generalizations of this family; namely, the maps z ↦ zt + c for real t ≥ 2 and the rational maps z ↦ zn + c + a/zn.
AN INTERMEDIATE REGIME FOR EXIT PHENOMENA DRIVEN BY NON-GAUSSIAN LÉVY NOISES

A dynamical system driven by non-Gaussian Levy noises of small intensity is considered. The first exit time of solution orbits from a bounded neighborhood of an attracting equilibrium state is estimated. For a class of non-Gaussian Levy noises, it is shown that the mean exit time is asymptotically faster than exponential (the well-known Gaussian Brownian noise case) but slower than polynomial (the stable Levy noise case), in terms of the reciprocal of the small noise intensity.
Spatial Morphing Kernel Regression for Feature Interpolation

In recent years, geotagged social media has become popular as a novel source for geographic knowledge discovery. Ground-level images and videos provide a different perspective than overhead imagery and can be applied to a range of applications such as land use mapping, activity detection, pollution mapping, etc. The sparse and uneven distribution of this data presents a problem, however, for generating dense maps. We therefore investigate the problem of spatially interpolating the high-dimensional features extracted from sparse social media to enable dense labeling using standard classifiers. Further, we show how prior knowledge about region boundaries can be used to improve the interpolation through spatial morphing kernel regression. We show that an interpolate-then-classify framework can produce dense maps from sparse observations but that care must be taken in choosing the interpolation method. We also show that the spatial morphing kernel improves the results.
Harmonic Analysis Techniques in Several Complex Variables

This talk concerns recent joint work with E. M. Stein on the extension to higher dimension of Calder on's and Coifman-McIntosh-Meyer's seminal results about
Six-day footraces in the post-pedestrianism era

In a six-day footrace, competitors accumulate as much distance as possible on foot over 144 consecutive hours by circumambulating a loop course. Now an obscure event on the fringe of ultra running and contested by amateurs, six-day races and the associated sport of pedestrianism used to be a lucrative professional athletic endeavor. Indeed, pedestrianism was the most popular spectator sport in America c. 1874–c. 1881. We analyzed data from 277 six-day races spanning 37 years in the post-pedestrianism era (1981–2018). Men outnumber women 3:1 in six-day race participation. The men’s (women’s) six-day world record is 644.2 (549.1) miles and the top 4% achieve 500 (450) miles. Adopting the forecasting model of Godsey (2012), we predict a 53% (21%) probability that the men’s (women’s) world record will be broken within the next decade.
Influence of Chain Structure and Swelling on the Elasticity of Rubbery Materials: Localization Model Description

Summary Classical network elasticity theories are based on the concept of flexible volumeless network chains fixed into a network in which there are no excluded volume, or even topological, interactions between the chains and where the chains explore accessible configurations by Brownian motion. In this type of ‘classical’ model of rubber elasticity, the elasticity of the deformed network derives from the entropic changes that arise from a deformation of the network junction positions. The shortcoming of this approach is evident from the observation that unswollen rubbery materials are nearly incompressible, reflecting the existence of strong intermolecular interactions that restrict the polymer chains to the exploration of their local tube-like molecular environments along their chain contours. The imposition of a deformation of these solid rubbery materials then necessitates a consideration of how the local molecular packing constraints become modified under deformation and the impact of these changes in chain confinement on the macroscopic elasticity of the material as a whole. Many researchers have struggled with this difficult many-body problem. The present paper focuses on the simple ‘localization model’ (LM) of rubber elasticity of Gaylord and Douglas (GD), which provides a simple minimal model for the network elasticity of rubbery materials in the dense polymer state. Particular emphasis in the present paper is given to the implications of this model for describing how network elasticity changes with solvent swelling, a phenomenon for which large deviations from classical elasticity have been observed and a situation highly relevant to numerous applications that involve rubbery materials. We also discuss the physical nature of ‘entanglement’ based on the same molecular packing picture and deduce general conditions for entanglement in terms of molecular parameters. Our predictions accord rather well with experimental correlations relating chain molecular structure to the entanglement molecular mass, changing elasticity with swelling, etc.
Spectral control of mobile robot networks

