cssi/SciSciGPT-SciSciNet huggingface dataset:
Learning rich geographical representations: Predicting colorectal cancer survival in the state of Iowa

Neural networks are capable of learning rich, nonlinear feature representations shown to be beneficial in many predictive tasks. In this work, we use these models to explore the use of geographical features in predicting colorectal cancer survival curves for patients in the state of Iowa, spanning the years 1989 to 2013. Specifically, we compare model performance using a newly defined metric – area between the curves (ABC) – to assess (a) whether survival curves can be reasonably predicted for colorectal cancer patients in the state of Iowa, (b) whether geographical features improve predictive performance, and (c) whether a simple binary representation or richer, spectral clustering-based representation perform better. Our findings suggest that survival curves can be reasonably estimated on average, with predictive performance deviating at the five-year survival mark. We also find that geographical features improve predictive performance, and that the best performance is obtained using richer, spectral analysis-elicited features.
Scheduling Resources for Executing a Partial Set of Jobs

In this paper, we consider the problem of choosing a minimum cost set of resources for executing a specified set of jobs. Each input job is an interval, determined by its start-time and end-time. Each resource is also an interval determined by its start-time and end-time; moreover, every resource has a capacity and a cost associated with it. We consider two versions of this problem. In the partial covering version, we are also given as input a number k, specifying the number of jobs that must be performed. The goal is to choose $k$ jobs and find a minimum cost set of resources to perform the chosen k jobs (at any point of time the capacity of the chosen set of resources should be sufficient to execute the jobs active at that time). We present an O(log n)-factor approximation algorithm for this problem. We also consider the prize collecting version, wherein every job also has a penalty associated with it. The feasible solution consists of a subset of the jobs, and a set of resources, to perform the chosen subset of jobs. The goal is to find a feasible solution that minimizes the sum of the costs of the selected resources and the penalties of the jobs that are not selected. We present a constant factor approximation algorithm for this problem.
Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the system when the distributions of some variables are known exactly, others are known only approximately, and perhaps others are not modeled as random variables at all. The main tool used is the duality between risk-sensitive integrals and relative entropy, and we obtain explicit bounds on standard performance measures (variances, exceedance probabilities) over families of distributions whose distance from a nominal distribution is measured by relative entropy. The evaluation of the risk-sensitive expectations is based on polynomial chaos expansions, which help keep the computational aspects tractable.
Modularity lifting beyond the Taylor–Wiles method

We prove new modularity lifting theorems for p-adic Galois representations in situations where the methods of Wiles and Taylor–Wiles do not apply. Previous generalizations of these methods have been restricted to situations where the automorphic forms in question contribute to a single degree of cohomology. In practice, this imposes several restrictions—one must be in a Shimura variety setting and the automorphic forms must be of regular weight at infinity. In this paper, we essentially show how to remove these restrictions. Our most general result is a modularity lifting theorem which, on the automorphic side, applies to automorphic forms on the group $$\mathrm {GL}(n)$$ over a general number field; it is contingent on a conjecture which, in particular, predicts the existence of Galois representations associated to torsion classes in the cohomology of the associated locally symmetric space. We show that if this conjecture holds, then our main theorem implies the following: if E is an elliptic curve over an arbitrary number field, then E is potentially automorphic and satisfies the Sato–Tate conjecture. In addition, we also prove some unconditional results. For example, in the setting of $$\mathrm {GL}(2)$$ over $$\mathbf {Q}$$ , we identify certain minimal global deformation rings with the Hecke algebras acting on spaces of p-adic Katz modular forms of weight 1. Such algebras may well contain p-torsion. Moreover, we also completely solve the problem (for p odd) of determining the multiplicity of an irreducible modular representation $$\overline{\rho }$$ in the Jacobian $$J_1(N)$$ , where N is the minimal level such that $$\overline{\rho }$$ arises in weight two.
CYP2B6 Genotype-Dependent Inhibition of CYP1A2 and Induction of CYP2A6 by the Antiretroviral Drug Efavirenz in Healthy Volunteers.

We investigated the effect of efavirenz on the activities of cytochrome P450 (CYP)1A2, CYP2A6, xanthine oxidase (XO), and N-acetyltransferase 2 (NAT2), using caffeine as a probe. A single 150 mg oral dose of caffeine was administered to healthy volunteers (n = 58) on two separate occasions; with a single 600 mg oral dose of efavirenz and after treatment with 600 mg/day efavirenz for 17 days. Caffeine and its metabolites in plasma and urine were quantified using liquid chromatography/tandem-mass spectrometry. DNA was genotyped for CYP2B6*4 (785A>G), CYP2B6*9 (516G>T), and CYP2B6*18 (983T>C) alleles using TaqMan assays. Relative to single-dose efavirenz treatment, multiple doses of efavirenz decreased CYP1A2 (by 38%) and increased CYP2A6 (by 85%) activities (P < 0.05); XO and NAT2 activities were unaffected. CYP2B6*6*6 genotype was associated with lower CYP1A2 activity following both single and multiple doses of efavirenz. No similar association was noted for CYP2A6 activity. This is the first report showing that efavirenz reduces hepatic CYP1A2 and suggesting chronic efavirenz exposure likely enhances the elimination of CYP2A6 substrates. This is also the first to report the extent of efavirenz-CYP1A2 interaction may be efavirenz exposure-dependent and CYP2B6 genotype-dependent.
Persistent homology of attractors for action recognition

