cssi/SciSciGPT-SciSciNet huggingface dataset:
Multi-view unsupervised feature selection by cross-diffused matrix alignment

Multi-view high-dimensional data become increasingly popular in the big data era. Feature selection is a useful technique for alleviating the curse of dimensionality in multi-view learning. In this paper, we study unsupervised feature selection for multi-view data, as class labels are usually expensive to obtain. Traditional feature selection methods are mostly designed for single-view data and cannot fully exploit the rich information from multi-view data. Existing multi-view feature selection methods are usually based on noisy cluster labels which might not preserve sufficient information from multi-view data. To better utilize multi-view information, we propose a method, CDMA-FS, to select features for each view by performing alignment on a cross diffused matrix. We formulate it as a constrained optimization problem and solve it using Quasi-Newton based method. Experiments results on four real-world datasets show that the proposed method is more effective than the state-of-the-art methods in multi-view setting.
COMPUTING LINKS AND ACCESSING ARCS

Sucient conditions are given for the computation of accessing arcs and arcs that links boundary components of multiply connected domains. The existence of a not-computably-accessible but computable point on a com- putably compact arc is also demonstrated.
Correlated-photon imaging with cancellation of object-induced aberration

We show that a recently discussed apparatus for aberration-canceled interferometry may be modified to perform correlated-photon imaging in the so-called “ghost” imaging configuration. For objects in the vicinity of a particular plane, the images are free of object-induced phase distortions. This apparatus has the distinctive feature that it may be used to superimpose images of two objects in a manner that could lead to useful effects and applications. We show that the apparatus works using either quantum-entangled or classically correlated light sources.
On the Variety of Shapes in Digital Trees

We study the joint distribution of the number of occurrences of members of a collection of nonoverlapping motifs in digital data. We deal with finite and countably infinite collections. For infinite collections, the setting requires that we be very explicit about the specification of the underlying measure-theoretic formulation. We show that (under appropriate normalization) for such a collection, any linear combination of the number of occurrences of each of the motifs in the data has a limiting normal distribution. In many instances, this can be interpreted in terms of the number of occurrences of individual motifs: They have a multivariate normal distribution. The methods of proof include combinatorics on words, integral transforms, and poissonization.
Minibatch Gibbs Sampling on Large Graphical Models

Gibbs sampling is the de facto Markov chain Monte Carlo method used for inference and learning on large scale graphical models. For complicated factor graphs with lots of factors, the performance of Gibbs sampling can be limited by the computational cost of executing a single update step of the Markov chain. This cost is proportional to the degree of the graph, the number of factors adjacent to each variable. In this paper, we show how this cost can be reduced by using minibatching: subsampling the factors to form an estimate of their sum. We introduce several minibatched variants of Gibbs, show that they can be made unbiased, prove bounds on their convergence rates, and show that under some conditions they can result in asymptotic single-update-run-time speedups over plain Gibbs sampling.
Structured sparsity via alternating direction methods

We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm that incorporates prior knowledge of the group structure of the features. Such problems often pose a considerable challenge to optimization algorithms due to the non-smoothness and non-separability of the regularization term. In this paper, we focus on two commonly adopted sparsity-inducing regularization terms, the overlapping Group Lasso penalty l1/l2-norm and the l1/l∞-norm. We propose a unified framework based on the augmented Lagrangian method, under which problems with both types of regularization and their variants can be efficiently solved. As one of the core building-blocks of this framework, we develop new algorithms using a partial-linearization/splitting technique and prove that the accelerated versions of these algorithms require O(1/√e) iterations to obtain an e-optimal solution. We compare the performance of these algorithms against that of the alternating direction augmented Lagrangian and FISTA methods on a collection of data sets and apply them to two real-world problems to compare the relative merits of the two norms.
The American Space Exploration Narrative from the Cold War Through the Obama Administration

