cssi/SciSciGPT-SciSciNet huggingface dataset:
Asymmetric syntheses of (-)-8-epi-swainsonine triacetate and (+)-1, 2-Di-epi-swainsonine. Carbonyl addition thwarted by an unprecedented aza-pinacol rearrangement.

Indolizidines (-)-8-epi-swainsonine triacetate and (+)-1, 2-di-epi-swainsonine were synthesized from the O'Donnell Schiff base ester 1 derived from D-serine. Reductive-alkenylation of 1 with (i)()Bu(5)Al(2)H/H(2)C=CHMgBr followed by substrate-directed dihydroxylation of the pendant allylic group with OsO(4), reduction of imine, and cyclization with Ph(3)P/CCl(4) gave the polyhydroxylated pyrrolidines 8a and 8b as advanced intermediates. Efficient protecting group manipulations converted pyrrolidines 8a and 8b to their corresponding partially protected analogues 10a and 10b, which upon Swern oxidation and diastereoselective Keck-type allylation with BF(3).Et(2)O afforded the required three-carbon homologues (10a, >20:1 de; 10b, 3.5:1 de). Use of the chelating Lewis acid MgBr(2) instead of BF(3).Et(2)O with 10a led to a novel aza-pinacol rearrangement and allylation at the alpha-carbon to yield amino alcohol 17, which is similar to a hydride migration in the biosynthetic pathway of indolizidine alkaloids. Subsequent hydroboration, cyclization, and deprotection furnished (-)-8-epi-swainsonine triacetate 15a and (+)-1,2-di-epi-swainsonine 16b in good overall yields (6.3% for 1 --> 15a, 13 steps, and 4.0% for 1 --> 16b, 14 steps).
Human Germline Mutation and the Erratic Evolutionary Clock.

Our understanding of the chronology of human evolution relies on the “molecular clock” provided by the steady accumulation of substitutions on an evolutionary lineage. Recent analyses of human pedigrees have called this understanding into question by revealing unexpectedly low germline mutation rates, which imply that substitutions accrue more slowly than previously believed. Translating mutation rates estimated from pedigrees into substitution rates is not as straightforward as it may seem, however. We dissect the steps involved, emphasizing that dating evolutionary events requires not “a mutation rate” but a precise characterization of how mutations accumulate in development in males and females—knowledge that remains elusive.
Intraindividual variability of sleep/wake patterns in adolescents with and without attention-deficit/hyperactivity disorder

Background Prior studies examining the sleep of adolescents with and without attention-deficit/hyperactivity disorder (ADHD) have relied on mean values such as average sleep duration, which masks intraindividual variability (IIV). The objective was to investigate whether adolescents with ADHD have greater IIV of sleep/wake patterns than adolescents without ADHD using actigraphy and daily sleep diaries. Method Adolescents (ages 13.17 ± 0.40 years; 45% female) with (n = 162) and without (n = 140) ADHD were recruited from middle schools at two sites. Participants wore actigraphs and completed sleep diaries for an average of 2 weeks. Results Multilevel models were conducted with sex, sleep medication use, ADHD medication use, number of days with data, and social jetlag controlled for in analyses. For actigraphy, adolescents with ADHD had greater variability for time in bed, sleep onset and offset, and wake after sleep onset than adolescents without ADHD. For sleep diary data, adolescents with ADHD had greater variability in bedtime, wake time, sleep duration, sleep onset latency, sleep quality, and night wakings than adolescents without ADHD. Social jetlag was a significant predictor of variability in sleep measures based on both actigraph and daily diaries; however, ADHD status was not associated with social jetlag. Conclusions This is the first study to show that adolescents with ADHD have more variable sleep/wake patterns than their peers using both objective and subjective sleep measures. IIV of sleep/wake patterns may be important for clinicians to assess and monitor as part of treatment. Research is needed to understand the mechanisms underlying increased IIV of sleep/wake patterns in adolescents with ADHD and potential consequences for daytime functioning.
Students’ views about the nature of experimental physics

Laboratory physics courses typically do not help students develop more expertlike beliefs about experimental physics.
A polyhedral proof of a wreath product identity

In 2013, Beck and Braun proved and generalized multiple identities involving permutation statistics via discrete geometry. Namely, they recognized the identities as specializations of integer point transform identities for certain polyhedral cones. They extended many of their proof techniques to obtain identities involving wreath products, but some identities were resistant to their proof attempts. In this article, we provide a geometric justification of one of these wreath product identities, which was first established by Biagioli and Zeng.
Molding CNNs for text: non-linear, non-consecutive convolutions

