cssi/SciSciGPT-SciSciNet huggingface dataset:
Clustering subgaussian mixtures by semidefinite programming

We introduce a model-free relax-and-round algorithm for k-means clustering based on a semidefinite relaxation due to Peng and Wei. The algorithm interprets the SDP output as a denoised version of the original data and then rounds this output to a hard clustering. We provide a generic method for proving performance guarantees for this algorithm, and we analyze the algorithm in the context of subgaussian mixture models. We also study the fundamental limits of estimating Gaussian centers by k-means clustering in order to compare our approximation guarantee to the theoretically optimal k-means clustering solution.
A Residual Bootstrap for High-Dimensional Regression with Near Low-Rank Designs

We study the residual bootstrap (RB) method in the context of high-dimensional linear regression. Specifically, we analyze the distributional approximation of linear contrasts $c^{\top}(\hat{\beta}_{\rho}-\beta)$, where $\hat{\beta}_{\rho}$ is a ridge-regression estimator. When regression coefficients are estimated via least squares, classical results show that RB consistently approximates the laws of contrasts, provided that p ≪ n, where the design matrix is of size n × p. Up to now, relatively little work has considered how additional structure in the linear model may extend the validity of RB to the setting where p/n ≍ 1. In this setting, we propose a version of RB that resamples residuals obtained from ridge regression. Our main structural assumption on the design matrix is that it is nearly low rank — in the sense that its singular values decay according to a power-law profile. Under a few extra technical assumptions, we derive a simple criterion for ensuring that RB consistently approximates the law of a given contrast. We then specialize this result to study confidence intervals for mean response values X⊤i β, where X⊤i is the ith row of the design. More precisely, we show that conditionally on a Gaussian design with near low-rank structure, RB simultaneously approximates all of the laws $X_i^{\top}(\hat{\beta}_{\rho}-\beta)$, i = 1,..., n. This result is also notable as it imposes no sparsity assumptions on β. Furthermore, since our consistency results are formulated in terms of the Mallows (Kantorovich) metric, the existence of a limiting distribution is not required.
Cohen-Macaulayness of Rees algebras of diagonal ideals

Given two determinantal rings over a field $k$, we consider the Rees algebra of the diagonal ideal, the kernel of the multiplication map. The special fiber ring of the diagonal ideal is the homogeneous coordinate ring of the secant variety. When the Rees algebra and the symmetric algebra coincide, we show that the Rees algebra is Cohen-Macaulay.
Saturation numbers for Ramsey-minimal graphs

Given graphs $H_1, \dots, H_t$, a graph $G$ is $(H_1, \dots, H_t)$-Ramsey-minimal if every $t$-coloring of the edges of $G$ contains a monochromatic $H_i$ in color $i$ for some $i\in\{1, \dots, t\}$, but any proper subgraph of $G $ does not possess this property. We define $\mathcal{R}_{\min}(H_1, \dots, H_t)$ to be the family of $(H_1, \dots, H_t)$-Ramsey-minimal graphs. A graph $G$ is \dfn{$\mathcal{R}_{\min}(H_1, \dots, H_t)$-saturated} if no element of $\mathcal{R}_{\min}(H_1, \dots, H_t)$ is a subgraph of $G$, but for any edge $e$ in $\overline{G}$, some element of $\mathcal{R}_{\min}(H_1, \dots, H_t)$ is a subgraph of $G + e$. We define $sat(n, \mathcal{R}_{\min}(H_1, \dots, H_t))$ to be the minimum number of edges over all $\mathcal{R}_{\min}(H_1, \dots, H_t)$-saturated graphs on $n$ vertices. In 1987, Hanson and Toft conjectured that $sat(n, \mathcal{R}_{\min}(K_{k_1}, \dots, K_{k_t}) )= (r - 2)(n - r + 2)+\binom{r - 2}{2} $ for $n \ge r$, where $r=r(K_{k_1}, \dots, K_{k_t})$ is the classical Ramsey number for complete graphs. The first non-trivial case of Hanson and Toft's conjecture for sufficiently large $n$ was setteled in 2011, and is so far the only settled case. Motivated by Hanson and Toft's conjecture, we study the minimum number of edges over all $\mathcal{R}_{\min}(K_3, \mathcal{T}_k)$-saturated graphs on $n$ vertices, where $\mathcal{T}_k$ is the family of all trees on $k$ vertices. We show that for $n \ge 18$, $sat(n, \mathcal{R}_{\min}(K_3, \mathcal{T}_4)) =\lfloor {5n}/{2}\rfloor$. For $k \ge 5$ and $n \ge 2k + (\lceil k/2 \rceil +1) \lceil k/2 \rceil -2$, we obtain an asymptotic bound for $sat(n, \mathcal{R}_{\min}(K_3, \mathcal{T}_k))$.
Explicit computational wave propagation in micro-heterogeneous media