Abstract We document how the narrative and the policies of space exploration in the United States have changed from the Eisenhower through the Obama administrations. We first examine the history of U.S. space exploration and also assess 3 current conditions of the field of space exploration including (1) the increasing role of the private sector, (2) the influence of global politics and specifically the emergence of China as a global space power, and (3) the focus on a human mission to Mars. To further understand the narrative of U.S. space exploration, we identify 5 rhetorical themes: competition, prestige, collaboration, leadership, and “a new paradigm.” These themes are then used to analyze the content of 40 documents over the course of space exploration history in the U.S. from 8 U.S. presidential administrations. The historical narrative and content analysis together suggest that space exploration has developed from a discourse about a bipolar world comprised of the United States and the Soviet Union into a complicated field that encompasses many new players in the national to the industrial realms. The results also suggest that the United States was at a crossroads in 2017 on the issues of how it participates in this changing field of space exploration. From this, we make 3 observations regarding recent U.S. space policy: (1) there is a disconnect between stated policy goals in American space exploration efforts and the implementation of those goals, (2) the United States communicates mixed messages regarding its intent to be both the dominant leader in the field of space exploration and also committed as a participant in international collaboration, and (3) the United States cannot remain a true pioneer of space exploration if it does not embrace the realities of globalization and the changing dynamics within the field of space exploration. We conclude with 3 suggestions: (1) the U.S. government and NASA should critically examine space exploration priorities and commit to implementing a program that will further realistic and robust stated policy and goals, (2) the U.S. should reexamine its intention to play a dominant leadership role in space exploration and consider emphasizing a commitment toward active participation in international collaboration in space, and (3) the U.S. should fully embrace the new paradigm of space exploration by lowering barriers such as International Traffic in Arms Regulations that hinder the competitiveness of the American space industry. The U.S. should review the challenges and advantages of collaborative endeavors with rising spacefaring nations such as China and abandon Cold War era thinking, thus paving the way to Mars by encouraging the participation of many nations and space agencies on future human missions.
A Vector Field Method Approach to Improved Decay for Solutions to the Wave Equation on a Slowly Rotating Kerr Black Hole

We prove that sufficiently regular solutions to the wave equationgK� = 0 on the exterior of a sufficiently slowly rotating Kerr black hole obey the estimates |�| � C(t � ) 3 2 +� on a compact region of r. This is proved with the help of a new vector field commutator that is analogous to the scaling vector field on Minkowski and Schwarzschild spacetime. This result improves the known robust decay rates that are proved using the vector field method in the region of finite r and along the event horizon.
Estimating trends in the global mean temperature record

Abstract. Given uncertainties in physical theory and numerical climate simulations, the historical temperature record is often used as a source of empirical information about climate change. Many historical trend analyses appear to de-emphasize physical and statistical assumptions: examples include regression models that treat time rather than radiative forcing as the relevant covariate, and time series methods that account for internal variability in nonparametric rather than parametric ways. However, given a limited data record and the presence of internal variability, estimating radiatively forced temperature trends in the historical record necessarily requires some assumptions. Ostensibly empirical methods can also involve an inherent conflict in assumptions: they require data records that are short enough for naive trend models to be applicable, but long enough for long-timescale internal variability to be accounted for. In the context of global mean temperatures, empirical methods that appear to de-emphasize assumptions can therefore produce misleading inferences, because the trend over the twentieth century is complex and the scale of temporal correlation is long relative to the length of the data record. We illustrate here how a simple but physically motivated trend model can provide better-fitting and more broadly applicable trend estimates and can allow for a wider array of questions to be addressed. In particular, the model allows one to distinguish, within a single statistical framework, between uncertainties in the shorter-term vs. longer-term response to radiative forcing, with implications not only on historical trends but also on uncertainties in future projections. We also investigate the consequence on inferred uncertainties of the choice of a statistical description of internal variability. While nonparametric methods may seem to avoid making explicit assumptions, we demonstrate how even misspecified parametric statistical methods, if attuned to the important characteristics of internal variability, can result in more accurate uncertainty statements about trends.
Large-Scale Distributed Kalman Filtering via an Optimization Approach

Abstract Large-scale distributed systems such as sensor networks, often need to achieve filtering and consensus on an estimated parameter from high-dimensional measurements. Running a Kalman filter on every node in such a network is computationally intensive; in particular the matrix inversion in the Kalman gain update step is expensive. In this paper, we extend previous results in distributed Kalman filtering and large-scale machine learning to propose a gradient descent step for updating an estimate of the error covariance matrix; this is then embedded and analyzed in the context of distributed Kalman filtering. We provide properties of the resulting filters, in addition to a number of applications throughout the paper.
Learning Actionable Representations with Goal Conditioned Policies

Representation learning is a central challenge across a range of machine learning areas. In reinforcement learning, effective and functional representations have the potential to tremendously accelerate learning progress and solve more challenging problems. Most prior work on representation learning has focused on generative approaches, learning representations that capture all underlying factors of variation in the observation space in a more disentangled or well-ordered manner. In this paper, we instead aim to learn functionally salient representations: representations that are not necessarily complete in terms of capturing all factors of variation in the observation space, but rather aim to capture those factors of variation that are important for decision making -- that are "actionable." These representations are aware of the dynamics of the environment, and capture only the elements of the observation that are necessary for decision making rather than all factors of variation, without explicit reconstruction of the observation. We show how these representations can be useful to improve exploration for sparse reward problems, to enable long horizon hierarchical reinforcement learning, and as a state representation for learning policies for downstream tasks. We evaluate our method on a number of simulated environments, and compare it to prior methods for representation learning, exploration, and hierarchical reinforcement learning.
On the Convergence of Asynchronous Parallel Iteration with Unbounded Delays