The success of deep learning often derives from well-chosen operational building blocks. In this work, we revise the temporal convolution operation in CNNs to better adapt it to text processing. Instead of concatenating word representations, we appeal to tensor algebra and use low-rank n-gram tensors to directly exploit interactions between words already at the convolution stage. Moreover, we extend the n-gram convolution to non-consecutive words to recognize patterns with intervening words. Through a combination of lowrank tensors, and pattern weighting, we can efficiently evaluate the resulting convolution operation via dynamic programming. We test the resulting architecture on standard sentiment classification and news categorization tasks. Our model achieves state-of-the-art performance both in terms of accuracy and training speed. For instance, we obtain 51.2% accuracy on the fine-grained sentiment classification task. 1
Compressed Sensing and Matrix Completion with Constant Proportion of Corruptions

In this paper, we improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. (1) In compressed sensing, we show that if the m×n sensing matrix has independent Gaussian entries, then one can recover a sparse signal x exactly by tractable l 1 minimization even if a positive fraction of the measurements are arbitrarily corrupted, provided the number of nonzero entries in x is O(m/(log(n/m)+1)). (2) In the very general sensing model introduced in Candes and Plan (IEEE Trans. Inf. Theory 57(11):7235–7254, 2011) and assuming a positive fraction of corrupted measurements, exact recovery still holds if the signal now has O(m/(log2 n)) nonzero entries. (3) Finally, we prove that one can recover an n×n low-rank matrix from m corrupted sampled entries by tractable optimization provided the rank is on the order of O(m/(nlog2 n)); again, this holds when there is a positive fraction of corrupted samples.
Zero-Shot Dialog Generation with Cross-Domain Latent Actions

This paper introduces zero-shot dialog generation (ZSDG), as a step towards neural dialog systems that can instantly generalize to new situations with minimum data. ZSDG requires an end-to-end generative dialog system to generalize to a new domain for which only a domain description is provided and no training dialogs are available. Then a novel learning framework, Action Matching, is proposed. This algorithm can learn a cross-domain embedding space that models the semantics of dialog responses which in turn, enables a neural dialog generation model to generalize to new domains. We evaluate our methods on two datasets, a new synthetic dialog dataset, and an existing human-human multi-domain dialog dataset. Experimental results show that our method is able to achieve superior performance in learning dialog models that can rapidly adapt their behavior to new domains and suggests promising future research.
Refined knot invariants and Hilbert schemes

Abstract We consider the construction of refined Chern–Simons torus knot invariants by M. Aganagic and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a proof of Cherednik's conjecture on the stabilization of superpolynomials, and then use the results of O. Schiffmann and E. Vasserot to relate knot invariants to the Hilbert scheme of points on C 2 . Then we use the methods of the second author to compute these invariants explicitly in the uncolored case. We also propose a conjecture relating these constructions to the rational Cherednik algebra, as in the work of the first author, A. Oblomkov, J. Rasmussen and V. Shende. Among the combinatorial consequences of this work is a statement of the m n shuffle conjecture.
Low-temperature phonoemissive tunneling rates in single molecule magnets

Abstract Tunneling between the two lowest energy levels of single molecule magnets with Ising type anisotropy, accompanied by the emission or absorption of phonons, is considered. Quantitatively accurate calculations of the rates for such tunneling are performed for a model Hamiltonian especially relevant to the best studied example, Fe8. Two different methods are used: high-order perturbation theory in the spin–phonon interaction and the non-Ising-symmetric parts of the spin Hamiltonian, and a novel semiclassical approach based on spin-coherent-state-path-integral instantons. The methods are found to be in good quantitative agreement with other, and consistent with previous approaches to the problem. The implications of these results for magnetization of molecular solids of these molecules are discussed briefly.
Learning without Recall: A Case for Log-Linear Learning

Abstract We analyze a model of learning and belief formation in networks in which agents follow Bayes rule yet they do not recall their history of past observations and cannot reason about how other agents’ beliefs are formed. They do so by making rational inferences about their observations which include a sequence of independent and identically distributed private signals as well as the beliefs of their neighboring agents at each time. Fully rational agents would successively apply Bayes rule to the entire history of observations. This leads to forebodingly complex inferences due to lack of knowledge about the global network structure that causes those observations. To address these complexities, we consider a “Learning without Recall” model, which in addition to providing a tractable framework for analyzing the behavior of rational agents in social networks, can also provide a behavioral foundation for the variety of non-Bayesian update rules in the literature. We present the implications of various choices for time-varying priors of such agents and how this choice affects learning and its rate.
Object Ordering with Bidirectional Matchings for Visual Reasoning

Visual reasoning with compositional natural language instructions, e.g., based on the newly-released Cornell Natural Language Visual Reasoning (NLVR) dataset, is a challenging task, where the model needs to have the ability to create an accurate mapping between the diverse phrases and the several objects placed in complex arrangements in the image. Further, this mapping needs to be processed to answer the question in the statement given the ordering and relationship of the objects across three similar images. In this paper, we propose a novel end-to-end neural model for the NLVR task, where we first use joint bidirectional attention to build a two-way conditioning between the visual information and the language phrases. Next, we use an RL-based pointer network to sort and process the varying number of unordered objects (so as to match the order of the statement phrases) in each of the three images and then pool over the three decisions. Our model achieves strong improvements (of 4-6% absolute) over the state-of-the-art on both the structured representation and raw image versions of the dataset.
Reflection statistics of weakly disordered optical medium when its mean refractive index is different from an outside medium