In this paper, we propose a novel framework for dynamical analysis of human actions from 3D motion capture data using topological data analysis. We model human actions using the topological features of the attractor of the dynamical system. We reconstruct the phase-space of time series corresponding to actions using time-delay embedding, and compute the persistent homology of the phase-space reconstruction. In order to better represent the topological properties of the phase-space, we incorporate the temporal adjacency information when computing the homology groups. The persistence of these homology groups encoded using persistence diagrams are used as features for the actions. Our experiments with action recognition using these features demonstrate that the proposed approach outperforms other baseline methods.
Statistical Inference Using SGD

We present a novel method for frequentist statistical inference in M-estimation problems, based on stochastic gradient descent (SGD) with a fixed step size: we demonstrate that the average of such SGD sequences can be used for statistical inference, after proper scaling. An intuitive analysis using the Ornstein-Uhlenbeck process suggests that such averages are asymptotically normal. To show the merits of our scheme, we apply it to both synthetic and real data sets, and demonstrate that its accuracy is comparable to classical statistical methods, while requiring potentially far less computation.
Vaccines, contagion, and social networks

Consider the causal effect that one individual’s treatment may have on another individual’s outcome when the outcome is contagious, with specific application to the effect of vaccination on an infectious disease outcome. The effect of one individual’s vaccination on another’s outcome can be decomposed into two different causal effects, called the “infectiousness” and “contagion” effects. We present identifying assumptions and estimation or testing procedures for infectiousness and contagion effects in two different settings: (1) using data sampled from independent groups of observations, and (2) using data collected from a single interdependent social network. The methods that we propose for social network data require fitting generalized linear models (GLMs). GLMs and other statistical models that require independence across subjects have been used widely to estimate causal effects in social network data, but, because the subjects in networks are presumably not independent, the use of such models is generally invalid, resulting in inference that is expected to be anticonservative. We introduce a way to ensure that GLM residuals are uncorrelated across subjects despite the fact that outcomes are non-independent. This simultaneously demonstrates the possibility of using GLMs and related statistical models for network data and highlights their limitations.
Uncovering hidden macromolecular dynamics with Modulated Orientation Sensitive Terahertz Spectroscopy

We introduce Modulated Orientation Sensitive Terahertz Spectroscopy (MOSTS) that can both increase contrast between adjacent modes and remove the broad band librational background to allow mode identification for large macro molecules such as proteins.
Measures of maximal entropy for suspension flows over the full shift

We consider suspension flows with continuous roof function over the full shift $$\Sigma $$ on a finite alphabet. For any positive entropy subshift of finite type $$Y \subset \Sigma $$, we explicitly construct a roof function such that the measure(s) of maximal entropy for the suspension flow over $$\Sigma $$ are exactly the lifts of the measure(s) of maximal entropy for Y. In the case when Y is transitive, this gives a unique measure of maximal entropy for the flow which is not fully supported. If Y has more than one transitive component, all with the same entropy, this gives explicit examples of suspension flows over the full shift with multiple measures of maximal entropy. This contrasts with the case of a Holder continuous roof function where it is well known the measure of maximal entropy is unique and fully supported.
Generate tensor network state by sequential single-photon scattering in waveguide QED systems

We propose a scheme to generate photonic tensor network states by sequential scattering of photons in waveguide QED systems. We show that sequential scatterings can convert a series of unentangled photons into any type of matrix product states. We also demonstrate the possibility of generating projected entangled pair states with an arbitrary graph structure by photon re-scattering.We propose a scheme to generate photonic tensor network states by sequential scattering of photons in waveguide QED systems. We show that sequential scatterings can convert a series of unentangled photons into any type of matrix product states. We also demonstrate the possibility of generating projected entangled pair states with an arbitrary graph structure by photon re-scattering.
Secondary Spectrum Auctions for Markets With Communication Constraints