Recent years have witnessed the surge of asynchronous parallel (async-parallel) iterative algorithms due to problems involving very large-scale data and a large number of decision variables. Because of asynchrony, the iterates are computed with outdated information, and the age of the outdated information, which we call delay, is the number of times it has been updated since its creation. Almost all recent works prove convergence under the assumption of a finite maximum delay and set their stepsize parameters accordingly. However, the maximum delay is practically unknown. This paper presents convergence analysis of an async-parallel method from a probabilistic viewpoint, and it allows for large unbounded delays. An explicit formula of stepsize that guarantees convergence is given depending on delays’ statistics. With $$p+1$$ identical processors, we empirically measured that delays closely follow the Poisson distribution with parameter p, matching our theoretical model, and thus, the stepsize can be set accordingly. Simulations on both convex and nonconvex optimization problems demonstrate the validness of our analysis and also show that the existing maximum-delay-induced stepsize is too conservative, often slows down the convergence of the algorithm.
The list chromatic index of simple graphs whose odd cycles intersect in at most one edge

Abstract We study the class of simple graphs G ∗ for which every pair of distinct odd cycles intersect in at most one edge. We give a structural characterization of the graphs in G ∗ and prove that every G ∈ G ∗ satisfies the list-edge-coloring conjecture. When Δ ( G ) ≥ 4 , we in fact prove a stronger result about kernel-perfect orientations in L ( G ) which implies that G is ( m Δ ( G ) : m ) -edge-choosable and Δ ( G ) -edge-paintable for every m ≥ 1 .
Election with Bribed Voter Uncertainty: Hardness and Approximation Algorithm

Bribery in election (or computational social choice in general) is an important problem that has received a considerable amount of attention. In the classic bribery problem, the briber (or attacker) bribes some voters in attempting to make the briber’s designated candidate win an election. In this paper, we introduce a novel variant of the bribery problem, “Election with Bribed Voter Uncertainty” or BVU for short, accommodating the uncertainty that the vote of a bribed voter may or may not be counted. This uncertainty occurs either because a bribed voter may not cast its vote in fear of being caught, or because a bribed voter is indeed caught and therefore its vote is discarded. As a first step towards ultimately understanding and addressing this important problem, we show that it does not admit any multiplicative O(1)-approximation algorithm modulo standard complexity assumptions. We further show that there is an approximation algorithm that returns a solution with an additive-e error in FPT time for any fixed e.
Human-in-the-Loop SLAM

Building large-scale, globally consistent maps is a challenging problem, made more difficult in environments with limited access, sparse features, or when using data collected by novice users. For such scenarios, where state-of-the-art mapping algorithms produce globally inconsistent maps, we introduce a systematic approach to incorporating sparse human corrections, which we term Human-in-the-Loop Simultaneous Localization and Mapping (HitL-SLAM). Given an initial factor graph for pose graph SLAM, HitL-SLAM accepts approximate, potentially erroneous, and rank-deficient human input, infers the intended correction via expectation maximization (EM), back-propagates the extracted corrections over the pose graph, and finally jointly optimizes the factor graph including the human inputs as human correction factor terms, to yield globally consistent large-scale maps. We thus contribute an EM formulation for inferring potentially rank-deficient human corrections to mapping, and human correction factor extensions to the factor graphs for pose graph SLAM that result in a principled approach to joint optimization of the pose graph while simultaneously accounting for multiple forms of human correction. We present empirical results showing the effectiveness of HitL-SLAM at generating globally accurate and consistent maps even when given poor initial estimates of the map.
Finite groups with a trivial Chermak–Delgado subgroup

The Chermak-Delgado lattice of a finite group is a modular, self-dual sublattice of the lattice of subgroups of $G$. The least element of the Chermak-Delgado lattice of $G$ is known as the Chermak-Delgado subgroup of $G$. This paper concerns groups with a trivial Chermak-Delgado subgroup. We prove that if the Chermak-Delgado lattice of such a group is lattice isomorphic to a Cartesian product of lattices, then the group splits as a direct product, with the Chermak-Delgado lattice of each direct factor being lattice isomorphic to one of the lattices in the Cartesian product. We establish many properties of such groups and properties of subgroups in the Chermak-Delgado lattice. We define a CD-minimal group to be an indecomposable group with a trivial Chermak-Delgado subgroup. We establish lattice theoretic properties of Chermak-Delgado lattices of CD-minimal groups. We prove an extension theorem for CD-minimal groups, and use the theorem to produce twelve examples of CD-minimal groups, each having different CD lattices. Curiously, quasi-antichain $p$-group lattices play a major role in the author's constructions.
Finite-time analysis for the knowledge-gradient policy