Abstract Statistical properties of light waves reflected from a one-dimensional (1D) disordered optical medium [ n(x) = n 0 + dn(x), =0 ] have been well studied, however, most of the studies have focused on the situation when the mean refractive index of the optical medium matched with the outside medium, i.e., n 0 = n out =1 . Further, considering dn ( x ) as a Gaussian color noise refractive index medium with exponential spatial correlation decay length l c and k as the incident wave vector, it has been shown that for smaller correlation length limit, i.e., kl c and std of r , σ(r) , have same value, and they follow the relation = σ(r) ∝ 2 > l c . However, when the refractive index of the sample medium is different from the outside medium, the reflection statistics may have interesting features, which has not been well studied or understood. We studied the reflection statistics of a 1D weakly disordered optical medium with the mean background refractive index n 0 being different from the outside medium n out (≠ n 0 ), to see the effect of mismatching (i.e., value of n 0 - n out ) on the reflection statistics. In the mismatched case, the results show that the mean reflection coefficient r> follows a form similar to that of the matched refractive-index case, i.e., c )>∝ 2 > l c , with a linear increased shift, which is due to 1D uniform background reflection from a slab. However, σ(r) is shown to be σ(r) ∝ ( 2 >l c ) 1/2 , which is different from the matched case. This change in std of r is attributed to the interference between the mismatched-crerated edge mediated multiple scattering that are coupled with the random scattering. Applications to light scattering from random layered media and biological cells are discussed.
The Hagedorn–Hermite Correspondence

We investigate the relationship between the semiclassical wave packets of Hagedorn and the Hermite functions by establishing a relationship between their ladder operators. This Hagedorn–Hermite correspondence provides a unified view as well as simple proofs of some essential results on the Hagedorn wave packets. Particularly, we show that Hagedorn’s ladder operators are a natural set of ladder operators obtained from the position and momentum operators using the symplectic group. This construction reveals an algebraic structure of the Hagedorn wave packets, and explains the relative simplicity of Hagedorn’s parametrization compared to the rather intricate construction of the generalized squeezed states. We apply our formulation to show the existence of minimal uncertainty products for the Hagedorn wave packets, generalizing Hagedorn’s one-dimensional result to multi-dimensions. The Hagedorn–Hermite correspondence also leads to an alternative derivation of the generating function for the Hagedorn wave packets based on the generating function for the Hermite functions. This result, in turn, reveals the relationship between the Hagedorn polynomials and the Hermite polynomials.
Exploiting negative curvature in deterministic and stochastic optimization

This paper addresses the question of whether it can be beneficial for an optimization algorithm to follow directions of negative curvature. Although prior work has established convergence results for algorithms that integrate both descent and negative curvature steps, there has not yet been extensive numerical evidence showing that such methods offer consistent performance improvements. In this paper, we present new frameworks for combining descent and negative curvature directions: alternating two-step approaches and dynamic step approaches. The aspect that distinguishes our approaches from ones previously proposed is that they make algorithmic decisions based on (estimated) upper-bounding models of the objective function. A consequence of this aspect is that our frameworks can, in theory, employ fixed stepsizes, which makes the methods readily translatable from deterministic to stochastic settings. For deterministic problems, we show that instances of our dynamic framework yield gains in performance compared to related methods that only follow descent steps. We also show that gains can be made in a stochastic setting in cases when a standard stochastic-gradient-type method might make slow progress.
A structure theorem for multiplicative functions over the Gaussian integers and applications

We prove a structure theorem for multiplicative functions on the Gaussian integers, showing that every bounded multiplicative function on the Gaussian integers can be decomposed into a term which is approximately periodic and another which has a small U3-Gowers uniformity norm. We apply this to prove partition regularity results over the Gaussian integers for certain equations involving quadratic forms in three variables. For example, we show that for any finite coloring of the Gaussian integers, there exist distinct nonzero elements x and y of the same color such that x2−y2 = n2 for some Gaussian integer n. The analog of this statement over Z remains open.
Localization for uniform algebras generated by real-analytic functions

It is shown that if $A$ is a uniform algebra generated by real-analytic functions on a suitable compact subset $K$ of a real-analytic variety such that the maximal ideal space of $A$ is $K$, and every continuous function on $K$ is locally a uniform limit of functions in $A$, then $A=C(K)$. This gives an affirmative answer to a special case of a question from the Proceedings of the Symposium on Function Algebras held at Tulane University in 1965.
Comments on: High-dimensional simultaneous inference with the bootstrap