Explicit time stepping schemes are popular for linear acoustic and elastic wave propagation due to their simple nature which does not require sophisticated solvers for the inversion of the stiffness matrices. However, explicit schemes are only stable if the time step size is bounded by the mesh size in space subject to the so-called CFL condition. In micro-heterogeneous media, this condition is typically prohibitively restrictive because spatial oscillations of the medium need to be resolved by the discretization in space. This paper presents a way to reduce the spatial complexity in such a setting and, hence, to enable a relaxation of the CFL condition. This is done using the Localized orthogonal decomposition method as a tool for numerical homogenization. A complete convergence analysis is presented with appropriate, weak regularity assumptions on the initial data.
Deep Reinforcement Learning in Parameterized Action Space

Abstract: Recent work has shown that deep neural networks are capable of approximating both value functions and policies in reinforcement learning domains featuring continuous state and action spaces. However, to the best of our knowledge no previous work has succeeded at using deep neural networks in structured (parameterized) continuous action spaces. To fill this gap, this paper focuses on learning within the domain of simulated RoboCup soccer, which features a small set of discrete action types, each of which is parameterized with continuous variables. The best learned agent can score goals more reliably than the 2012 RoboCup champion agent. As such, this paper represents a successful extension of deep reinforcement learning to the class of parameterized action space MDPs.
Bias vs structure of polynomials in large fields, and applications in effective algebraic geometry and coding theory

Let f be a polynomial of degree d in n variables over a nite eld F. The polynomial is said to be unbiased if the distribution of f(x) for a uniform input x2 F n is close to the uniform distribution over F, and is called biased otherwise. The polynomial is said to have low rank if it can be expressed as a composition of a few lower degree polynomials. Green and Tao [Contrib. Discrete Math 2009] and Kaufman and Lovett [FOCS 2008] showed that bias implies low rank for xed degree polynomials over
The Simulation Powers and Limitations of Higher Temperature Hierarchical Self-Assembly Systems *

In this paper, we extend existing results about simulation and intrinsic universality in a model of tile-based self-assembly. Namely, we work within the 2-Handed Assembly Model (2HAM), which is a model of self-assembly in which assemblies are formed by square tiles that are allowed to combine, using glues along their edges, individually or as pairs of arbitrarily large assemblies in a hierarchical manner, and we explore the abilities of these systems to simulate each other when the simulating systems have a higher "temperature" parameter, which is a system wide threshold dictating how many glue bonds must be formed between two assemblies to allow them to combine. It has previously been shown that systems with lower temperatures cannot simulate arbitrary systems with higher temperatures, and also that systems at some higher temperatures can simulate those at particular lower temperatures, creating an infinite set of infinite hierarchies of 2HAM systems with strictly increasing simulation power within each hierarchy. These previous results relied on two different definitions of simulation, one (strong simulation) seemingly more restrictive than the other (standard simulation), but which have previously not been proven to be distinct. Here we prove distinctions between them by first fully characterizing the set of pairs of temperatures such that the high temperature systems are intrinsically universal for the lower temperature systems (i.e. one tile set at the higher temperature can simulate any at the lower) using strong simulation. This includes the first impossibility result for simulation downward in temperature. We then show that lower temperature systems which cannot be simulated by higher temperature systems using the strong definition, can in fact be simulated using the standard definition, proving the distinction between the types of simulation.
Private graphon estimation for sparse graphs

We design algorithms for fitting a high-dimensional statistical model to a large, sparse network without revealing sensitive information of individual members. Given a sparse input graph G, our algorithms output a node-differentially private nonparametric block model approximation. By node-differentially private, we mean that our output hides the insertion or removal of a vertex and all its adjacent edges. If G is an instance of the network obtained from a generative nonparametric model defined in terms of a graphon W, our model guarantees consistency: as the number of vertices tends to infinity, the output of our algorithm converges to W in an appropriate version of the L2 norm. In particular, this means we can estimate the sizes of all multi-way cuts in G. Our results hold as long as W is bounded, the average degree of G grows at least like the log of the number of vertices, and the number of blocks goes to infinity at an appropriate rate. We give explicit error bounds in terms of the parameters of the model; in several settings, our bounds improve on or match known nonprivate results.
Accelerating flux balance calculations in genome-scale metabolic models by localizing the application of loopless constraints.

Background Genome-scale metabolic network models and constraint-based modeling techniques have become important tools for analyzing cellular metabolism. Thermodynamically infeasible cycles (TICs) causing unbounded metabolic flux ranges are often encountered. TICs satisfy the mass balance and directionality constraints but violate the second law of thermodynamics. Current practices involve implementing additional constraints to ensure not only optimal but also loopless flux distributions. However, the mixed integer linear programming problems required to solve become computationally intractable for genome-scale metabolic models. Results We aimed to identify the fewest needed constraints sufficient for optimality under the loopless requirement. We found that loopless constraints are required only for the reactions that share elementary flux modes representing TICs with reactions that are part of the objective function. We put forth the concept of localized loopless constraints (LLCs) to enforce this minimal required set of loopless constraints. By combining with a novel procedure for minimal null-space calculation, the computational time for loopless flux variability analysis (ll-FVA) is reduced by a factor of 10-150 compared to the original loopless constraints and by 4-20 times compared to the current fastest method Fast-SNP with the percent improvement increasing with model size. Importantly, LLCs offer a scalable strategy for loopless flux calculations for multi-compartment/multi-organism models of large sizes, for example, shortening the CPU time for ll-FVA from 35 h to less than 2 h for a model with more than104 reactions. Availability and implementation Matlab functions are available in the Supplementary Material or at https://github.com/maranasgroup/lll-FVA. Supplementary information Supplementary data are available at Bioinformatics online.
$p$-adic dimensions in symmetric tensor categories in characteristic $p$