We consider sequential decision problems in which we adaptively choose one of finitely many alternatives and observe a stochastic reward. We offer a new perspective on interpreting Bayesian ranking and selection problems as adaptive stochastic multiset maximization problems and derive the first finite-time bound of the knowledge-gradient policy for adaptive submodular objective functions. In addition, we introduce the concept of prior-optimality and provide another insight into the performance of the knowledge-gradient policy based on the submodular assumption on the value of information. We demonstrate submodularity for the two-alternative case and provide other conditions for more general problems, bringing out the issue and importance of submodularity in learning problems. Empirical experiments are conducted to further illustrate the finite-time behavior of the knowledge-gradient policy.
Toeplitz subshifts with trivial centralizers and positive entropy

Given a dynamical system $(X,G)$, the centralizer $C(G)$ denotes the group of all homeomorphisms of $X$ which commute with the action of $G$. This group is sometimes called the automorphism group of the dynamical system $(X,G)$. In this note, we generalize the construction of Bulatek and Kwiatkowski (1992) to $\mathbb Z^d$-Toepltiz systems by identifying a class of $\mathbb Z^d$-Toeplitz systems that have trivial centralizers. We show that this class of $\mathbb Z^d$-Toeplitz with trivial centralizers contains systems with positive topological entropy.
Partitioning Random Graphs into Monochromatic Components

Erdős , Gyarfas , and Pyber (1991) conjectured that every $r$ -colored complete graph can be partitioned into at most $r-1$ monochromatic components; this is a strengthening of a conjecture of Lov asz (1975) and Ryser (1970) in which the components are only required to form a cover. An important partial result of Haxell and Kohayakawa (1995) shows that a partition into $r$ monochromatic components is possible for sufficiently large $r$ -colored complete graphs. We start by extending Haxell and Kohayakawa's result to graphs with large minimum degree, then we provide some partial analogs of their result for random graphs. In particular, we show that if $p\ge \left(\frac{27\log n}{n}\right)^{1/3}$ , then a.a.s. in every $2$ -coloring of $G(n,p)$ there exists a partition into two monochromatic components, and for $r\geq 2$ if $p\ll \left(\frac{r\log n}{n}\right)^{1/r}$ , then a.a.s. there exists an $r$ -coloring of $G(n,p)$ such that there does not exist a cover with a bounded number of components. Finally, we consider a random graph version of a classic result of Gyarfa s (1977) about large monochromatic components in $r$ -colored complete graphs. We show that if $p=\frac{\omega(1)}{n}$ , then a.a.s. in every $r$ -coloring of $G(n,p)$ there exists a monochromatic component of order at least $(1-o(1))\frac{n}{r-1}$ .
The Weyl algebra as a fixed ring

Abstract We prove that the Weyl algebra over C cannot be a fixed ring of any domain under a nontrivial action of a finite group by algebra automorphisms, thus settling a 30-year old problem. In fact, we prove the following much more general result. Let X be a smooth affine variety over C , let D ( X ) denote the ring of algebraic differential operators on X, and let Γ be a finite group. If D ( X ) is isomorphic to the ring of Γ-invariants of a C -domain R on which Γ acts faithfully by C -algebra automorphisms, then R is isomorphic to the ring of differential operators on a Γ-Galois covering of X.
Training Symbol-Based Equalization for Quadrature Duobinary PDM-FTN Systems

A training symbol-based equalization algorithm is proposed for polarization de-multiplexing in quadrature duobinary (QDB) modulated polarization division multiplexed faster than-Nyquist (FTN) coherent optical systems. The proposed algorithm is based on the least mean square algorithm, and multiple location candidates of a symbol are considered in order to make use of the training symbols with QDB modulation. Results show that an excellent convergence performance is obtained using the proposed algorithm under different polarization alignment scenarios. The optical signal-to-noise ratio required to attain a bit error rate of $2\times 10^{-2}$ is reduced by 1.7 and 1.8 dB using the proposed algorithm, compared with systems using the constant modulus algorithm with differential coding for four-ary quadrature amplitude modulation (4-QAM) and 16-QAM systems with symbol-by-symbol detection, respectively. Furthermore, comparisons with the Tomlinson–Harashima precoding-based FTN systems illustrate that QDB is preferable when 4-QAM is utilized.
Continuous-time random walks for the numerical solution of stochastic differential equations

This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These schemes are obtained by spatially discretizing the Kolmogorov equation associated with the SDE in such a way that the resulting semi-discrete equation generates a Markov jump process that can be realized exactly using a Monte Carlo method. In this construction the spatial increment of the approximation can be bounded uniformly in space, which guarantees that the schemes are numerically stable for both finite and long time simulation of SDEs. By directly analyzing the generator of the approximation, we prove that the approximation has a sharp stochastic Lyapunov function when applied to an SDE with a drift field that is locally Lipschitz continuous and weakly dissipative. We use this stochastic Lyapunov function to extend a local semimartingale representation of the approximation. This extension permits to analyze the complexity of the approximation. Using the theory of semigroups of linear operators on Banach spaces, we show that the approximation is (weakly) accurate in representing finite and infinite-time statistics, with an order of accuracy identical to that of its generator. The proofs are carried out in the context of both fixed and variable spatial step sizes. Theoretical and numerical studies confirm these statements, and provide evidence that these schemes have several advantages over standard methods based on time-discretization. In particular, they are accurate, eliminate nonphysical moves in simulating SDEs with boundaries (or confined domains), prevent exploding trajectories from occurring when simulating stiff SDEs, and solve first exit problems without time-interpolation errors. 2010 Mathematics Subject Classification. Primary 65C30; Secondary, 60J25, 60J75.
Pin(2)-Equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture

We define Pin(2)-equivariant Seiberg-Witten Floer homology for rational homology 3-spheres equipped with a spin structure. The analogue of Froyshov’s correction term in this setting is an integer-valued invariant of homology cobordism whose mod 2 reduction is the Rokhlin invariant. As an application, we show that there are no homology 3-spheres Y of Rokhlin invariant one such that Y #Y bounds an acyclic smooth 4-manifold. By previous work of Galewski-Stern and Matumoto, this implies the existence of non-triangulable high-dimensional manifolds.
HAUSDORFF DIMENSION OF GENERALIZED FIBONACCI WORD FRACTALS

Fibonacci word fractals are a class of fractals that have been studied recently, though the words the fractals are generated from are well known in the combinatorics literature. The Fibonacci word can be used to draw a curve which possesses self-similarities determined by the recursive structure of the word. The Hausdorff dimension of the scaling limit of the finite Fibonacci word curves is computed for i-Fibonacci curves and any drawing angle between 0 and π/2.
Probabilistic Prediction of Vehicle Semantic Intention and Motion

Accurately predicting the possible behaviors of traffic participants is an essential capability for future autonomous vehicles. The majority of current researches fix the number of driving intentions by considering only a specific scenario. However, distinct driving environments usually contain various possible driving maneuvers. Therefore, a intention prediction method that can adapt to different traffic scenarios is needed. To further improve the overall vehicle prediction performance, motion information is usually incorporated with classified intentions. As suggested in some literature, the methods that directly predict possible goal locations can achieve better performance for long-term motion prediction than other approaches due to their automatic incorporation of environment constraints. Moreover, by obtaining the temporal information of the predicted destinations, the optimal trajectories for predicted vehicles as well as the desirable path for ego autonomous vehicle could be easily generated. In this paper, we propose a Semantic based Intention and Motion Prediction (SIMP) method, which can be adapted to any driving scenarios by using semantic defined vehicle behaviors. It utilizes a probabilistic framework based on deep neural network to estimate the intentions, final locations, and the corresponding time information for surrounding vehicles. An exemplar real-world scenario was used to implement and examine the proposed method.
Guess & check codes for deletions and synchronization

We consider the problem of constructing codes that can correct δ deletions occurring in an arbitrary binary string of length n bits. Varshamov-Tenengolts (VT) codes can correct all possible single deletions (δ = 1) with an asymptotically optimal redundancy. Finding similar codes for δ ≥ 2 deletions is an open problem. We propose a new family of codes, that we call Guess & Check (GC) codes, that can correct, with high probability, a constant number of deletions δ occurring at uniformly random positions within an arbitrary string. The GC codes are based on MDS codes and have an asymptotically optimal redundancy that is Θ (δ log n). We provide deterministic polynomial time encoding and decoding schemes for these codes. We also describe the applications of GC codes to file synchronization.
Practical Implementation of Adaptive Analog Nonlinear Filtering for Impulsive Noise Mitigation

It is well known that the performance of OFDM- based Powerline Communication (PLC) systems is impacted by impulsive noise. In this work, we propose a practical blind adaptive analog nonlinear filter to efficiently detect and mitigate impulsive noise. Specially, we design an Adaptive Canonical Differential Limiter (ACDL) which is constructed from a Clipped Mean Tracking Filter (CMTF) and Quartile Tracking Filters (QTFs). The QTFs help to determine a real-time range that excludes outliers. This range is fed into the CMTF which is responsible for mitigating impulsive noise. The CMTF is a nonlinear analog filter and its nonlinearity is controlled by the aforementioned range. Proper selection of this range ensures the improvement of the desired signal quality in impulsive environment. It is important to note that the proposed ACDL behaves like a linear filter in case of no impulsive noise. In this context, the traditional matched filter construction is modified to ensure distortionless processing of the desired signal. The performance improvement of the proposed ACDL is due to the fact that unlike other nonlinear methods, the ACDL is implemented in the analog domain where the outliers are still broadband and distinguishable. Simulation results in PRIME (OFDM-based narrowband PLC system) demonstrate the superior BER performance of ACDL relative to other nonlinear approaches such as blanking and clipping in impulsive noise environments.
Efficient feature group sequencing for anytime linear prediction

