cssi/SciSciGPT-SciSciNet huggingface dataset:
SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS

We construct infinitely many compact, smooth 4-manifolds which are homotopy equivalent to $S^{2}$ but do not admit a spine (that is, a piecewise linear embedding of $S^{2}$ that realizes the homotopy equivalence). This is the remaining case in the existence problem for codimension-2 spines in simply connected manifolds. The obstruction comes from the Heegaard Floer $d$ invariants.
Cluster algebras of Grassmannians are locally acyclic

Considered as commutative algebras, cluster algebras can be very unpleasant objects. However, the first author introduced a condition known as "local acyclicity" which implies that cluster algebras behave reasonably. One of the earliest and most fundamental examples of a cluster algebra is the homogenous coordinate ring of the Grassmannian. We show that the Grassmannian is locally acyclic. Morally, we are in fact showing the stronger result that all positroid varieties are locally acyclic. However, it has not been shown that all positroid varieties have cluster structure, so what we actually prove is that certain cluster varieties associated to Postnikov's alternating strand diagrams are locally acylic. Moreover, we actually establish a slightly stronger property than local acyclicity, which we term the Louise property, that is designed to facilitate proofs involving the Mayer-Vietores sequence.
Addendum to computational complexity and black hole horizons

In this addendum to [arXiv:1402.5674] two points are discussed. In the first additional evidence is provided for a dual connection between the geometric length of an Einstein-Rosen bridge and the computational complexity of the quantum state of the dual CFT's. The relation between growth of complexity and Page's ``Extreme Cosmic Censorship" principle is also remarked on. The second point involves a gedanken experiment in which Alice measures a complete set of commuting observables at her end of an Einstein-Rosen bridge is discussed. An apparent paradox is resolved by appealing to the properties of GHZ tripartite entanglement.
Some recent developments in Lagrangian mean curvature flows

We review some recent results on the mean curvature flows of Lagrangian submanifolds from the perspective of geometric partial differential equations. These include global existence and convergence results, characterizations of first-time singularities, and constructions of self-similar solutions.
Convergence of Value Aggregation for Imitation Learning

Value aggregation is a general framework for solving imitation learning problems. Based on the idea of data aggregation, it generates a policy sequence by iteratively interleaving policy optimization and evaluation in an online learning setting. While the existence of a good policy in the policy sequence can be guaranteed non-asymptotically, little is known about the convergence of the sequence or the performance of the last policy. In this paper, we debunk the common belief that value aggregation always produces a convergent policy sequence with improving performance. Moreover, we identify a critical stability condition for convergence and provide a tight non-asymptotic bound on the performance of the last policy. These new theoretical insights let us stabilize problems with regularization, which removes the inconvenient process of identifying the best policy in the policy sequence in stochastic problems.
f-vectors of simplicial posets that are balls

Results of R. Stanley and M. Masuda completely characterize the h-vectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where the order complex is a ball. Using the face rings of these posets, we develop a series of new conditions on their h-vectors. We also present new methods for constructing poset balls with specific h-vectors. Combining this work with a new result of S. Murai we are able to give a complete characterization of the h-vectors of simplicial poset balls in all even dimensions, as well as odd dimensions less than or equal to five.
Deep Learning with Limited Numerical Precision

Training of large-scale deep neural networks is often constrained by the available computational resources. We study the effect of limited precision data representation and computation on neural network training. Within the context of lowprecision fixed-point computations, we observe the rounding scheme to play a crucial role in determining the network's behavior during training. Our results show that deep networks can be trained using only 16-bit wide fixed-point number representation when using stochastic rounding, and incur little to no degradation in the classification accuracy. We also demonstrate an energy-efficient hardware accelerator that implements low-precision fixed-point arithmetic with stochastic rounding.
Incentives for P2P-assisted content distribution: If you can't beat 'em, join 'em

The rapid growth of content distribution on the Internet has brought with it proportional increases in the costs of distributing content. Adding to distribution costs is the fact that digital content is easily duplicable, and hence can be shared in an illicit peer-to-peer (P2P) manner that generates no revenue for the content provider. In this paper, we study whether the content provider can recover lost revenue through a more innovative approach to distribution. In particular, we evaluate the benefits of a hybrid revenue-sharing system that combines a legitimate P2P swarm and a centralized client-server approach. We show how the revenue recovered by the content provider using a server-supported legitimate P2P swarm can exceed that of the monopolistic scheme by an order of magnitude. Our analytical results are obtained in a fluid model, and supported by stochastic simulations.
Particle image velocimetry (PIV) uncertainty quantification using moment of correlation (MC) plane