The eigenvalue spectrum of the adjacency matrix of a network is closely related to the behavior of many dynamical processes run over the network. In the field of robotics, this spectrum has important implications in many problems that require some form of distributed coordination within a team of robots. In this paper, we propose a continuous-time control scheme that modifies the structure of a position-dependent network of mobile robots so that it achieves a desired set of adjacency eigenvalues. For this, we employ a novel abstraction of the eigenvalue spectrum by means of the adjacency matrix spectral moments. Since the eigenvalue spectrum is uniquely determined by its spectral moments, this abstraction provides a way to indirectly control the eigenvalues of the network. Our construction is based on artificial potentials that capture the distance of the network's spectral moments to their desired values. Minimization of these potentials is via a gradient descent closed-loop system that, under certain convexity assumptions, ensures convergence of the network topology to one with the desired set of moments and, therefore, eigenvalues. We illustrate our approach in nontrivial computer simulations.
Mechanisms for total and spectral solar irradiance variations

The total and spectral irradiance varies over short time scales, i.e. from days to months, and longer time scales from years to decades, centuries, and beyond. In this talk we review the current understanding of irradiance changes from days to decades. We present the current status of observations and discuss proposed reconstruction approaches to understand these variations. The main question that ultimately needs to be answered is what are the physical processes that could explain the enhanced heating of the photosphere, chromosphere, transition region, and corona, leading to a change in the solar radiative output at various wavelengths. As semi-empirical models allow us to reproduce the solar spectrum over a broad wavelength range, they offer a powerful tool to determine the energy necessary to heat certain layers and at the same time balance the radiative losses.
Double shuffle relations for multiple Dedekind zeta values

Abstract This paper contains examples of shuffle relations among multiple Dedekind zeta values. Dedekind zeta values were defined by the author in [H3]. Here we concentrate on the cases of real or imaginary quadratic fields with up to double iteration. We give examples of integral shuffle relation in terms of iterated integrals over membranes and of infinite sum shuffle relation, sometimes called stuffle relation. Using both types of shuffles for the product ζK,C(2)ζK,C(2), we find relations among multiple Dedekind zeta values for real and for imaginary quadratic fields.
Boundary Regularity for Conformally Compact Einstein Metrics in Even Dimensions

We study boundary regularity for conformally compact Einstein metrics in even dimensions by generalizing the ideas of Anderson (2003, 2006). Our method of approach is to view the vanishing of the Ambient Obstruction tensor as an nth order system of equations for the components of a compactification of the given metric. This, together with boundary conditions that the compactification is shown to satisfy provide enough information to apply classical boundary regularity results. These results then provide local and global versions of finite boundary regularity for the components of the compactification.
Using Liquid Metal in an Electromechanical Motor With Breathing Mode Motion

Electromechanical actuators exploit the Lorentz force law to convert electrical energy into rotational or linear mechanical energy. In these electromagnetically induced motions, the electrical current flows through wires that are rigid and consequently the types of motion generated are limited. Recent advances in preparing liquid metal alloys permit wires that are flexible. Such wires have been used to fabricate various forms of flexible connections, but very little has been done to use liquid metal as an actuator. In this paper we propose and have tested a new type of motor using liquid metal conductors in which radial (or breathing) modes are activated.
PRODUCTS OF IDEALS MAY NOT BE GOLOD

Abstract We exhibit an example of a product of two proper monomial ideals such that the residue class ring is not Golod. We also discuss the strongly Golod property for rational powers of monomial ideals, and introduce some sufficient conditions for weak Golodness of monomial ideals. Along the way, we ask some related questions.
Analysis of a Double Kruskal Theorem

The strength of an extension of Kruskal's Theorem to certain pairs of cohabitation trees is calibrated.
Distributed storage codes meet multiple-access wiretap channels

We consider i) the overhead minimization of maximum-distance separable (MDS) storage codes for the repair of a single failed node and ii) the total secure degrees-of-freedom (S-DoF) maximization in a multiple-access compound wiretap channel. We show that the two problems are connected. Specifically, the overhead minimization for a single node failure of an optimal MDS code, i.e. one that can achieve the information theoretic overhead minimum, is equivalent to maximizing the S-DoF in a multiple-access compound wiretap channel. Additionally, we show that maximizing the S-DoF in a multiple-access compound wiretap channel is equivalent to minimizing the overhead of an MDS code for the repair of a departed node. An optimal MDS code maps to a full S-DoF channel and a full S-DoF channel maps to an MDS code with minimum repair overhead for one failed node. We also state a general framework for code-to-channel and channel-to-code mappings and performance bounds between the two settings. The underlying theme for all connections presented is interference alignment (IA). The connections between the two problems become apparent when we restate IA as an optimization problem. Specifically, we formulate the overhead minimization and the S-DoF maximization as rank constrained, sum-rank and max-rank minimization problems respectively. The derived connections allow us to map repair strategies of recently discovered repair codes to beamforming matrices and characterize the maximum S-DoF for the single antenna multiple-access compound wiretap channel.
Query Complexity of Clustering with Side Information