We consider anytime linear prediction in the common machine learning setting, where features are in groups that have costs. We achieve anytime (or interruptible) predictions by sequencing the computation of feature groups and reporting results using the computed features at interruption. We extend Orthogonal Matching Pursuit (OMP) and Forward Regression (FR) to learn the sequencing greedily under this group setting with costs. We theoretically guarantee that our algorithms achieve near-optimal linear predictions at each budget when a feature group is chosen. With a novel analysis of OMP, we improve its theoretical bound to the same strength as that of FR. In addition, we develop a novel algorithm that consumes cost 4B to approximate the optimal performance of any cost B, and prove that with cost less than 4B, such an approximation is impossible. To our knowledge, these are the first anytime bounds at all budgets. We test our algorithms on two real-world data-sets and evaluate them in terms of anytime linear prediction performance against cost-weighted Group Lasso and alternative greedy algorithms.
Proof of the HRT conjecture for (2,2) configurations

We prove a particular case of the so-called “HRT conjecture”. More precisely, we show that given any planar trapezoid with vertices (tj,ξj)j=14∈R2 and given any nontrivial L2(R) function f, there is no linear dependence between the time-frequency translates f(x+tj)e2πiξjx. Our methods are mostly number theoretical.
Improved variational autoencoders for text modeling using dilated convolutions

Recent work on generative text modeling has found that variational autoencoders (VAE) with LSTM decoders perform worse than simpler LSTM language models (Bowman et al., 2015). This negative result is so far poorly understood, but has been attributed to the propensity of LSTM decoders to ignore conditioning information from the encoder. In this paper, we experiment with a new type of decoder for VAE: a dilated CNN. By changing the decoder's dilation architecture, we control the size of context from previously generated words. In experiments, we find that there is a trade-off between contextual capacity of the decoder and effective use of encoding information. We show that when carefully managed, VAEs can outperform LSTM language models. We demonstrate perplexity gains on two datasets, representing the first positive language modeling result with VAE. Further, we conduct an in-depth investigation of the use of VAE (with our new decoding architecture) for semi-supervised and unsupervised labeling tasks, demonstrating gains over several strong baselines.
Asymptotic multiplicities of graded families of ideals and linear series

Abstract We find simple necessary and sufficient conditions on a local ring R of dimension d for the limit lim n → ∞ ⁡ l R ( R / I n ) n d to exist whenever { I n } is a graded family of m R -primary ideals, and give a number of applications. We also give simple necessary and sufficient conditions on projective schemes over a field k for asymptotic limits of the growth of all graded linear series of a fixed Kodaira–Iitaka dimension to exist.
What can space resources do for astronomy and planetary science

Abstract The rapid cost growth of flagship space missions has created a crisis for astronomy and planetary science. We have hit the funding wall. For the past 3 decades scientists have not had to think much about how space technology would change within their planning horizon. However, this time around enormous improvements in space infrastructure capabilities and, especially, costs are likely on the 20-year gestation periods for large space telescopes. Commercial space will lower launch and spacecraft costs substantially, enable cost-effective on-orbit servicing, cheap lunar landers and “interplanetary cubesats” by the early 2020s. A doubling of flagship launch rates is not implausible. On a longer timescale it will enable large structures to be assembled and constructed in space. These developments will change how we plan and design missions.
Paradoxes in Fair Computer-Aided Decision Making

Computer-aided decision making--where a human decision-maker is aided by a computational classifier in making a decision--is becoming increasingly prevalent. For instance, judges in at least nine states make use of algorithmic tools meant to determine "recidivism risk scores" for criminal defendants in sentencing, parole, or bail decisions. A subject of much recent debate is whether such algorithmic tools are "fair" in the sense that they do not discriminate against certain groups (e.g., races) of people. Our main result shows that for "non-trivial" computer-aided decision making, either the classifier must be discriminatory, or a rational decision-maker using the output of the classifier is forced to be discriminatory. We further provide a complete characterization of situations where fair computer-aided decision making is possible.
Bounded Verification with On-the-Fly Discrepancy Computation

Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing reachtubes from simulations. In this paper, we eliminate this requirement by presenting an algorithm for computing piecewise exponential discrepancy functions. The algorithm relies on computing local convergence or divergence rates of trajectories along a simulation using a coarse over-approximation of the reach set and bounding the maximal eigenvalue of the Jacobian over this over-approximation. The resulting discrepancy function preserves the soundness and the relative completeness of the verification algorithm. We also provide a coordinate transformation method to improve the local estimates for the convergence or divergence rates in practical examples. We extend the method to get the input-to-state discrepancy of nonlinear dynamical systems which can be used for compositional analysis. Our experiments show that the approach is effective in terms of running time for several benchmark problems, scales reasonably to larger dimensional systems, and compares favorably with respect to available tools for nonlinear models.
High-Girth matrices and polarization