Wireless spectrum sharing techniques have become very important due to the increasing demand for spectrum. Hence, there is growing interest in using real-time auctions for economically incentivizing users to share their excess spectrum. However, the communication and control requirements of real-time secondary spectrum auctions would be overwhelming for wireless networks. Prior literature has not considered critical communication constraints such as bid price quantization and error prone bid revelation. These schemes also have high overheads which cannot be accommodated in wireless standards. We propose auction schemes where a central clearing authority auctions spectrum to bidders, while explicitly accounting for these communication constraints. Our techniques are related to the posterior matching scheme, which is used in systems with channel output feedback. We consider several scenarios where the clearing authority’s objective is to award spectrum to bidders who value spectrum the most. We prove that this objective is asymptotically attained by our scheme when bidders are nonstrategic with constant bids. We propose separate schemes to make strategic users reveal their private values truthfully, auction multiple subchannels among strategic users, and track slowly time-varying bid prices. We provide extensive simulation results to illustrate the performance and effectiveness of our algorithms.
Traces of Hypergraphs

Let $\text{Tr}(n,m,k)$ denote the largest number of distinct projections onto $k$ coordinates guaranteed in any family of $m$ binary vectors of length $n$. The classical Sauer-Perles-Shelah Lemma implies that $\text{Tr}(n, n^r, k) = 2^k$ for $k \le r$. While determining $\text{Tr}(n,n^r,k)$ precisely for general $k$ seems hopeless even for constant $r$, estimating it, and more generally estimating the function $\text{Tr}(n,m,k)$ for all range of the parameters, remains a widely open problem with connections to important questions in computer science and combinatorics. Here we essentially resolve this problem when $k$ is linear and $m=n^r$ where $r$ is constant, proving that, for any constant $\alpha>0$, $\text{Tr}(n,n^r,\alpha n) = \tilde\Theta(n^C)$ with $C=C(r,\alpha)=\frac{r+1-\log(1+\alpha)}{2-\log(1+\alpha)}$. For the proof we establish a "sparse" version of another classical result, the Kruskal-Katona Theorem, which gives a stronger guarantee when the hypergraph does not induce dense sub-hypergraphs. Furthermore, we prove that the parameters in our sparse Kruskal-Katona theorem are essentially best possible. Finally, we mention two simple applications which may be of independent interest.
Finite atomic lattices and resolutions of monomial ideals

Abstract In this paper we primarily study monomial ideals and their minimal free resolutions by studying their associated lcm-lattices. In particular, we formally define the notion of coordinatizing a finite atomic lattice P to produce a monomial ideal whose lcm-lattice is P, and we give a characterization of all such coordinatizations. We prove that all relations in the lattice L ( n ) of all finite atomic lattices with n ordered atoms can be realized as deformations of exponents of monomial ideals. We also give structural results for L ( n ) . Moreover, we prove that the cellular structure of a minimal free resolution of a monomial ideal M can be extended to minimal resolutions of certain monomial ideals whose lcm-lattices are greater than that of M in L ( n ) .
Semi-Supervised Learning for Neural Keyphrase Generation

We study the problem of generating keyphrases that summarize the key points for a given document. While sequence-to-sequence (seq2seq) models have achieved remarkable performance on this task (Meng et al., 2017), model training often relies on large amounts of labeled data, which is only applicable to resource-rich domains. In this paper, we propose semi-supervised keyphrase generation methods by leveraging both labeled data and large-scale unlabeled samples for learning. Two strategies are proposed. First, unlabeled documents are first tagged with synthetic keyphrases obtained from unsupervised keyphrase extraction methods or a self-learning algorithm, and then combined with labeled samples for training. Furthermore, we investigate a multi-task learning framework to jointly learn to generate keyphrases as well as the titles of the articles. Experimental results show that our semi-supervised learning-based methods outperform a state-of-the-art model trained with labeled data only.
Two steps to obfuscation

Abstract This note addresses the historical antecedents of the 1998 PageRank measure of centrality. An identity relation links it to the 1990–1991 models of Friedkin and Johnsen.
A description of the logmodular subalgebras in the finite-dimensional $C^*$-algebras

We show that every logmodular subalgebra of $M_n(\mathbb{C})$ is unitary equivalent to an algebra of block upper triangular matrices, which was conjectured in \cite{VM}. In particular, this shows that every unital contractive representation of a logmodular subalgebra of $M_n(\mathbb{C})$ is automatically completely contractive.
On the direct summand conjecture and its derived variant

Andre recently gave a beautiful proof of Hochster’s direct summand conjecture in commutative algebra using perfectoid spaces; his two main results are a generalization of the almost purity theorem (the perfectoid Abhyankar lemma) and a construction of certain faithfully flat extensions of perfectoid algebras where “discriminants” acquire all p-power roots. In this paper, we explain a quicker proof of Hochster’s conjecture that circumvents the perfectoid Abhyankar lemma; instead, we prove and use a quantitative form of Scholze’s Hebbarkeitssatz (the Riemann extension theorem) for perfectoid spaces. The same idea also leads to a proof of a derived variant of the direct summand conjecture put forth by de Jong.
Learning to Segment via Cut-and-Paste