We present a new uncertainty estimation method for particle image velocimetry (PIV), that uses the correlation plane as a model for the probability density function (PDF) of displacements and calculates the second order moment of the correlation (MC). The cross-correlation between particle image patterns is the summation of all particle matches convolved with the apparent particle image diameter. MC uses this property to estimate the PIV uncertainty from the shape of the cross-correlation plane. In this new approach, the generalized cross-correlation (GCC) plane corresponding to a PIV measurement is obtained by removing the particle image diameter contribution. The GCC primary peak represents a discretization of the displacement PDF, from which the standard uncertainty is obtained by convolving the GCC plane with a Gaussian function. Then a Gaussian least-squares-fit is applied to the peak region, accounting for the stretching and rotation of the peak, due to the local velocity gradients and the effect of the convolved Gaussian. The MC method was tested with simulated image sets and the predicted uncertainties show good sensitivity to the error sources and agreement with the expected RMS error. Subsequently, the method was demonstrated in three PIV challenge cases and two experimental datasets and was compared with the published image matching (IM) and correlation statistics (CS) techniques. Results show that the MC method has a better response to spatial variation in RMS error and the predicted uncertainty is in good agreement with the expected standard uncertainty. The uncertainty prediction was also explored as a function of PIV interrogation window size. Overall, the MC method performance establishes itself as a valid uncertainty estimation tool for planar PIV.
Student-teacher learning for BLSTM mask-based speech enhancement

Spectral mask estimation using bidirectional long short-term memory (BLSTM) neural networks has been widely used in various speech enhancement applications, and it has achieved great success when it is applied to multichannel enhancement techniques with a mask-based beamformer. However, when these masks are used for single channel speech enhancement they severely distort the speech signal and make them unsuitable for speech recognition. This paper proposes a student-teacher learning paradigm for single channel speech enhancement. The beamformed signal from multichannel enhancement is given as input to the teacher network to obtain soft masks. An additional cross-entropy loss term with the soft mask target is combined with the original loss, so that the student network with single-channel input is trained to mimic the soft mask obtained with multichannel input through beamforming. Experiments with the CHiME-4 challenge single channel track data shows improvement in ASR performance.
Computing All Space Curve Solutions of Polynomial Systems by Polyhedral Methods

A polyhedral method to solve a system of polynomial equations exploits its sparse structure via the Newton polytopes of the polynomials. We propose a hybrid symbolic-numeric method to compute a Puiseux series expansion for every space curve that is a solution of a polynomial system. The focus of this paper concerns the difficult case when the leading powers of the Puiseux series of the space curve are contained in the relative interior of a higher dimensional cone of the tropical prevariety. We show that this difficult case does not occur for polynomials with generic coefficients. To resolve this case, we propose to apply polyhedral end games to recover tropisms hidden in the tropical prevariety.
DeepDiff: DEEP-learning for predicting DIFFerential gene expression from histone modifications

Motivation Computational methods that predict differential gene expression from histone modification signals are highly desirable for understanding how histone modifications control the functional heterogeneity of cells through influencing differential gene regulation. Recent studies either failed to capture combinatorial effects on differential prediction or primarily only focused on cell type-specific analysis. In this paper we develop a novel attention-based deep learning architecture, DeepDiff, that provides a unified and end-to-end solution to model and to interpret how dependencies among histone modifications control the differential patterns of gene regulation. DeepDiff uses a hierarchy of multiple Long Short-Term Memory (LSTM) modules to encode the spatial structure of input signals and to model how various histone modifications cooperate automatically. We introduce and train two levels of attention jointly with the target prediction, enabling DeepDiff to attend differentially to relevant modifications and to locate important genome positions for each modification. Additionally, DeepDiff introduces a novel deep-learning based multi-task formulation to use the cell-type-specific gene expression predictions as auxiliary tasks, encouraging richer feature embeddings in our primary task of differential expression prediction. Results Using data from Roadmap Epigenomics Project (REMC) for ten different pairs of cell types, we show that DeepDiff significantly outperforms the state-of-the-art baselines for differential gene expression prediction. The learned attention weights are validated by observations from previous studies about how epigenetic mechanisms connect to differential gene expression. Availability and implementation Codes and results are available at deepchrome.org. Supplementary information Supplementary data are available at Bioinformatics online.
A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes

How can we efficiently gather information to optimize an unknown function, when presented with multiple, mutually dependent information sources with different costs? For example, when optimizing a physical system, intelligently trading off computer simulations and real-world tests can lead to significant savings. Existing multi-fidelity Bayesian optimization methods, such as multi-fidelity GP-UCB or Entropy Search-based approaches, either make simplistic assumptions on the interaction among different fidelities or use simple heuristics that lack theoretical guarantees. In this paper, we study multi-fidelity Bayesian optimization with complex structural dependencies among multiple outputs, and propose MF-MI-Greedy, a principled algorithmic framework for addressing this problem. In particular, we model different fidelities using additive Gaussian processes based on shared latent relationships with the target function. Then we use cost-sensitive mutual information gain for efficient Bayesian optimization. We propose a simple notion of regret which incorporates the varying cost of different fidelities, and prove that MF-MI-Greedy achieves low regret. We demonstrate the strong empirical performance of our algorithm on both synthetic and real-world datasets.
Combinatorial Miller–Hagberg Algorithm for Randomization of Dense Networks