The girth of a matrix is the least number of linearly dependent columns, in contrast to the rank which is the largest number of linearly independent columns. This paper considers the construction of high-girth matrices, whose probabilistic girth is close to their rank. Random matrices can be used to show the existence of high-girth matrices. This paper uses a recursive construction based on conditional ranks (inspired by polar codes) to obtain a deterministic and efficient construction of high-girth matrices for arbitrary relative ranks. Interestingly, the construction is agnostic to the underlying field and applies to both finite and continuous fields with the same binary matrix. The construction gives in particular the following: (i) over the binary field, high-girth matrices are equivalent to capacity-achieving codes, and our construction turns out to match exactly the BEC polar codes (even at finite block length). It hence gives a different interpretation of BEC polar codes, using the parity-check matrix instead of the generator matrix, and basic linear algebra instead of the mutual information, and generalizes to larger fields; (ii) for the BSC, our construction gives an operational meaning to the Bhattacharyya upper-bound process used in polar codes; (iii) for the reals, it gives an explicit candidate matrix for sparse recovery.
A data-driven statistical model for predicting the critical temperature of a superconductor

Abstract We estimate a statistical model to predict the superconducting critical temperature based on the features extracted from the superconductor’s chemical formula. The statistical model gives reasonable out-of-sample predictions: ±9.5 K based on root-mean-squared-error. Features extracted based on thermal conductivity, atomic radius, valence, electron affinity, and atomic mass contribute the most to the model’s predictive accuracy. It is crucial to note that our model does not predict whether a material is a superconductor or not; it only gives predictions for superconductors.
General strong polarization

Arikan’s exciting discovery of polar codes has provided an altogether new way to efficiently achieve Shannon capacity. Given a (constant-sized) invertible matrix M, a family of polar codes can be associated with this matrix and its ability to approach capacity follows from the polarization of an associated [0,1]-bounded martingale, namely its convergence in the limit to either 0 or 1 with probability 1. Arikan showed appropriate polarization of the martingale associated with the matrix G2 = ( [complex formula not displayed] ) to get capacity achieving codes. His analysis was later extended to all matrices M which satisfy an obvious necessary condition for polarization. While Arikan’s theorem does not guarantee that the codes achieve capacity at small blocklengths (specifically in length which is a polynomial in 1/є where є is the difference between the capacity of a channel and the rate of the code), it turns out that a “strong” analysis of the polarization of the underlying martingale would lead to such constructions. Indeed for the martingale associated with G2 such a strong polarization was shown in two independent works ([Guruswami and Xia, IEEE IT ’15] and [Hassani et al., IEEE IT’14]), thereby resolving a major theoretical challenge associated with the efficient attainment of Shannon capacity. In this work we extend the result above to cover martingales associated with all matrices that satisfy the necessary condition for (weak) polarization. In addition to being vastly more general, our proofs of strong polarization are (in our view) also much simpler and modular. Key to our proof is a notion of local polarization that only depends on the evolution of the martingale in a single time step. We show that local polarization always implies strong polarization. We then apply relatively simple reasoning about conditional entropies to prove local polarization in very general settings. Specifically, our result shows strong polarization over all prime fields and leads to efficient capacity-achieving source codes for compressing arbitrary i.i.d. sources, and capacity-achieving channel codes for arbitrary symmetric memoryless channels.
Confinement-induced orbital breathing, fusion, fission and re-ordering in semifilled shell atoms

Alternate contraction and drastic expansion, i.e., ?breathing? of electronic subshells, the effects of the fusion of two subshells into one subshell and its subsequent fission (splitting) into the original subshells, as well as multiple alteration of the order of subshells in confined semifilled shell atoms with a progressively narrowing confinement are theoretically discovered. The confinement is represented by a repulsive penetrable spherical potential of an inner radius r0. The effects are exemplified by calculated data for confined semifilled shell atoms from the second, third and fourth rows of Mendeleev's table?Li, N, P and Cr atoms with semifilled 2s1, 2p3, 3p3 and 3d5 subshells, respectively?for the completeness of the study. The underlying physics behind the discovered effects is explained.
Conversing by Reading: Contentful Neural Conversation with On-demand Machine Reading.