This paper presents a weakly-supervised approach to object instance segmentation. Starting with known or predicted object bounding boxes, we learn object masks by playing a game of cut-and-paste in an adversarial learning setup. A mask generator takes a detection box and Faster R-CNN features, and constructs a segmentation mask that is used to cut-and-paste the object into a new image location. The discriminator tries to distinguish between real objects, and those cut and pasted via the generator, giving a learning signal that leads to improved object masks. We verify our method experimentally using Cityscapes, COCO, and aerial image datasets, learning to segment objects without ever having seen a mask in training. Our method exceeds the performance of existing weakly supervised methods, without requiring hand-tuned segment proposals, and reaches \(90\%\) of supervised performance.
Structure on the set of closure operations of a commutative ring

Abstract We investigate the algebraic structure on the set of closure operations of a ring. We show the set of closure operations is not a monoid under composition for a discrete valuation ring. Even the set of semiprime operations over a DVR is not a monoid; however, it is the union of two monoids, one being the left but not right act of the other. We also determine all semiprime operations over the ring K 〚 t 2 , t 3 〛 .
The Hilbert’s-Tenth-Problem Operator

For a ring R, Hilbert’s Tenth Problem HTP(R) is the set of polynomial equations over R, in several variables, with solutions in R. We view HTP as an operator, mapping each set W of prime numbers to HTP(ℤ[W−1]), which is naturally viewed as a set of polynomials in ℤ[X1, X2,…]. For W = O, it is a famous result of Matijasevic, Davis, Putnam and Robinson that the jump O′ is Turing-equivalent to HTP(ℤ). More generally, HTP(ℤ[W−1]) is always Turing-reducible to W′, but not necessarily equivalent. We show here that the situation with W = O is anomalous: for almost all W, the jump W′ is not diophantine in HTP(ℤ[W−1]). We also show that the HTP operator does not preserve Turing equivalence: even for complementary sets U and $$\bar U$$ , HTP(ℤ[U−1]) and $$HTP(\mathbb{Z}{[\bar U]^{ - 1}})$$ can differ by a full jump. Strikingly, reversals are also possible, with V <TW but HTP(ℤ[W−1]) <THTP(ℤ[V−1]).
Algorithms with logarithmic or sublinear regret for constrained contextual bandits

We study contextual bandits with budget and time constraints, referred to as constrained contextual bandits. The time and budget constraints significantly complicate the exploration and exploitation tradeoff because they introduce complex coupling among contexts over time. To gain insight, we first study unit-cost systems with known context distribution. When the expected rewards are known, we develop an approximation of the oracle, referred to Adaptive-Linear-Programming (ALP), which achieves near-optimality and only requires the ordering of expected rewards. With these highly desirable features, we then combine ALP with the upper-confidence-bound (UCB) method in the general case where the expected rewards are unknown a priori. We show that the proposed UCB-ALP algorithm achieves logarithmic regret except for certain boundary cases. Further, we design algorithms and obtain similar regret bounds for more general systems with unknown context distribution and heterogeneous costs. To the best of our knowledge, this is the first work that shows how to achieve logarithmic regret in constrained contextual bandits. Moreover, this work also sheds light on the study of computationally efficient algorithms for general constrained contextual bandits.
Derived categories of sheaves on singular schemes with an application to reconstruction

Abstract We prove that the bounded derived category of coherent sheaves with proper support is equivalent to the category of locally-finite, cohomological functors on the perfect derived category of a quasi-projective scheme over a field. We introduce the notions of pseudo-adjoints and Rouquier functors and study them. As an application of these ideas and results, we extend the reconstruction result of Bondal and Orlov to Gorenstein projective varieties.
Comparing 2-handle additions to a genus 2 boundary component

We prove that knots obtained by attaching a band to a split link satisfy the cabling conjecture. We also give new proofs that unknotting number one knots are prime and that genus is superadditive under band sum. Additionally, we prove a collection of results comparing two 2-handle additions to a genus two boundary component of a compact, orientable 3-manifold. These results give a near complete solution to a conjecture of Scharlemann and provide evidence for a conjecture of Scharlemann and Wu. The proofs make use of a new theorem concerning the effects of attaching a 2-handle to a suture in the boundary of a sutured manifold.
On semisimplicial sets satisfying the Kan condition

A semisimplicial set has face maps but not degeneracies. A basic fact, due to Rourke and Sanderson, is that a semisimplicial set satisfying the Kan condition can be given a simplicial structure. The present paper gives a combinatorial proof of this fact and a generalization to multisemisimplicial sets.
More Analysis of Double Hashing for Balanced Allocations.