We propose a slightly revised Miller–Hagberg (MH) algorithm that efficiently generates a random network from a given expected degree sequence. The revision was to replace the approximated edge probability between a pair of nodes with a combinatorically calculated edge probability that better captures the likelihood of edge presence especially, where edges are dense. The computational complexity of this combinatorial MH algorithm is still in the same order as the original one. We evaluated the proposed algorithm through several numerical experiments. The results demonstrated that the proposed algorithm was particularly good at accurately representing high-degree nodes in dense, heterogeneous networks. This algorithm may be a useful alternative to other more established network randomization methods, given that the data are increasingly becoming larger and denser in today’s network science research.
Self-learning to detect and segment cysts in lung CT images without manual annotation

Image segmentation is a fundamental problem in medical image analysis. In recent years, deep neural networks achieve impressive performances on many medical image segmentation tasks by supervised learning on large manually annotated data. However, expert annotations on big medical datasets are tedious, expensive or sometimes unavailable. Weakly supervised learning could reduce the effort for annotation but still required certain amounts of expertise. Recently, deep learning shows a potential to produce more accurate predictions than the original erroneous labels. Inspired by this, we introduce a very weakly supervised learning method, for cystic lesion detection and segmentation in lung CT images, without any manual annotation. Our method works in a self-learning manner, where segmentation generated in previous steps (first by unsupervised segmentation then by neural networks) is used as ground truth for the next level of network learning. Experiments on a cystic lung lesion dataset show that the deep learning could perform better than the initial unsupervised annotation, and progressively improve itself after self-learning.
Finding bottlenecks: Predicting student attrition with unsupervised classifier

With pressure to increase graduation rates and reduce time to degree in higher education, it is important to identify at-risk students early. Automated early warning systems are therefore highly desirable. In this paper, we use unsupervised clustering techniques to predict the graduation status of declared majors in five departments at California State University Northridge (CSUN), based on a minimal number of lower division courses in each major. In addition, we use the detected clusters to identify hidden bottleneck courses.
Plug-and-Play ADMM for Image Restoration: Fixed-Point Convergence and Applications

Alternating direction method of multiplier (ADMM) is a widely used algorithm for solving constrained optimization problems in image restoration. Among many useful features, one critical feature of the ADMM algorithm is its modular structure, which allows one to plug in any off-the-shelf image denoising algorithm for a subproblem in the ADMM algorithm. Because of the plug-in nature, this type of ADMM algorithms is coined the name “Plug-and-Play ADMM.” Plug-and-Play ADMM has demonstrated promising empirical results in a number of recent papers. However, it is unclear under what conditions and by using what denoising algorithms would it guarantee convergence. Also, since Plug-and-Play ADMM uses a specific way to split the variables, it is unclear if fast implementation can be made for common Gaussian and Poissonian image restoration problems. In this paper, we propose a Plug-and-Play ADMM algorithm with provable fixed-point convergence. We show that for any denoising algorithm satisfying an asymptotic criteria, called bounded denoisers, Plug-and-Play ADMM converges to a fixed point under a continuation scheme. We also present fast implementations for two image restoration problems on superresolution and single-photon imaging. We compare Plug-and-Play ADMM with state-of-the-art algorithms in each problem type and demonstrate promising experimental results of the algorithm.
A Ricci flow proof of a result by Gromov on lower bounds for scalar curvature

In this note we reprove a theorem of Gromov using Ricci flow. The theorem states that a, possibly non-constant, lower bound on the scalar curvature is stable under $C^0$-convergence of the metric.
Proximal Distance Algorithms: Theory and Practice.

Author(s): Keys, Kevin L; Zhou, Hua; Lange, Kenneth | Abstract: Proximal distance algorithms combine the classical penalty method of constrained minimization with distance majorization. If f(x) is the loss function, and C is the constraint set in a constrained minimization problem, then the proximal distance principle mandates minimizing the penalized loss f(x)+ρ2dist(x,C)2 and following the solution x ρ to its limit as ρ tends to ∞. At each iteration the squared Euclidean distance dist(x,C)2 is majorized by the spherical quadratic ‖x- P C (x k )‖2, where P C (x k ) denotes the projection of the current iterate x k onto C. The minimum of the surrogate function f(x)+ρ2‖x-PC(xk)‖2 is given by the proximal map prox ρ -1f [P C (x k )]. The next iterate x k+1 automatically decreases the original penalized loss for fixed ρ. Since many explicit projections and proximal maps are known, it is straightforward to derive and implement novel optimization algorithms in this setting. These algorithms can take hundreds if not thousands of iterations to converge, but the simple nature of each iteration makes proximal distance algorithms competitive with traditional algorithms. For convex problems, proximal distance algorithms reduce to proximal gradient algorithms and therefore enjoy well understood convergence properties. For nonconvex problems, one can attack convergence by invoking Zangwill's theorem. Our numerical examples demonstrate the utility of proximal distance algorithms in various high-dimensional settings, including a) linear programming, b) constrained least squares, c) projection to the closest kinship matrix, d) projection onto a second-order cone constraint, e) calculation of Horn's copositive matrix index, f) linear complementarity programming, and g) sparse principal components analysis. The proximal distance algorithm in each case is competitive or superior in speed to traditional methods such as the interior point method and the alternating direction method of multipliers (ADMM). Source code for the numerical examples can be found at https://github.com/klkeys/proxdist.
From discrete flow of Beckner to continuous flow of Janson in complex hypercontractivity