The authors should be congratulated on their insightful article proposing forms of residual and paired bootstrap methodologies in the context of simultaneous testing in sparse and high-dimensional linear models. We appreciate the clear exposition of their work, and the effectiveness of the proposed method. The authors advocate for the bootstrap of a complete high-dimensional estimate rather than the linearized part of the test statistic. We appreciate the opportunity to comment on several aspects of this article.
Capacity Approximations for Gaussian Relay Networks

Consider a Gaussian relay network where a source node communicates to a destination node with the help of several layers of relays. Recent work has shown that compress-and-forward-based strategies can achieve the capacity of this network within an additive gap. Here, the relays quantize their received signals at the noise level and map them to random Gaussian codebooks. The resultant gap to capacity is independent of the SNRs of the channels in the network and the topology, but is linear in the total number of nodes. In this paper, we provide an improved lower bound on the rate achieved by the compress-and-forward-based strategies (noisy network coding in particular) in arbitrary Gaussian relay networks, whose gap to capacity depends on the network not only through the total number of nodes but also through the degrees of freedom of the min cut of the network. We illustrate that for many networks, this refined lower bound can lead to a better approximation of the capacity. In particular, we demonstrate that it leads to a logarithmic rather than linear capacity gap in the total number of nodes for certain classes of layered networks. The improvement comes from quantizing the received signals of the relays at a resolution decreasing with the total number of nodes in the network. This suggests that the rule-of-thumb in the literature of quantizing the received signals at the noise level can be highly suboptimal.
An ensemble method for interval-censored time-to-event data

Interval-censored data analysis is important in biomedical statistics for any type of time-to-event response where the time of response is not known exactly, but rather only known to occur between two assessment times. Many clinical trials and longitudinal studies generate interval-censored data; one common example occurs in medical studies that entail periodic follow-up. In this article, we propose a survival forest method for interval-censored data based on the conditional inference framework. We describe how this framework can be adapted to the situation of interval-censored data. We show that the tuning parameters have a non-negligible effect on the survival forest performance and guidance is provided on how to tune the parameters in a data-dependent way to improve the overall performance of the method. Using Monte Carlo simulations, we find that the proposed survival forest is at least as effective as a survival tree method when the underlying model has a tree structure, performs similarly to an interval-censored Cox proportional hazards model fit when the true relationship is linear, and outperforms the survival tree method and Cox model when the true relationship is nonlinear. We illustrate the application of the method on a tooth emergence data set.
Minimal representations of Lie algebras with non-trivial Levi decomposition

We obtain minimal dimension matrix representations for each of the Lie algebras of dimensions five, six, seven and eight obtained by Turkowski that have a non-trivial Levi decomposition. The key technique involves using the invariant subspaces associated to a particular representation of a semi-simple Lie algebra to help in the construction of the radical in the putative Levi decomposition. Open image in new window
Large‐Deviation Principle for Interacting Brownian Motions

We prove the large-deviation principle for the empirical process in a system of locally interacting Brownian motions in the nonequilibrium. Such a phenomenon has been proven only for two lattice systems: the symmetric simple exclusion process and the zero-range process. Therefore, we have achieved the third result in this context and moreover the first result for the diffusion-type interacting particle system.© 2016 Wiley Periodicals, Inc.
Toric codes and finite geometries

Abstract The theory of affine geometries over the rings Z / 〈 q − 1 〉 can be used to understand the properties of toric and generalized toric codes over F q . The standard generator matrices of these codes are produced by evaluating collections of monomials in m variables at the points of the algebraic torus ( F q ⁎ ) m . The exponent vector of such a monomial can be viewed as a point in one of these affine geometries and the minimum distance of the resulting code is strongly tied to the lines in the finite geometry that contain those points. We argue that this connection is, in fact, even more direct than the connection with the lattice geometry of those exponent vectors considered as elements of Z 2 or R 2 . This point of view should be useful both as a way to visualize properties of these codes and as a guide to heuristic searches for good codes constructed in this fashion. In particular, we will use these ideas to see a reason why these constructions have been so successful over the field F 8 , but less successful in other cases.
ON CHARACTERISTIC INTEGRALS OF TODA FIELD THEORIES

Characteristic integrals of Toda field theories associated to general simple Lie algebras are constructed using systematic techniques, and complete mathematical proofs are provided. Plenty of examples illustrating the results are presented in explicit forms.
APX-Hardness of Maximizing Nash Social Welfare with Indivisible Items

Abstract We study the problem of allocating a set of indivisible items to agents with additive utilities to maximize the Nash social welfare. Cole and Gkatzelis [5] recently proved that this problem admits a constant factor approximation. We complement their result by showing that this problem is APX-hard.
Background field method and nonrelativistic QED matching