Although neural conversational models are effective in learning how to produce fluent responses, their primary challenge lies in knowing what to say to make the conversation contentful and non-vacuous. We present a new end-to-end approach to contentful neural conversation that jointly models response generation and on-demand machine reading. The key idea is to provide the conversation model with relevant long-form text on the fly as a source of external knowledge. The model performs QA-style reading comprehension on this text in response to each conversational turn, thereby allowing for more focused integration of external knowledge than has been possible in prior approaches. To support further research on knowledge-grounded conversation, we introduce a new large-scale conversation dataset grounded in external web pages (2.8M turns, 7.4M sentences of grounding). Both human evaluation and automated metrics show that our approach results in more contentful responses compared to a variety of previous methods, improving both the informativeness and diversity of generated output.
An adaptive algorithm for synchronization in diffusively-coupled systems

We present an adaptive algorithm that guarantees synchronization in diffusively-coupled systems. We first consider compartmental systems of ODEs where variables in each compartment are interconnected through diffusion terms with like variables in other compartments. Each set of variables may have its own weighted undirected graph describing the topology of the interconnection between compartments. The link weights are updated adaptively according to the magnitude of the difference between neighboring agents connected by the link. We next consider reaction-diffusion PDEs with Neumann boundary conditions and derive an analogous algorithm guaranteeing spatial homogenization of the solutions. We provide several numerical examples demonstrating the results.
Face Recognition with Hybrid Efficient Convolution Algorithms on FPGAs

Deep Convolutional Neural Networks (CNN) have become a Swiss knife in solving critical arti cial intelligence tasks. However, deploying deep CNN models for latency-critical tasks remains to be challenging because of the complex nature of CNNs. Recently, FPGA has become a favorable device to accelerate deep CNNs thanks to its high parallel processing capability and energy e ciency. In this work, we explore di erent fast convolution algorithms including Winograd and Fast Fourier Transform (FFT), and nd an optimal strategy to apply them together on di erent types of convolutions. We also propose an optimization scheme to exploit parallelism on novel CNN architectures such as Inception modules in GoogLeNet. We implement a con gurable IP-based face recognition acceler- ation system based on FaceNet using High-Level Synthesis. Our implementation on a Xilinx Ultrascale device achieves 3.75x la- tency speedup compared to a high-end NVIDIA GPU and surpasses previous FPGA results signi cantly.
d -Complete Posets: Local Structural Axioms, Properties, and Equivalent Definitions

Although d-complete posets arose along the interface between algebraic combinatorics and Lie theory, they are defined using only requirements on their local structure. These posets are a mutual generalization of rooted trees, shapes, and shifted shapes. They possess Stanley’s hook product property for their P-partition generating functions and Schutzenberger’s well-defined jeu de taquin rectification property. The original definition of d-complete poset was lengthy, but more succinct definitions were later developed. Here several definitions are shown to be equivalent. The basic properties of d-complete posets are summarized. Background and a partial bibliography for these posets is given.
Dynamical Isometry and a Mean Field Theory of CNNs: How to Train 10,000-Layer Vanilla Convolutional Neural Networks

In recent years, state-of-the-art methods in computer vision have utilized increasingly deep convolutional neural network architectures (CNNs), with some of the most successful models employing hundreds or even thousands of layers. A variety of pathologies such as vanishing/exploding gradients make training such deep networks challenging. While residual connections and batch normalization do enable training at these depths, it has remained unclear whether such specialized architecture designs are truly necessary to train deep CNNs. In this work, we demonstrate that it is possible to train vanilla CNNs with ten thousand layers or more simply by using an appropriate initialization scheme. We derive this initialization scheme theoretically by developing a mean field theory for signal propagation and by characterizing the conditions for dynamical isometry, the equilibration of singular values of the input-output Jacobian matrix. These conditions require that the convolution operator be an orthogonal transformation in the sense that it is norm-preserving. We present an algorithm for generating such random initial orthogonal convolution kernels and demonstrate empirically that they enable efficient training of extremely deep architectures.
Efficient, optimal k-leader selection for coherent, one-dimensional formations

We study the problem of optimal leader selection in consensus networks with noisy relative information. The objective is to identify the set of k leaders that minimizes the formation's deviation from the desired trajectory established by the leaders. An optimal leader set can be found by an exhaustive search over all possible leader sets; however, this approach is not scalable to large networks. In recent years, several works have proposed approximation algorithms to the k-leader selection problem, yet the question of whether there exists an efficient, non-combinatorial method to identify the optimal leader set remains open. This work takes a first step towards answering this question. We show that, in one-dimensional weighted graphs, namely path graphs and ring graphs, the k-leader selection problem can be solved in polynomial time (in both k and the network size n). We give an O(n3) solution for optimal k-leader selection in path graphs and an O(kn3) solution for optimal k-leader selection in ring graphs.
Optimal strong stationary times for random walks on the chambers of a hyperplane arrangement

This paper studies Markov chains on the chambers of real hyperplane arrangements, a model that generalizes famous examples, such as the Tsetlin library and riffle shuffles. We discuss cutoff for the Tsetlin library for general weights, and we give an exact formula for the separation distance for the hyperplane arrangement walk. We introduce lower bounds, which allow for the first time to study cutoff for hyperplane arrangement walks under certain conditions. Using similar techniques, we also prove a uniform lower bound for the mixing time of Glauber dynamics on a monotone system.