Abstract We show how Beckner's montonicity result on Hamming cube easily implies the monotonicity of a flow introduced by Janson in Hausdorff–Young inequality
Adaptive Bayesian Sampling with Monte Carlo EM

We present a novel technique for learning the mass matrices in samplers obtained from discretized dynamics that preserve some energy function. Existing adaptive samplers use Riemannian preconditioning techniques, where the mass matrices are functions of the parameters being sampled. This leads to significant complexities in the energy reformulations and resultant dynamics, often leading to implicit systems of equations and requiring inversion of high-dimensional matrices in the leapfrog steps. Our approach provides a simpler alternative, by using existing dynamics in the sampling step of a Monte Carlo EM framework, and learning the mass matrices in the M step with a novel online technique. We also propose a way to adaptively set the number of samples gathered in the E step, using sampling error estimates from the leapfrog dynamics. Along with a novel stochastic sampler based on Nos\'{e}-Poincar\'{e} dynamics, we use this framework with standard Hamiltonian Monte Carlo (HMC) as well as newer stochastic algorithms such as SGHMC and SGNHT, and show strong performance on synthetic and real high-dimensional sampling scenarios; we achieve sampling accuracies comparable to Riemannian samplers while being significantly faster.
Filtrations, 1-parameter subgroups, and rational injectivity

Abstract We investigate rational G-modules M for a linear algebraic group G over an algebraically closed field k of characteristic p > 0 using filtrations by sub-coalgebras of the coordinate algebra k [ G ] of G. Even in the special case of the additive group G a , interesting structures and examples are revealed. The “degree” filtration we consider for unipotent algebraic groups leads to a “filtration by exponential degree” applicable to rational G modules for any linear algebraic group G of exponential type; this filtration is defined in terms of 1-parameter subgroups and is related to support varieties introduced recently by the author for such rational G-modules. We formulate in terms of this filtration a necessary and sufficient condition for rational injectivity for rational G-modules. Our investigation leads to the consideration of two new classes of rational G-modules: those that are “mock injective” and those that are “mock trivial”.
Representations of the Kauffman bracket skein algebra III: closed surfaces and naturality

This is the third article in the series begun with [BonWon3, BonWon4], devoted to finite-dimensional representations of the Kauffman bracket skein algebra of an oriented surface $S$. In [BonWon3] we associated a classical shadow to an irreducible representation $\rho$ of the skein algebra, which is a character $r_\rho \in \mathcal R_{\mathrm{SL}_2(\mathbb C)}(S)$ represented by a group homomorphism $\pi_1(S) \to \mathrm{SL}_2(\mathbb C)$. The main result of the current article is that, when the surface $S$ is closed, every character $r\in \mathcal R_{\mathrm{SL}_2(\mathbb C)}(S)$ occurs as the classical shadow of an irreducible representation of the Kauffman bracket skein algebra. We also prove that the construction used in our proof is natural, and associates to each group homomorphism $r\colon \pi_1(S) \to \mathrm{SL}_2(\mathbb C)$ a representation of the skein algebra $\mathcal S^A(S)$ that is uniquely determined up to isomorphism.
Powers of ideals and fibers of morphisms

Let $X\subset \PP^n=\PP^n_F$ be a projective scheme over a field $F$, and let $\phi:X\to Y$ be a finite morphism. Our main result is a formula, in terms of global data, for the maximum of $\reg \phi^{-1}(y)$, the Castelnuovo-Mumford regularity of a fiber of $\phi$ over a point $y\in Y$, where the fiber $\phi^{-1}(y)$ is considered as a subscheme of $\PP^n$. For example, Cutkosky-Herzog-Trung \cite{CHT1999} and Kodiyalam \cite{Kodiyalam2000} showed that for any homogeneous ideal $I$ in a standard graded algebra $S$, $\reg I^t$ can be written as $ dt+\epsilon$ for some non-negative integers $d,\epsilon$ and all large $t$. If $I$ contains a power of $S_+$ and is generated by forms of a single degree, then it determines a morphism $\phi: X:= \Proj(S) \to Y :=\PP^m$ as above. In this situation our theorem states that the maximum of the regularities of the fibers of $\phi$ is precisely $\epsilon+1$. Our formula also gives new information about powers of ideals generated by generic forms in polynomial rings.
Iterative Visual Reasoning Beyond Convolutions