With double hashing, for a key x, one generates two hash values f(x) and g(x), and then uses combinations (f(x) + ig(x)) mod n for i = 0, 1, 2, . . . to generate multiple hash values in the range [0, n− 1] from the initial two. For balanced allocations, keys are hashed into a hash table where each bucket can hold multiple keys, and each key is placed in the least loaded of d choices. It has been shown previously that asymptotically the performance of double hashing and fully random hashing is the same in the balanced allocation paradigm using fluid limit methods. Here we extend a coupling argument used by Lueker and Molodowitch to show that double hashing and ideal uniform hashing are asymptotically equivalent in the setting of open address hash tables to the balanced allocation setting, providing further insight into this phenomenon. We also discuss the potential for and bottlenecks limiting the use this approach for other multiple choice hashing schemes.
Supervised Attentions for Neural Machine Translation

In this paper, we improve the attention or alignment accuracy of neural machine translation by utilizing the alignments of training sentence pairs. We simply compute the distance between the machine attentions and the "true" alignments, and minimize this cost in the training procedure. Our experiments on large-scale Chinese-to-English task show that our model improves both translation and alignment qualities significantly over the large-vocabulary neural machine translation system, and even beats a state-of-the-art traditional syntax-based system.
Quantum algorithms for Gibbs sampling and hitting-time estimation

We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Z and polynomial in log(1/e), where N is the Hilbert space dimension, β is the inverse temperature, Z is the partition function, and e is the desired precision of the output state. Our quantum algorithm exponentially improves the complexity dependence on 1/e and polynomially improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. For a sparse stochastic matrix P, it runs in time almost linear in 1/(eΔ3/2), where e is the absolute precision in the estimation and Δ is a parameter determined by P, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the complexity dependence on 1/e and 1/Δ of the analog classical algorithm for hitting-time estimation. Both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.
Approximating sparse PCA from incomplete data

We study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the original data matrix, then one can recover a near optimal solution to the optimization problem by using the sketch. In particular, we use this approach to obtain sparse principal components and show that for m data points in n dimensions, O(∊-2k max{m, n}) elements gives an ∊-additive approximation to the sparse PCA problem (k is the stable rank of the data matrix). We demonstrate our algorithms extensively on image, text, biological and financial data. The results show that not only are we able to recover the sparse PCAs from the incomplete data, but by using our sparse sketch, the running time drops by a factor of five or more.
Joint Topic Modeling and Factor Analysis of Textual Information and Graded Response Data

machine learning methods are critical to the de- velopment of large-scale personalized learning systems that cater directly to the needs of individual learners. The re- cently developed SPARse Factor Analysis (SPARFA) frame- work provides a new statistical model and algorithms for machine learning-based learning analytics, which estimate a learner's knowledge of the latent concepts underlying a domain, and content analytics, which estimate the relation- ships among a collection of questions and the latent con- cepts. SPARFA estimates these quantities given only the binary-valued graded responses to a collection of questions. In order to better interpret the estimated latent concepts, SPARFA relies on a post-processing step that utilizes user- defined tags (e.g., topics or keywords) available for each question. In this paper, we relax the need for user-defined tags by extending SPARFA to jointly process both graded learner responses and the text of each question and its asso- ciated answer(s) or other feedback. Our purely data-driven approach (i) enhances the interpretability of the estimated latent concepts without the need of explicitly generating a set of tags or performing a post-processing step, (ii) improves the prediction performance of SPARFA, and (iii) scales to large test/assessments where human annotation would prove burdensome. We demonstrate the efficacy of the proposed approach on two real educational datasets.
Finite type domains with hyperbolic orbit accumulation points

Abstract In this paper, finite type domains with hyperbolic orbit accumulation points are studied. We prove, in case of C 2 , it has to be a (global) pseudoconvex domain, after an assumption of boundary regularity. Moreover, one of the applications will realize the classification of domains within this class, precisely the domain is biholomorphic to one of the ellipsoids { ( z , w ) : | z | 2 m + | w | 2 1 , m ∈ Z + } . This application generalizes [4] in which the boundary is assumed to be real analytic for the case of hyperbolic orbit accumulation points.
An Achievable Rate-Distortion Region for Multiple Descriptions Source Coding Based on Coset Codes

We consider the problem of multiple descriptions (MDs) source coding and propose new coding strategies involving both unstructured and structured coding layers. Previously, the most general achievable rate-distortion (RD) region for the $l$ -descriptions problem was the combinatorial message sharing with binning (CMSB) region. The CMSB scheme utilizes unstructured quantizers and unstructured binning. In the first part of the paper, we show that this strategy can be improved upon using more general unstructured quantizers and a more general unstructured binning method. In the second part, structured coding strategies are considered. First, structured coding strategies are developed by considering the specific MD examples involving three or more descriptions. We show that the application of structured quantizers results in strict RD improvements when there are more than two descriptions. Furthermore, we show that a structured binning also yields improvements. These improvements are in addition to the ones derived in the first part of the paper. This suggests that structured coding is essential when coding over more than two descriptions. Using the ideas developed through these examples, we provide a new unified coding strategy by considering several structured coding layers. Finally, we characterize its performance in the form of an inner bound to the optimal RD region using computable single-letter information quantities. The new RD region strictly contains all of the previous known achievable regions.
Risk-Averse Matchings over Uncertain Graph Databases