Suppose, we are given a set of $n$ elements to be clustered into $k$ (unknown) clusters, and an oracle/expert labeler that can interactively answer pair-wise queries of the form, ``do two elements $u$ and $v$ belong to the same cluster?''. The goal is to recover the optimum clustering by asking the minimum number of queries. In this paper, we provide a rigorous theoretical study of this basic problem of query complexity of interactive clustering, and give strong information theoretic lower bounds, as well as nearly matching upper bounds. Most clustering problems come with a similarity matrix, which is used by an automated process to cluster similar points together. To improve accuracy of clustering, a fruitful approach in recent years has been to ask a domain expert or crowd to obtain labeled data interactively. Many heuristics have been proposed, and all of these use a similarity function to come up with a querying strategy. Even so, there is a lack systematic theoretical study. Our main contribution in this paper is to show the dramatic power of side information aka similarity matrix on reducing the query complexity of clustering. A similarity matrix represents noisy pair-wise relationships such as one computed by some function on attributes of the elements. A natural noisy model is where similarity values are drawn independently from some arbitrary probability distribution $f_+$ when the underlying pair of elements belong to the same cluster, and from some $f_-$ otherwise. We show that given such a similarity matrix, the query complexity reduces drastically from $\Theta(nk)$ (no similarity matrix) to $O(\frac{k^2\log{n}}{\cH^2(f_+\|f_-)})$ where $\cH^2$ denotes the squared Hellinger divergence. Moreover, this is also information-theoretic optimal within an $O(\log{n})$ factor. Our algorithms are all efficient, and parameter free, i.e., they work without any knowledge of $k, f_+$ and $f_-$, and only depend logarithmically with $n$.
Hierarchical exchangeability of pure states in mean field spin glass models

The main result in this paper is motivated by the Mezard–Parisi ansatz which predicts a very special structure for the distribution of spins in diluted mean field spin glass models, such as the random $$K$$ -sat model at positive temperature. Using the fact that one can safely assume the validity of the Ghirlanda–Guerra identities in these models, we prove hierarchical exchangeability of pure states for the asymptotic Gibbs measures, which allows us to apply a representation result for hierarchically exchangeable arrays recently proved in Austin and Panchenko in Probab. Theory Relat. Fields 2013. Comparing this representation with the predictions of the Mezard–Parisi ansatz, one can see that the key property still missing is that the multi-overlaps between pure states depend only on their overlaps.
The Riemann Zeta Function on Vertical Arithmetic Progressions

We show that the twisted second moments of the Riemann zeta function averaged over the arithmetic progression 12 + i(an + b) with a > 0, b real, exhibits a remarkable correspondance with the analogous continuous average and derive several consequences. For example, motivated by the linear independence conjecture, we show at least one third of the elements in the arithmetic progression an + b are not the ordinates of some zero of ζ(s) lying on the critical line. This improves on earlier work of Martin and Ng. We then complement this result by producing large and small values of ζ(s) on arithmetic progressions which are of the same quality as the best Ω results currently known for ζ( 12 + it) with t real.
Evaluation of Unsupervised Compositional Representations

We evaluated various compositional models, from bag-of-words representations to compositional RNN-based models, on several extrinsic supervised and unsupervised evaluation benchmarks. Our results confirm that weighted vector averaging can outperform context-sensitive models in most benchmarks, but structural features encoded in RNN models can also be useful in certain classification tasks. We analyzed some of the evaluation datasets to identify the aspects of meaning they measure and the characteristics of the various models that explain their performance variance.
Poitou–Tate without restrictions on the order

The Poitou-Tate sequence relates Galois cohomology with restricted ramification of a finite Galois module $M$ over a global field to that of the dual module under the assumption that $\#M$ is a unit away from the allowed ramification set. We remove the assumption on $\#M$ by proving a generalization that allows arbitrary "ramification sets" that contain the archimedean places. We also prove that restricted products of local cohomologies that appear in the Poitou-Tate sequence may be identified with derived functor cohomology of an adele ring. In our proof of the generalized sequence we adopt this derived functor point of view and exploit properties of a natural topology carried by cohomology of the adeles.
Lagrangian tori in four-dimensional Milnor fibres