We discuss the resolution of an inconsistency between lattice background field methods and nonrelativistic QED matching conditions. In particular, we show that lack of on-shell conditions in lattice QCD with time-dependent background fields generally requires that certain operators related by equations of motion should be retained in an effective field theory to correctly describe the behavior of Green’s functions. The coefficients of such operators in a nonrelativistic hadronic theory are determined by performing a robust nonrelativistic expansion of QED for relativistic scalar and spin-half hadrons including nonminimal electromagnetic couplings. Provided that nonrelativistic QED is augmented with equation-of-motion operators, we find that the background field method can be reconciled with the nonrelativistic QED matching conditions without any inconsistency. We further investigate whether nonrelativistic QED can be employed in the analysis of lattice QCD correlation function in background fields, but we are confronted with difficulties. Instead, we argue that the most desirable approach is a hybrid one which relies on a relativistic hadronic theory with operators chosen based on their relevance in the nonrelativistic limit. Using this hybrid framework, we obtain practically useful forms of correlation functions for scalar and spin-half hadrons in uniform electric and magnetic fields.
The strong AJ conjecture for cables of torus knots

The AJ conjecture, formulated by Garoufalidis, relates the A-polynomial and the colored Jones polynomial of a knot in the 3-sphere. It has been confirmed for all torus knots, some classes of two-bridge knots and pretzel knots, and most cable knots over torus knots. The strong AJ conjecture, formulated by Sikora, relates the A-ideal and the colored Jones polynomial of a knot. It was confirmed for all torus knots. In this paper we confirm the strong AJ conjecture for most cable knots over torus knots.
Transfer learning from deep features for remote sensing and poverty mapping

The lack of reliable data in developing countries is a major obstacle to sustainable development, food security, and disaster relief. Poverty data, for example, is typically scarce, sparse in coverage, and labor-intensive to obtain. Remote sensing data such as high-resolution satellite imagery, on the other hand, is becoming increasingly available and inexpensive. Unfortunately, such data is highly unstructured and currently no techniques exist to automatically extract useful insights to inform policy decisions and help direct humanitarian efforts. We propose a novel machine learning approach to extract large-scale socioeconomic indicators from high-resolution satellite imagery. The main challenge is that training data is very scarce, making it difficult to apply modern techniques such as Convolutional Neural Networks (CNN). We therefore propose a transfer learning approach where nighttime light intensities are used as a data-rich proxy. We train a fully convolutional CNN model to predict nighttime lights from daytime imagery, simultaneously learning features that are useful for poverty prediction. The model learns filters identifying different terrains and man-made structures, including roads, buildings, and farmlands, without any supervision beyond nighttime lights. We demonstrate that these learned features are highly informative for poverty mapping, even approaching the predictive performance of survey data collected in the field.
Lassoing line outages in the smart power grid

Fast and accurate unveiling of power line outages is of paramount importance not only for preventing faults that may lead to blackouts, but also for routine monitoring and control tasks of the smart grid, including state estimation and optimal power flow. Existing approaches are either challenged by the combinatorial complexity issues involved, and are thus limited to identifying single- and double-line outages; or, they invoke less pragmatic assumptions such as conditionally independent phasor angle measurements available across the grid. Using only a subset of voltage phasor angle data, the present paper develops a near real-time algorithm for identifying multiple line outages at the affordable complexity of solving a quadratic program via block coordinate descent iterations. The novel approach relies on reformulating the DC linear power flow model as a sparse overcomplete expansion, and leveraging contemporary advances in compressive sampling and variable selection using the least-absolute shrinkage and selection operator (Lasso). Analysis and simulated tests on the standard IEEE 118-bus system confirm the effectiveness of lassoing line changes in the smart power grid.
Deep reinforcement learning: framework, applications, and embedded implementations

The recent breakthroughs of deep reinforcement learning (DRL) technique in Alpha Go and playing Atari have set a good example in handling large state and actions spaces of complicated control problems. The DRL technique is comprised of (i) an offline deep neural network (DNN) construction phase, which derives the correlation between each state-action pair of the system and its value function, and (ii) an online deep Q-learning phase, which adaptively derives the optimal action and updates value estimates.In this paper, we first present the general DRL framework, which can be widely utilized in many applications with different optimization objectives. This is followed by the introduction of three specific applications: the cloud computing resource allocation problem, the residential smart grid task scheduling problem, and building HVAC system optimal control problem. The effectiveness of the DRL technique in these three cyber-physical applications have been validated. Finally, this paper investigates the stochastic computing-based hardware implementations of the DRL framework, which consumes a significant improvement in area efficiency and power consumption compared with binary-based implementation counterparts.
Dynamical Isometry and a Mean Field Theory of RNNs: Gating Enables Signal Propagation in Recurrent Neural Networks