In this work we study a problem that naturally arises in the context of several important applications, such as online dating, kidney exchanges, and team formation.
Codimension two souls and cancellation phenomena

Abstract For each m ≥ 0 we find an open ( 4 m + 9 ) -dimensional simply connected manifold with complete nonnegatively curved metrics whose souls are nondiffeomorphic, homeomorphic, and have codimension 2. We give a diffeomorphism classification of the pairs ( N , soul ) when N is the total space of a nontrivial complex line bundle over S 7 × CP 2 ; up to diffeomorphism there are precisely three such pairs, distinguished by their nondiffeomorphic souls.
On Splits of Computably Enumerable Sets

Our focus will be on the computably enumerable (c.e.) sets and trivial, non-trivial, Friedberg, and non-Friedberg splits of the c.e. sets. Every non-computable set has a non-trivial Friedberg split. Moreover, this theorem is uniform. V. Yu. Shavrukov recently answered the question which c.e. sets have a non-trivial non-Friedberg splitting and we provide a different proof of his result. We end by showing there is no uniform splitting of all c.e. sets such that all non-computable sets are non-trivially split and, in addition, all sets with a non-trivial non-Friedberg split are split accordingly.
Further solvable analogues of the Baer–Suzuki theorem and generation of nonsolvable groups

Abstract Let G be an almost simple group. We prove that if x ∈ G has prime order p ⩾ 5 , then there exists an involution y such that 〈 x , y 〉 is not solvable. Also, if x is an involution then there exist three conjugates of x that generate a nonsolvable group, unless x belongs to a short list of exceptions, which are described explicitly. We also prove that if x has order 6 or 9, then there exist two conjugates that generate a nonsolvable group.
A Psychopathological Approach to Safety Engineering in AI and AGI

The complexity of dynamics in AI techniques is already approaching that of complex adaptive systems, thus curtailing the feasibility of formal controllability and reachability analysis in the context of AI safety. It follows that the envisioned instances of Artificial General Intelligence (AGI) will also suffer from challenges of complexity. To tackle such issues, we propose the modeling of deleterious behaviors in AI and AGI as psychological disorders, thereby enabling the employment of psychopathological approaches to analysis and control of misbehaviors. Accordingly, we present a discussion on the feasibility of the psychopathological approaches to AI safety, and propose general directions for research on modeling, diagnosis, and treatment of psychological disorders in AGI.
Universal local parametrizations via heat kernels and eigenfunctions of the Laplacian

We use heat kernels or eigenfunctions of the Laplacian to construct local coordinates on large classes of Euclidean domains and Riemannian manifolds (not necessarily smooth, e.g. with C α metric). These coordinates are bi-Lipschitz on embedded balls of the domain or manifold, with distortion constants that depend only on natural geometric properties of the domain or manifold. The proof of these results relies on estimates, from above and below, for the heat kernel and its gradient, as well as for the eigenfunctions of the Laplacian and their gradient. These estimates hold in the non-smooth category, and are stable with respect to perturbations within this category. Finally, these coordinate systems are intrinsic and efficiently computable, and are of value in applications.
Super-Resolution for Overhead Imagery Using DenseNets and Adversarial Learning

Recent advances in Generative Adversarial Learning allow for new modalities of image super-resolution by learning low to high resolution mappings. In this paper we present our work using Generative Adversarial Networks (GANs) with applications to overhead and satellite imagery. We have experimented with several state-of-the-art architectures. We propose a GAN-based architecture using densely connected convolutional neural networks (DenseNets) to be able to super-resolve overhead imagery with a factor of up to 8x. We have also investigated resolution limits of these networks. We report results on several publicly available datasets, including SpaceNet data and IARPA Multi-View Stereo Challenge, and compare performance with other state-of-the-art architectures.
Convolutional Social Pooling for Vehicle Trajectory Prediction

Forecasting the motion of surrounding vehicles is a critical ability for an autonomous vehicle deployed in complex traffic. Motion of all vehicles in a scene is governed by the traffic context, i.e., the motion and relative spatial configuration of neighboring vehicles. In this paper we propose an LSTM encoder-decoder model that uses convolutional social pooling as an improvement to social pooling layers for robustly learning interdependencies in vehicle motion. Additionally, our model outputs a multi-modal predictive distribution over future trajectories based on maneuver classes. We evaluate our model using the publicly available NGSIM US-101 and I-80 datasets. Our results show improvement over the state of the art in terms of RMS values of prediction error and negative log-likelihoods of true future trajectories under the model's predictive distribution. We also present a qualitative analysis of the model's predicted distributions for various traffic scenarios.
Generalized Binary Search For Split-Neighborly Problems.