The Milnor fibre of any isolated hypersurface singularity contains many exact Lagrangian spheres: the vanishing cycles associated to a Morsification of the singularity. Moreover, for simple singularities, it is known that the only possible exact Lagrangians are spheres. We construct exact Lagrangian tori in the Milnor fibres of all non-simple singularities of real dimension four. This gives examples of Milnor fibres whose Fukaya categories are not generated by vanishing cycles. Also, this allows progress towards mirror symmetry for unimodal singularities, which are one level of complexity up from the simple ones.
Modeling and analysis of RNA-seq data: a review from a statistical perspective

Since the invention of next-generation RNA sequencing (RNA-seq) technologies, they have become a powerful tool to study the presence and quantity of RNA molecules in biological samples and have revolutionized transcriptomic studies. The analysis of RNA-seq data at four different levels (samples, genes, transcripts, and exons) involve multiple statistical and computational questions, some of which remain challenging up to date. We review RNA-seq analysis tools at the sample, gene, transcript, and exon levels from a statistical perspective. We also highlight the biological and statistical questions of most practical considerations. The development of statistical and computational methods for analyzing RNA-seq data has made significant advances in the past decade. However, methods developed to answer the same biological question often rely on diverse statistical models and exhibit different performance under different scenarios. This review discusses and compares multiple commonly used statistical models regarding their assumptions, in the hope of helping users select appropriate methods as needed, as well as assisting developers for future method development.
The changing source of X-ray reflection in the radio-intermediate Seyfert 1 galaxy III Zw 2

We report on X-ray observations of the radio-intermediate, X-ray bright Seyfert 1 galaxy, III Zw 2, obtained with XMM-Newton, Suzaku, and Swift over the past 17-years. The source brightness varies significantly over yearly time scales, but more modestly over periods of days. Pointed observations with XMM-Newton in 2000 and Suzaku in 2011 show spectral differences despite comparable X-ray fluxes. The Suzaku spectra are consistent with a power law continuum and a narrow Gaussian emission feature at ~6.4 keV, whereas the earlier XMM-Newton spectrum requires a broader Gaussian profile and soft-excess below ~2 keV. A potential interpretation is that the primary power law emission, perhaps from a jet base, preferentially illuminates the inner accretion disc in 2000, but the distant torus in 2011. The interpretation could be consistent with the hypothesised precessing radio jet in III Zw 2 that may have originated from disc instabilities due to an ongoing merging event.
Computational Beauty: Aesthetic Judgment at the Intersection of Art and Science

In part one of the Critique of Judgment, Immanuel Kant wrote that “the judgment of taste ... is not a cognitive judgment, and so not logical, but is aesthetic [1].” While the condition of aesthetic discernment has long been the subject of philosophical discourse, the role of the arbiters of that judgment has more often been assumed than questioned. The art historian, critic, connoisseur, and curator have long held the esteemed position of the aesthetic judge, their training, instinct, and eye part of the inimitable subjective processes that Kant described as occurring upon artistic evaluation. Although the concept of intangible knowledge in regard to aesthetic theory has been much explored, little discussion has arisen in response to the development of new types of artificial intelligence as a challenge to the seemingly ineffable abilities of the human observer. This paper examines the developments in the field of computer vision analysis of paintings from canonical movements within the history of Western art and the reaction of art historians to the application of this technology in the field. Through an investigation of the ethical consequences of this innovative technology, the unquestioned authority of the art expert is challenged and the subjective nature of aesthetic judgment is brought to philosophical scrutiny once again.
Deep Neural Networks for Physics Analysis on low-level whole-detector data at the LHC

There has been considerable recent activity applying deep convolutional neural nets (CNNs) to data from particle physics experiments. Current approaches on ATLAS/CMS have largely focussed on a subset of the calorimeter, and for identifying objects or particular particle types. We explore approaches that use the entire calorimeter, combined with track information, for directly conducting physics analyses: i.e. classifying events as known-physics background or new-physics signals. We use an existing RPV-Supersymmetry analysis as a case study and explore CNNs on multi-channel, high-resolution sparse images: applied on GPU and multi-node CPU architectures (including Knights Landing (KNL) Xeon Phi nodes) on the Cori supercomputer at NERSC.