Recurrent neural networks have gained widespread use in modeling sequence data across various domains. While many successful recurrent architectures employ a notion of gating, the exact mechanism that enables such remarkable performance is not well understood. We develop a theory for signal propagation in recurrent networks after random initialization using a combination of mean field theory and random matrix theory. To simplify our discussion, we introduce a new RNN cell with a simple gating mechanism that we call the minimalRNN and compare it with vanilla RNNs. Our theory allows us to define a maximum timescale over which RNNs can remember an input. We show that this theory predicts trainability for both recurrent architectures. We show that gated recurrent networks feature a much broader, more robust, trainable region than vanilla RNNs, which corroborates recent experimental findings. Finally, we develop a closed-form critical initialization scheme that achieves dynamical isometry in both vanilla RNNs and minimalRNNs. We show that this results in significantly improvement in training dynamics. Finally, we demonstrate that the minimalRNN achieves comparable performance to its more complex counterparts, such as LSTMs or GRUs, on a language modeling task.
Harnessing Deep Neural Networks with Logic Rules

Combining deep neural networks with structured logic rules is desirable to harness flexibility and reduce uninterpretability of the neural models. We propose a general framework capable of enhancing various types of neural networks (e.g., CNNs and RNNs) with declarative first-order logic rules. Specifically, we develop an iterative distillation method that transfers the structured information of logic rules into the weights of neural networks. We deploy the framework on a CNN for sentiment analysis, and an RNN for named entity recognition. With a few highly intuitive rules, we obtain substantial improvements and achieve state-of-the-art or comparable results to previous best-performing systems.
Log-concave polynomials II: high-dimensional walks and an FPRAS for counting bases of a matroid

We design an FPRAS to count the number of bases of any matroid given by an independent set oracle, and to estimate the partition function of the random cluster model of any matroid in the regime where 0
W*–superrigidity for Bernoulli actions of property (T) groups

We consider group measure space ∥_1 factors M = L^(∞)(X) ⋊ Γ arising from Bernoulli actions of ICC property (T) groups Γ (more generally, of groups Γ containing an infinite normal subgroup with the relative property (T)) and prove a rigidity result for *-homomorphisms Θ: → M⊗(overbar)M We deduce that the action Γ ↷ X is W^*-superrigid, i.e. if Γ ↷ Y is any free, ergodic, measure preserving action such that the factors M = L^(∞)(X) ⋊ Γ and M =L^(∞)(Y) ⋊ Γ are isomorphic, then the actions Γ ↷ X and Γ ↷ Y must be conjugate. Moreover, we show that if p ∈ M\{1} is a projection, then pMp does not admit a group measure space decomposition nor a group von Neumann algebra decomposition (the latter under the additional assumption that Γ is torsion free). We also prove a rigidity result for *-homomorphisms Θ: M → M this time for Γ in a larger class of groups than above, now including products of non-amenable groups. For certain groups Γ, e.g. Γ = F_2 × F_2 we deduce that M does not embed into pMp, for any projection p ∈ M\{1}, and obtain a description of the endomorphism semigroup of M.
Some Probabilistic Trees with Algebraic Roots

We consider several probabilistic processes defining a random graph. One of these processes appeared recently in connection with a factorization problem in the symmetric group. For each process, we prove that the probability for the random graph to be a tree has an unexpectedly simple expression, which is independent of most parameters of the problem. This raises many open questions.
A representation theoretic characterization of simple closed curves on a surface

We produce a sequence of finite dimensional representations of the fundamental group $\pi_1(S)$ of a closed surface where all simple closed curves act with finite order, but where each non--simple closed curve eventually acts with infinite order. As a consequence, we obtain a representation theoretic algorithm which decides whether or not a given element of $\pi_1(S)$ is freely homotopic to a simple closed curve. The construction of these representations combines ideas from TQFT representations of mapping class groups with effective versions of LERF for surface groups.
Question Type Guided Attention in Visual Question Answering

Visual Question Answering (VQA) requires integration of feature maps with drastically different structures. Image descriptors have structures at multiple spatial scales, while lexical inputs inherently follow a temporal sequence and naturally cluster into semantically different question types. A lot of previous works use complex models to extract feature representations but neglect to use high-level information summary such as question types in learning. In this work, we propose Question Type-guided Attention (QTA). It utilizes the information of question type to dynamically balance between bottom-up and top-down visual features, respectively extracted from ResNet and Faster R-CNN networks. We experiment with multiple VQA architectures with extensive input ablation studies over the TDIUC dataset and show that QTA systematically improves the performance by more than 5% across multiple question type categories such as “Activity Recognition”, “Utility” and “Counting” on TDIUC dataset compared to the state-of-art. By adding QTA on the state-of-art model MCB, we achieve 3% improvement in overall accuracy. Finally, we propose a multi-task extension to predict question types which generalizes QTA to applications that lack question type, with a minimal performance loss.
The Degree of the Dormant Operatic Locus

Let $X$ be a smooth, projective curve of genus $g\geq 2$ over an algebraically closed field of characteristic $p>0$. I provide a conjectural formula for the degree of the scheme of dormant ${\rm PGL}(r)$-opers on $X$ where $r\geq 2$ (I assume that $p$ is greater than an explicit constant depending on $g,r$). For $r=2$ a dormant ${\rm PGL}(2)$-oper is a dormant indigenous bundle on $X$ in the sense of Shinichi Mochuzki (and his work provides a formula only for $g=2,r=2,p\geq 5$, from a different point of view). Recently Yasuhiro Wakabayashi has shown that my conjectural formula holds for $X$ generic, $r\geq 2$ and $p$ large.
A simple characterization of Du Bois singularities