We present a novel framework for iterative visual reasoning. Our framework goes beyond current recognition systems that lack the capability to reason beyond stack of convolutions. The framework consists of two core modules: a local module that uses spatial memory [4] to store previous beliefs with parallel updates; and a global graph-reasoning module. Our graph module has three components: a) a knowledge graph where we represent classes as nodes and build edges to encode different types of semantic relationships between them; b) a region graph of the current image where regions in the image are nodes and spatial relationships between these regions are edges; c) an assignment graph that assigns regions to classes. Both the local module and the global module roll-out iteratively and cross-feed predictions to each other to refine estimates. The final predictions are made by combining the best of both modules with an attention mechanism. We show strong performance over plain ConvNets, e.g. achieving an 8.4% absolute improvement on ADE [55] measured by per-class average precision. Analysis also shows that the framework is resilient to missing regions for reasoning.
Flexibility of entropies for surfaces of negative curvature

We consider a smooth closed surface M of fixed genus ⩾ 2 with a Rie-mannian metric g of negative curvature with fixed total area. The second author has shown that the topological entropy of geodesic flow for g is greater than or equal to the topological entropy for the metric of constant negative curvature on M with the same total area which is greater than or equal to the metric entropy with respect to the Liouville measure of geodesic flow for g. Equality holds only in the case of constant negative curvature. We prove that those are the only restrictions on the values of topological and metric entropies for metrics of negative curvature.
Secondary power operations and the Brown-Peterson spectrum at the prime 2

The dual Steenrod algebra has a canonical subalgebra isomorphic to the homology of the Brown-Peterson spectrum. We will construct a secondary operation in mod-2 homology and show that this canonical subalgebra is not closed under it. This allows us to conclude that the 2-primary Brown-Peterson spectrum does not admit the structure of an E_n-algebra for any n greater than or equal to 12, answering a question of May in the negative.
The geometry of nodal sets and outlier detection

Abstract Let ( M , g ) be a compact manifold and let − Δ ϕ k = λ k ϕ k be the sequence of Laplacian eigenfunctions. We present a curious new phenomenon which, so far, we only managed to understand in a few highly specialized cases: the family of functions f N : M → R ≥ 0 f N ( x ) = ∑ k ≤ N 1 λ k | ϕ k ( x ) | ‖ ϕ k ‖ L ∞ ( M ) and their extrema seem strangely suited for the detection of anomalous points on the manifold. It may be heuristically interpreted as the sum over distances to the nearest nodal line and potentially hints at a new phenomenon in spectral geometry. We give rigorous statements on the unit square [ 0 , 1 ] 2 (where minima localize in Q 2 ) and on Paley graphs (where f N recovers the geometry of quadratic residues of the underlying finite field F p ). Numerical examples show that the phenomenon seems to arise on fairly generic manifolds.
Inviscid criterion for decomposing scales

Length scale in a flow depends on the decryption key used to decipher length scales and the communications between them. Analysis shows that some of the decryption keys widely used can, in fact, obfuscate the physics, whereas one of them allows us to unravel the correct multiscale dynamics.
An equivalence relation on the symmetric group and multiplicity-free flag $h$-vectors

We consider the equivalence relation ∼ on the symmetric group Sn generated by the interchange of any two adjacent elements ai and ai+1 of w = a1 · · · an ∈ Sn such that |ai − ai+1| = 1. We count the number of equivalence classes and the sizes of the equivalence classes. The results are generalized to permutations of multisets. In the original problem, the equivalence class containing the identity permutation is the set of linear extensions of a certain poset. Further investigation yields a characterization of all finite graded posets whose flag h-vector takes on only the values 0,±1.
Linear and bilinear restriction to certain rotationally symmetric hypersurfaces

Conditional on Fourier restriction estimates for elliptic hypersurfaces, we prove optimal restriction estimates for polynomial hypersurfaces of revolution for which the defining polynomial has non-negative coefficients. In particular, we obtain uniform--depending only on the dimension and polynomial degree--estimates for restriction with affine surface measure, slightly beyond the bilinear range. The main step in the proof of our linear result is an (unconditional) bilinear adjoint restriction estimate for pieces at different scales.
Conversational Flow in Oxford-style Debates

Public debates are a common platform for presenting and juxtaposing diverging views on important issues. In this work we propose a methodology for tracking how ideas flow between participants throughout a debate. We use this approach in a case study of Oxford-style debates---a competitive format where the winner is determined by audience votes---and show how the outcome of a debate depends on aspects of conversational flow. In particular, we find that winners tend to make better use of a debate's interactive component than losers, by actively pursuing their opponents' points rather than promoting their own ideas over the course of the conversation.
Entropy for expansive algebraic actions of residually finite groups