In sequential hypothesis testing, Generalized Binary Search (GBS) greedily chooses the test with the highest information gain at each step. It is known that GBS obtains the gold standard query cost of $O(\log n)$ for problems satisfying the $k$-neighborly condition, which requires any two tests to be connected by a sequence of tests where neighboring tests disagree on at most $k$ hypotheses. In this paper, we introduce a weaker condition, split-neighborly, which requires that for the set of hypotheses two neighbors disagree on, any subset is splittable by some test. For four problems that are not $k$-neighborly for any constant $k$, we prove that they are split-neighborly, which allows us to obtain the optimal $O(\log n)$ worst-case query cost.
ENDMEMBER EXTRACTION ON THE GRASSMANNIAN

Endmember extraction plays a prominent role in a variety of data analysis problems as endmembers often correspond to data representing the purest or best representative of some feature. Identifying endmembers then can be useful for further identification and classification tasks. In settings with high-dimensional data, such as hyperspectral imagery, it can be useful to consider endmembers that are subspaces as they are capable of capturing a wider range of variations of a signature. The endmember extraction problem in this setting thus translates to finding the vertices of the convex hull of a set of points on a Grassmannian. In the presence of noise, it can be less clear whether a point should be considered a vertex. In this paper, we propose an algorithm to extract endmembers on a Grassmannian, identify subspaces of interest that lie near the boundary of a convex hull, and demonstrate the use of the algorithm on a synthetic example and on the 220 spectral band AVIRIS Indian Pines hyperspectral image.
Directed closure measures for networks with reciprocity.

The study of triangles in graphs is a standard tool in network analysis, leading to measures such as the \emph{transitivity}, i.e., the fraction of paths of length $2$ that participate in triangles. Real-world networks are often directed, and it can be difficult to "measure" this network structure meaningfully. We propose a collection of \emph{directed closure values} for measuring triangles in directed graphs in a way that is analogous to transitivity in an undirected graph. Our study of these values reveals much information about directed triadic closure. For instance, we immediately see that reciprocal edges have a high propensity to participate in triangles. We also observe striking similarities between the triadic closure patterns of different web and social networks. We perform mathematical and empirical analysis showing that directed configuration models that preserve reciprocity cannot capture the triadic closure patterns of real networks.
Automatic Unsupervised Tensor Mining with Quality Assessment.

A popular tool for unsupervised modelling and mining multi-aspect data is tensor decomposition. In an exploratory setting, where and no labels or ground truth are available how can we automatically decide how many components to extract? How can we assess the quality of our results, so that a domain expert can factor this quality measure in the interpretation of our results? In this paper, we introduce AutoTen, a novel automatic unsupervised tensor mining algorithm with minimal user intervention, which leverages and improves upon heuristics that assess the result quality. We extensively evaluate AutoTen's performance on synthetic data, outperforming existing baselines on this very hard problem. Finally, we apply AutoTen on a variety of real datasets, providing insights and discoveries. We view this work as a step towards a fully automated, unsupervised tensor mining tool that can be easily adopted by practitioners in academia and industry.
Elliptic Curves with Everywhere Good Reduction

Abstract We consider the question of which quadratic fields have elliptic curves with everywhere good reduction. By revisiting work of Setzer, we expand on congruence conditions that determine the real and imaginary quadratic fields with elliptic curves of everywhere good reduction and rational j-invariant. Using this, we determine the density of such real and imaginary quadratic fields. If R ( X ) denotes the number of real quadratic fields K = Q [ m ] such that | Δ K | X and for which there exists an elliptic curve E / K with rational j-invariant that has everywhere good reduction, then R ( X ) ≫ X log ⁡ ( X ) . We also obtain a similar result for imaginary quadratic fields. To obtain these estimates we explicitly construct quadratic fields over which we can construct elliptic curves with everywhere good reduction. The estimates then follow from elementary multiplicative number theory. In addition, we obtain infinite families of real and imaginary quadratic fields such that there are no elliptic curves with everywhere good reduction over these fields.
Approximate Leave-One-Out for Fast Parameter Tuning in High Dimensions.

Consider the following class of learning schemes: $$\hat{\boldsymbol{\beta}} := \arg\min_{\boldsymbol{\beta}}\;\sum_{j=1}^n \ell(\boldsymbol{x}_j^\top\boldsymbol{\beta}; y_j) + \lambda R(\boldsymbol{\beta}),\qquad\qquad (1) $$ where $\boldsymbol{x}_i \in \mathbb{R}^p$ and $y_i \in \mathbb{R}$ denote the $i^{\text{th}}$ feature and response variable respectively. Let $\ell$ and $R$ be the loss function and regularizer, $\boldsymbol{\beta}$ denote the unknown weights, and $\lambda$ be a regularization parameter. Finding the optimal choice of $\lambda$ is a challenging problem in high-dimensional regimes where both $n$ and $p$ are large. We propose two frameworks to obtain a computationally efficient approximation ALO of the leave-one-out cross validation (LOOCV) risk for nonsmooth losses and regularizers. Our two frameworks are based on the primal and dual formulations of (1). We prove the equivalence of the two approaches under smoothness conditions. This equivalence enables us to justify the accuracy of both methods under such conditions. We use our approaches to obtain a risk estimate for several standard problems, including generalized LASSO, nuclear norm regularization, and support vector machines. We empirically demonstrate the effectiveness of our results for non-differentiable cases.
Partition functions from Rao-Blackwellized tempered sampling

Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often sampled using simulated tempering, which augments the target space with an auxiliary inverse temperature variable. Our method exploits the multinomial probability law of the inverse temperatures, and provides estimates of the partition function in terms of a simple quotient of Rao-Blackwellized marginal inverse temperature probability estimates, which are updated while sampling. We show that the method has interesting connections with several alternative popular methods, and offers some significant advantages. In particular, we empirically find that the new method provides more accurate estimates than Annealed Importance Sampling when calculating partition functions of large Restricted Boltzmann Machines (RBM); moreover, the method is sufficiently accurate to track training and validation log-likelihoods during learning of RBMs, at minimal computational cost.
Bounding differences in Jager Pairs

Abstract Symmetrical subdivisions in the space of Jager Pairs for continued fractions-like expansions will provide us with bounds on their differences. Results will also apply to the classical regular and backwards continued fractions expansions, which are realized as special cases.
Separable operations on pure states

We show that the possible ensembles produced when a separable operation acts on a single pure bipartite entangled state are completely characterized by a majorization condition, a collection of inequalities for Schmidt coefficients, which is identical to that already known for the particular case of local operations and classical communication (LOCC). As a consequence, various known results for LOCC, including some involving monotonicity of entanglement, can be extended to the class of all separable operations.
Grand challenges in the physics of the sun and sun-like stars

The study of stellar structure and evolution is one of the main building blocks of astrophysics, and the Sun has an importance both as the star that is most amenable to detailed study and as the star that has by far the biggest impact on the Earth and near-Earth environment through its radiative and particulate outputs. Over the past decades, studies of stars and of the Sun have become somewhat separate. But in recent years, the rapid advances in asteroseismology, as well as the quest to better understand solar and stellar dynamos, have emphasized once again the synergy between studies of the stars and the Sun. In this article I have selected two "grand challenges" both for their crucial importance and because I thnk that these two problems are tractable to significant progress in the next decade. They are (i) understanding how solar and stellar dynamos generate magnetic field, and (ii) improving the predictability of geo-effective space weather.
A Few Photons Among Many: Unmixing Signal and Noise for Photon-Efficient Active Imaging

Conventional LIDAR systems require hundreds or thousands of photon detections per pixel to form accurate depth and reflectivity images. Recent photon-efficient computational imaging methods are remarkably effective with only 1.0 to 3.0 detected photons per pixel, but they are not demonstrated at signal-to-background ratio (SBR) below 1.0 because their imaging accuracies degrade significantly in the presence of high background noise. We introduce a new approach to depth and reflectivity estimation that emphasizes the unmixing of contributions from signal and noise sources. At each pixel in an image, short-duration range gates are adaptively determined and applied to remove detections likely to be due to noise. For pixels with too few detections to perform this censoring accurately, data are combined from neighboring pixels to improve depth estimates, where the neighborhood formation is also adaptive to scene content. Algorithm performance is demonstrated on experimental data at varying levels of noise. Results show improved performance of both reflectivity and depth estimates over state-of-the-art methods, especially at low SBR. In particular, accurate imaging is demonstrated with SBR as low as 0.04. This validation of a photon-efficient, noise-tolerant method demonstrates the viability of rapid, long-range, and low-power LIDAR imaging.
On Cellular Automata Models of Traffic Flow with Look-Ahead Potential

We study the statistical properties of a cellular automata model of traffic flow with the look-ahead potential. The model defines stochastic rules for the movement of cars on a lattice. We analyze the underlying statistical assumptions needed for the derivation of the coarse-grained model and demonstrate that it is possible to relax some of them to obtain an improved coarse-grained ODE model. We also demonstrate that spatial correlations play a crucial role in the presence of the look-ahead potential and propose a simple empirical correction to account for the spatial dependence between neighboring cells.
Discrete differential geometry and the properties of conformal two-dimensional materials

Abstract Two-dimensional materials were first isolated no longer than ten years ago, and a comprehensive understanding of their properties under non-planar shapes is still being developed. Strictly speaking, the theoretical study of the properties of graphene and other two-dimensional materials is the most complete for planar structures and for structures with small deformations from planarity. The opposite limit of large deformations is yet to be studied comprehensively but that limit is extremely relevant because it determines material properties near the point of failure. We are exploring uses for discrete differential geometry within the context of graphene and other two-dimensional materials, and these concepts appear promising in linking materials properties to shape regardless of how large a given material deformation is. A brief account of additional contributions arising from our group to two-dimensional materials that include graphene, stanene and phosphorene is provided towards the end of this manuscript.