We prove the following theorem characterizing Du Bois singular- ities. Suppose that Y is smooth and that X is a reduced closed subscheme. Let � : e Y ! Y be a log resolution of X in Y that is an isomorphism outside of X. If E is the reduced pre-image of X in e Y , then X has Du Bois singularities if and only if the natural map OX ! R��OE is a quasi-isomorphism. We also deduce Kollar's conjecture that log canonical singularities are Du Bois in the special case of a local complete intersection and prove other results related to adjunction. 1. Introduction and Background In this paper, we prove a simple new characterization of Du Bois singularities. Inspired by this characterization, we deduce several new theorems, including results related to adjunction, and progress towards a conjecture of Kollar. Du Bois singularities were initially defined by Steenbrink as a setting where certain aspects of Hodge theory for smooth varieties still hold; see (Ste81a), (Ste81b) and (DB81). They are defined by the cohomology of a complex which is difficult to understand since it requires the computation of resolutions of singularities for several varieties (specifically a simplicial or cubic hyperresolution is required; see (Del74), (GNPP88), or (Car85)). Our new characterization of Du Bois singularities requires only a single resolution. Our main result is:
Supercongruences and complex multiplication

Abstract We study congruences involving truncated hypergeometric series of the form F 2 3 ( 1 / 2 , 1 / 2 , 1 / 2 1 , 1 ; λ ) ( m p s − 1 ) / 2 : = ∑ k = 0 ( m p s − 1 ) / 2 ( ( 1 / 2 ) k / k ! ) 3 λ k where p is a prime and m , s are positive integers. These truncated hypergeometric series are related to the arithmetic of a family of K3 surfaces. For special values of λ, with s = 1 , our congruences are stronger than those predicted by the theory of formal groups, because of the presence of elliptic curves with complex multiplications. They generalize a conjecture made by Stienstra and Beukers for the λ = 1 case and confirm some other supercongruence conjectures at special values of λ.
Optimal (t,r) broadcasts on the infinite grid

Abstract Let G = ( V , E ) be a graph and t , r be positive integers. The reception strength (or signal) that a vertex v receives from a tower of signal strength t located at vertex T is defined as s i g ( v , T ) = m a x ( t − d i s t ( v , T ) , 0 ) , where d i s t ( v , T ) denotes the distance between the vertices v and T . In 2015 Blessing, Insko, Johnson, and Mauretour defined a ( t , r ) broadcast dominating set, or simply a ( t , r ) broadcast, on G as a set T ⊆ V such that the sum of all signals received at each vertex v ∈ V is at least r . We say that T is optimal if | T | is minimal among all such sets T . The cardinality of an optimal ( t , r ) broadcast on a finite graph G is called the ( t , r ) broadcast domination number of G . The concept of ( t , r ) broadcast domination generalizes the classical problem of domination on graphs. In fact, the ( 2 , 1 ) broadcasts on a graph G are exactly the dominating sets of G . In their paper, Blessing et al. considered ( t , r ) ∈ { ( 2 , 2 ) , ( 3 , 1 ) , ( 3 , 2 ) , ( 3 , 3 ) } and gave optimal ( t , r ) broadcasts on G m , n , the grid graph of dimension m × n , for small values of m and n . They also provided upper bounds on the optimal ( t , r ) broadcast numbers for grid graphs of arbitrary dimensions. In this paper, we define the density of a ( t , r ) broadcast, which allows us to provide optimal ( t , r ) broadcasts on the infinite grid graph for all t ≥ 2 and r = 1 , 2 , and bound the density of the optimal ( t , 3 ) broadcast for all t ≥ 2 . In addition, we present a Python program to compute upper bounds on the density of a minimal ( t , r ) broadcast on the infinite grid, and compute these bounds for all 1 ≤ t ≤ 15 and 1 ≤ r ≤ 40 . Lastly, we construct a family of counterexamples to the conjecture of Blessing et al. that the optimal ( t , r ) and ( t + 1 , r + 2 ) broadcasts are identical for all t ≥ 1 and r ≥ 1 on the infinite grid.
Can Disorder Enhance Incoherent Exciton Diffusion

Recent experiments aimed at probing the dynamics of excitons have revealed that semiconducting films composed of disordered molecular subunits, unlike expectations for their perfectly ordered counterparts, can exhibit a time-dependent diffusivity in which the effective early time diffusion constant is larger than that of the steady state. This observation has led to speculation about what role, if any, microscopic disorder may play in enhancing exciton transport properties. In this article, we present the results of a model study aimed at addressing this point. Specifically, we introduce a general model, based upon Forster theory, for incoherent exciton diffusion in a material composed of independent molecular subunits with static energetic disorder. Energetic disorder leads to heterogeneity in molecule-to-molecule transition rates, which we demonstrate has two important consequences related to exciton transport. First, the distribution of local site-specific hopping rates is broadened in a manner that re...
Precoding by Priority: A UEP scheme for RaptorQ codes.