We prove a formula for the sofic entropy of expansive principal algebraic actions of residually finite groups, extending recent work of Deninger and Schmidt.
On the Energy Equality for Distributional Solutions to Navier-Stokes Equations

A classical result of J.-L. Lions asserts that if a solution to the Navier-Stokes equations is such that: (i) it is in the Leray-Hopf class, and (ii) belongs to $L^4(0,T;L^4)$, then it must satisfy the energy equality in the time interval $[0,T]$. In this note we show that assumption (i) is not necessary.
On the hereditary discrepancy of homogeneous arithmetic progressions

We show that the hereditary discrepancy of homogeneous arithmetic progressions is lower bounded by n1/O(loglogn). This bound is tight up to the constant in the exponent. Our lower bound goes via proving an exponential lower bound on the discrepancy of set systems of subcubes of the boolean cube {0,1}d
A Lyapunov-based Approach to Safe Reinforcement Learning

In many real-world reinforcement learning (RL) problems, besides optimizing the main objective function, an agent must concurrently avoid violating a number of constraints. In particular, besides optimizing performance, it is crucial to guarantee the safety of an agent during training as well as deployment (e.g., a robot should avoid taking actions - exploratory or not - which irrevocably harm its hard- ware). To incorporate safety in RL, we derive algorithms under the framework of constrained Markov decision processes (CMDPs), an extension of the standard Markov decision processes (MDPs) augmented with constraints on expected cumulative costs. Our approach hinges on a novel Lyapunov method. We define and present a method for constructing Lyapunov functions, which provide an effective way to guarantee the global safety of a behavior policy during training via a set of local linear constraints. Leveraging these theoretical underpinnings, we show how to use the Lyapunov approach to systematically transform dynamic programming (DP) and RL algorithms into their safe counterparts. To illustrate their effectiveness, we evaluate these algorithms in several CMDP planning and decision-making tasks on a safety benchmark domain. Our results show that our proposed method significantly outperforms existing baselines in balancing constraint satisfaction and performance.
Online Adaptive Image Reconstruction (OnAIR) Using Dictionary Models

Sparsity and low-rank models have been popular for reconstructing images and videos from limited or corrupted measurements. Dictionary or transform learning methods are useful in applications such as denoising, inpainting, and medical image reconstruction. In this paper, we propose a framework for online (or time-sequential) adaptive reconstruction of dynamic image sequences from linear (typically undersampled) measurements. We model the spatiotemporal patches of the underlying dynamic image sequence as sparse in a dictionary, and we simultaneously estimate the dictionary and the images sequentially from streaming measurements. Multiple constraints on the adapted dictionary are also considered such as a unitary matrix, or low-rank dictionary atoms that provide additional efficiency or robustness. The proposed online algorithms are memory efficient and involve simple updates of the dictionary atoms, sparse coefficients, and images. Numerical experiments demonstrate the usefulness of the proposed methods in inverse problems such as video reconstruction or inpainting from noisy, subsampled pixels, and dynamic magnetic resonance image reconstruction from very limited measurements.
Efficient Neutrino Oscillation Parameter Inference with Gaussian Process

Many experiments have been set-up to measure the parameters governing the neutrino oscillation probabilities accurately, with implications for the fundamental structure of the universe. Very often, this involves inferences from tiny samples of data which have complicated dependencies on multiple oscillation parameters simultaneously. This is typically carried out using the unified approach of Feldman and Cousins which is very computationally expensive, on the order of tens of millions of CPU hours. In this work, we propose an iterative method using Gaussian Process to efficiently find a confidence contour for the oscillation parameters and show that it produces the same results at a fraction of the computation cost.
Optimal Average-Case Reductions to Sparse PCA: From Weak Assumptions to Strong Hardness

In the past decade, sparse principal component analysis has emerged as an archetypal problem for illustrating statistical-computational tradeoffs. This trend has largely been driven by a line of research aiming to characterize the average-case complexity of sparse PCA through reductions from the planted clique (PC) conjecture - which conjectures that there is no polynomial-time algorithm to detect a planted clique of size $K = o(N^{1/2})$ in $\mathcal{G}(N, \frac{1}{2})$. All previous reductions to sparse PCA either fail to show tight computational lower bounds matching existing algorithms or show lower bounds for formulations of sparse PCA other than its canonical generative model, the spiked covariance model. Also, these lower bounds all quickly degrade with the exponent in the PC conjecture. Specifically, when only given the PC conjecture up to $K = o(N^\alpha)$ where $\alpha < 1/2$, there is no sparsity level $k$ at which these lower bounds remain tight. If $\alpha \le 1/3$ these reductions fail to even show the existence of a statistical-computational tradeoff at any sparsity $k$. We give a reduction from PC that yields the first full characterization of the computational barrier in the spiked covariance model, providing tight lower bounds at all sparsities $k$. We also show the surprising result that weaker forms of the PC conjecture up to clique size $K = o(N^\alpha)$ for any given $\alpha \in (0, 1/2]$ imply tight computational lower bounds for sparse PCA at sparsities $k = o(n^{\alpha/3})$. This shows that even a mild improvement in the signal strength needed by the best known polynomial-time sparse PCA algorithms would imply that the hardness threshold for PC is subpolynomial. This is the first instance of a suboptimal hardness assumption implying optimal lower bounds for another problem in unsupervised learning.
How do lenders monitor? A discussion of Shan, Tang, and Winton (2019)

Abstract Credit `default swaps (CDS) represent a major innovation in debt markets, allowing lenders to transfer credit risk to a counterparty by paying a premium. Shan, Tang, and Winton (2019) explore whether the availability of CDS affects the monitoring incentives of lenders. Their paper finds that CDS leads to looser loan terms (less collateral and looser covenants), consistent with a reduction in monitoring incentives. I examine several aspects of their study, including whether loan provisions and CDS should serve the same purpose, and differences between CDS and non-CDS borrowers. In total, although the authors present empirical evidence consistent with their prediction, the sample selection and research design potentially limit the generalizability of the authors’ results.
An Honest Day's Pay: Cooperation among Entrepreneurs vs. Students, and Linkages to Real‐World Business Success

The importance of cooperative behavior in business environments has been theorized in the field of management. However, measuring cooperation quantitatively is often challenging. We take advantage of experimental methods to overcome this issue. Particularly, we study the decisions that small‐scale entrepreneurs in Ulaanbaatar, Mongolia, make in a laboratory property rights dilemma experiment, comparing these to the decisions of student counterparts in the same and other countries, and looking for correlations between lab decisions and success in real‐world business sales. We find that Mongolian entrepreneurs generally achieve much higher cooperation levels and hence higher experimental earnings than Mongolian students. Also, among individual participants, producing and desisting from theft in the lab setting is correlated at the 1% level with real‐world business sales. Our findings align with the view that cooperative impulses or abidance of social norms can be an advantage in business relationships.
Nonlinear System Identification of Soft Robot Dynamics Using Koopman Operator Theory

Soft robots are challenging to model due in large part to the nonlinear properties of soft materials. Fortunately, this softness makes it possible to safely observe their behavior under random control inputs, making them amenable to large-scale data collection and system identification. This paper implements and evaluates a system identification method based on Koopman operator theory in which models of nonlinear dynamical systems are constructed via linear regression of observed data by exploiting the fact that every nonlinear system has a linear representation in the infinite-dimensional space of real-valued functions called observables. The approach does not suffer from some of the shortcomings of other nonlinear system identification methods, which typically require the manual tuning of training parameters and have limited convergence guarantees. A dynamic model of a pneumatic soft robot arm is constructed via this method, and used to predict the behavior of the real system. The total normalized-root-mean-square error (NRMSE) of its predictions is lower than that of several other identified models including a neural network, NLARX, nonlinear Hammerstein-Wiener, and linear state space model.
Algorithmic No-Cloning Theorem

We introduce notions of algorithmic mutual information and deficiency of randomness of quantum states. These definitions enjoy conservation inequalities over unitary transformations and partial traces. We show that a large majority of pure states have minute self-algorithmic information. We provide an algorithmic variant to the no-cloning theorem, by showing that only a small minority of quantum pure states can clone a nonnegligible amount of algorithmic information. We also provide a chain rule inequality for quantum algorithmic entropy. We show that deficiency of randomness does not increase under POVM measurements.
Serial collusion by multi-product firms

We provide empirical evidence that many multi-product firms have each participated in several cartels over the past 50 years. Standard analysis of cartel conduct, as well as enforcement policy, is rooted in the presumption that each cartel in which a given firm participates is a singular activity, independent of other cartel conduct by the firm. We argue that this analysis is deficient in many respects in the face of serial collusion by multi-product firms. We offer policy recommendations to reign in serial collusion, including a mandatory coordinated effects review for any merger involving a serial colluder, regardless of the apparent nature of the merger.
ASTROL—An associative structure-oriented language

The language ASTROL resulted from the search for a "small" language somewhat like LISP 1.5 which could be easily implemented on a minicomputer with about 32K bytes of store. The LISP cell was considered to be an example of the record—an object whose structure is specified by a set of field descriptors. However, the set of descriptors is often allocated at compile time, whereas it would be useful to be able to add descriptors to a record dynamically.
Working Hard or Hardly Working: Challenges of Integrating Typology into Neural Dependency Parsers

This paper explores the task of leveraging typology in the context of cross-lingual dependency parsing. While this linguistic information has shown great promise in pre-neural parsing, results for neural architectures have been mixed. The aim of our investigation is to better understand this state-of-the-art. Our main findings are as follows: 1) The benefit of typological information is derived from coarsely grouping languages into syntactically-homogeneous clusters rather than from learning to leverage variations along individual typological dimensions in a compositional manner; 2) Typology consistent with the actual corpus statistics yields better transfer performance; 3) Typological similarity is only a rough proxy of cross-lingual transferability with respect to parsing.
Quantum Simulation of Nanocrystalline Composite Thermoelectric Properties