Raptor codes are the first class of fountain codes with linear time encoding and decoding. These codes are recommended in standards such as Third Generation Partnership Project (3GPP) and digital video broadcasting. RaptorQ codes are an extension to Raptor codes, having better coding efficiency and flexibility. Standard Raptor and RaptorQ codes are systematic with equal error protection of the data. However, in many applications such as MPEG transmission, there is a need for Unequal Error Protection (UEP): namely, some data symbols require higher error correction capabilities compared to others. We propose an approach that we call Priority Based Precode Ratio (PBPR) to achieve UEP for systematic RaptorQ and Raptor codes. Our UEP assumes that all symbols in a source block belong to the same importance class. The UEP is achieved by changing the number of precode symbols depending on the priority of the information symbols in the source block. PBPR provides UEP with the same number of decoding overhead symbols for source blocks with different importance classes. We demonstrate consistent improvements in the error correction capability of higher importance class compared to the lower importance class across the entire range of channel erasure probabilities. We also show that PBPR does not result in a significant increase in decoding and encoding times compared to the standard implementation.
On near-cloak in acoustic scattering

Abstract Invisibility cloaking in acoustic scattering via the approach of transformation optics is considered. The near-cloaks of both passive medium and active/radiating object are investigated. From a practical viewpoint, we are especially interested in the cloaking of an arbitrary (but regular) content. It is shown that one cannot achieve the near-cloak unless some special mechanism is introduced into the construction. A general lossy layer is incorporated into the construction of our near-cloaking devices. We derive very accurate estimates of the scattering amplitude in terms of the regularization parameter and the material parameters of the lossy layer in different settings.
Mechanism Design for Demand Response Programs

Demand response (DR) programs serve to reduce the consumption of electricity at times when the supply is scarce and expensive. Consumers or agents with flexible consumption profiles are recruited by an aggregator who manages the DR program. The aggregator calls on a subset of its pool of recruited agents to reduce their electricity use during DR events. Agents are paid for reducing their energy consumption from contractually established baselines. Baselines are counter-factual consumption estimates of the energy an agent would have consumed if they were not participating in the DR program. Baselines are used to determine payments to agents. This creates an incentive for agents to inflate their baselines in order to increase the payments they receive. There are several newsworthy cases of agents gaming their baseline for economic benefit. We propose a novel self-reported baseline mechanism (SRBM) where each agent reports its baseline and marginal utility. These reports are strategic and need not be truthful. Based on the reported information, the aggregator selects or calls on agents with a certain probability to meet the load reduction target. Called agents are paid for observed reductions from their self-reported baselines. Agents who are not called face penalties for consumption shortfalls below their baselines. Under SRBM, we show that truthful reporting of baseline consumption and marginal utility is a dominant strategy. Thus, SRBM eliminates the incentive for agents to inflate baselines. SRBM is assured to meet the load reduction target. Finally, we show that SRBM is almost optimal in the metric of average cost of DR provision faced by the aggregator.
A First Step Toward Higher Order Chain Rules in Abelian Functor Calculus

One of the fundamental tools of undergraduate calculus is the chain rule. The notion of higher order directional derivatives was developed by Huang, Marcantognini, Young in Huang et al. (Math. Intell. 28(2):61–69, 2006), along with a corresponding higher order chain rule. When Johnson and McCarthy established abelian functor calculus, they proved a chain rule for functors that is analogous to the directional derivative chain rule when n = 1. In joint work with Bauer, Johnson, and Riehl, we defined an analogue of the iterated directional derivative and provided an inductive proof of the analogue to the chain rule of Huang et al.
Distant Supervision for Relation Extraction beyond the Sentence Boundary

The growing demand for structured knowledge has led to great interest in relation extraction, especially in cases with limited supervision. However, existing distance supervision approaches only extract relations expressed in single sentences. In general, cross-sentence relation extraction is under-explored, even in the supervised-learning setting. In this paper, we propose the first approach for applying distant supervision to cross-sentence relation extraction. At the core of our approach is a graph representation that can incorporate both standard dependencies and discourse relations, thus providing a unifying way to model relations within and across sentences. We extract features from multiple paths in this graph, increasing accuracy and robustness when confronted with linguistic variation and analysis error. Experiments on an important extraction task for precision medicine show that our approach can learn an accurate cross-sentence extractor, using only a small existing knowledge base and unlabeled text from biomedical research articles. Compared to the existing distant supervision paradigm, our approach extracted twice as many relations at similar precision, thus demonstrating the prevalence of cross-sentence relations and the promise of our approach.