The electrical transport properties of semiconductor nanocrystalline composite (NCC) thermoelectric structures were studied from a quantum point of view using a 2D non equilibrium Green's function (NEGF) computational approach. Previous researchers have shown enhancement in thermal properties of NCC devices but have not extensively studied their electrical transport properties for increased thermoelectric performance. The NCC structure was parameterized to determine the performance as a function of crystal spacing and crystal size. Results indicate that a silicon matrix (well) and a germanium crystal (barrier) configuration result in the highest Seebeck coefficient. Power factors of NCC devices were compared to equivalent superlattice devices, and greater performance was shown for equivalent NCC characteristic lengths.
SPECTRAHEDRAL LIFTS OF CONVEX SETS

Efficient representations of convex sets are of crucial importance for many algorithms that work with them. It is well-known that sometimes, a complicated convex set can be expressed as the projection of a much simpler set in higher dimensions called a lift of the original set. This is a brief survey of recent developments in the topic of lifts of convex sets. Our focus will be on lifts that arise from affine slices of real positive semidefinite cones known as psd or spectrahedral lifts. The main result is that projection representations of a convex set are controlled by factorizations, through closed convex cones, of an operator that comes from the convex set. This leads to several research directions and results that lie at the intersection of convex geometry, combinatorics, real algebraic geometry, optimization, computer science and more.
Rigidity theorems for circle domains

A circle domain $$\Omega $$ in the Riemann sphere is conformally rigid if every conformal map from $$\Omega $$ onto another circle domain is the restriction of a Mobius transformation. We show that circle domains satisfying a certain quasihyperbolic condition, which was considered by Jones and Smirnov (Ark Mat 38, 263–279, 2000), are conformally rigid. In particular, Holder circle domains and John circle domains are all conformally rigid. This provides new evidence for a conjecture of He and Schramm relating rigidity and conformal removability.
Voluntary Chronic Heavy Alcohol Consumption in Male Rhesus Macaques Suppresses Cancellous Bone Formation and Increases Bone Marrow Adiposity

Background Chronic heavy alcohol consumption is an established risk factor for bone fracture, but comorbidities associated with alcohol intake may contribute to increased fracture rates in alcohol abusers. To address the specific effects of alcohol on bone, we used a nonhuman primate model and evaluated voluntary alcohol consumption on: (i) global markers of bone turnover in blood and (ii) cancellous bone mass, density, microarchitecture, turnover, and microdamage in lumbar vertebra. Methods Following a 4-month induction period, 6-year-old male rhesus macaques (Macaca mulatta, n = 13) voluntarily self-administered water or ethanol (EtOH; 4% w/v) for 22 h/d, 7 d/wk, for a total of 12 months. Control animals (n = 9) consumed an isocaloric maltose-dextrin solution. Tetracycline hydrochloride was administered orally 17 and 3 days prior to sacrifice to label mineralizing bone surfaces. Global skeletal response to EtOH was evaluated by measuring plasma osteocalcin and carboxyterminal collagen cross-links (CTX). Local response was evaluated in lumbar vertebra using dual-energy X-ray absorptiometry, microcomputed tomography, static and dynamic histomorphometry, and histological assessment of microdamage. Results Monkeys in the EtOH group consumed an average of 2.8 ± 0.2 (mean ± SE) g/kg/d of EtOH (30 ± 2% of total calories), resulting in an average blood EtOH concentration of 88.3 ± 8.8 mg/dl 7 hours after the session onset. Plasma CTX and osteocalcin tended to be lower in EtOH-consuming monkeys compared to controls. Significant differences in bone mineral density in lumbar vertebrae 1 to 4 were not detected with treatment. However, cancellous bone volume fraction (in cores biopsied from the central region of the third vertebral body) was lower in EtOH-consuming monkeys compared to controls. Furthermore, EtOH-consuming monkeys had lower osteoblast perimeter and mineralizing perimeter, no significant difference in osteoclast perimeter, and higher bone marrow adiposity than controls. No significant differences between groups were detected in microcrack density (2nd lumbar vertebra). Conclusions Voluntary chronic heavy EtOH consumption reduces cancellous bone formation in lumbar vertebra by decreasing osteoblast-lined bone perimeter, a response associated with an increase in bone marrow adiposity.
GANCoder: An Automatic Natural Language-to-Programming Language Translation Approach based on GAN

We propose GANCoder, an automatic programming approach based on Generative Adversarial Networks (GAN), which can generate the same functional and logical programming language codes conditioned on the given natural language utterances. The adversarial training between generator and discriminator helps generator learn distribution of dataset and improve code generation quality. Our experimental results show that GANCoder can achieve comparable accuracy with the state-of-the-art methods and is more stable when programming languages.