To every object $X$ of a symmetric tensor category over a field of characteristic $p>0$ we attach $p$-adic integers $\text{Dim}_+(X)$ and $\text{Dim}_-(X)$ whose reduction modulo $p$ is the categorical dimension $\text{dim}(X)$ of $X$, coinciding with the usual dimension when $X$ is a vector space. We study properties of $\text{Dim}_{\pm}(X)$, and in particular show that they don't always coincide with each other, and can take any value in $\mathbb{Z}_p$. We also discuss the connection of $p$-adic dimensions with the theory of $\lambda$-rings and Brauer characters.
SemiContour: A Semi-Supervised Learning Approach for Contour Detection

Supervised contour detection methods usually require many labeled training images to obtain satisfactory performance. However, a large set of annotated data might be unavailable or extremely labor intensive. In this paper, we investigate the usage of semi-supervised learning (SSL) to obtain competitive detection accuracy with very limited training data (three labeled images). Specifically, we propose a semi-supervised structured ensemble learning approach for contour detection built on structured random forests (SRF). To allow SRF to be applicable to unlabeled data, we present an effective sparse representation approach to capture inherent structure in image patches by finding a compact and discriminative low-dimensional subspace representation in an unsupervised manner, enabling the incorporation of abundant unlabeled patches with their estimated structured labels to help SRF perform better node splitting. We re-examine the role of sparsity and propose a novel and fast sparse coding algorithm to boost the overall learning efficiency. To the best of our knowledge, this is the first attempt to apply SSL for contour detection. Extensive experiments on the BSDS500 segmentation dataset and the NYU Depth dataset demonstrate the superiority of the proposed method.
A Portalino to the Dark Sector

“Portal” models that connect the Standard Model to a Dark Sector allow for a wide variety of scenarios beyond the simplest WIMP models. Kinetic mixing of gauge fields in particular has allowed a broad range of new ideas. However, the models that evade CMB constraints are often non-generic, with new mass scales and operators to split states and suppress indirect detection signals. Models with a “portalino”, a neutral fermion that marries a linear combination of a standard model neutrino and dark sector fermion and carries a conserved quantum number, can be simpler. This is especially interesting for interacting dark sectors; then the unmarried linear combination which we identify as the standard model neutrino inherits these interactions too, and provides a new, effective interaction between the dark sector and the standard model. These interactions can be simple Z′ type interactions or lepton-flavor changing. Dark matter freezes out into neutrinos, thereby evading CMB constraints, and conventional direct detection signals are largely absent. The model offers different signals, however. The “portalino” mechanism itself predicts small corrections to the standard model neutrino couplings as well as the possibility of discovering the portalino particle in collider experiments. Possible cosmological and astroparticle signatures include monochromatic neutrino signals from annihilation, spectral features in high energy CR neutrinos as well as conventional signals of additional light species and dark matter interactions.
Alternating links and left-orderability

Let L \subset S^3 denote an alternating link and Sigma(L) its branched double-cover. We give a short proof of the fact that the fundamental group of Sigma(L) admits a left-ordering iff L is an unlink. This result is originally due to Boyer-Gordon-Watson.
Quadratic Thurston maps with few postcritical points

We use the theory of self-similar groups to enumerate all combinatorial classes of non-Euclidean quadratic Thurston maps with fewer than five postcritical points. The enumeration relies on our computation that the corresponding maps on moduli space can be realized by quadratic rational maps with fewer than four postcritical points.
Feedforward Architectures for Decentralized Precoding in Massive MU-MIMO Systems

Massive multi-user multiple-input multiple-output (MU-MIMO) enables significant gains in spectral efficiency and link reliability compared to conventional, small-scale MIMO technology. In addition, linear precoding using zero forcing or Wiener filter (WF) precoding is sufficient to achieve excellent error-rate performance in the massive MU-MIMO downlink. However, these methods typically require centralized processing at the base-station (BS), which causes (i) excessively high interconnect and chip input/output data rates, and (ii) high implementation complexity. We propose two feedforward architectures and corresponding decentralized WF precoders that parallelize precoding across multiple computing fabrics, effectively mitigating the limitations of centralized approaches. To demonstrate the efficacy of our decentralized precoders, we provide implementation results on a multi-GPU system, which show that our solutions achieve throughputs in the Gbit/s regime while achieving (near-)optimal error-rate performance in the massive MU-MIMO downlink.
HIGHER MOMENTS OF PRIMES IN SHORT INTERVALS II

Given good knowledge on the even moments, we derive asymptotic formulas for λth moments of primes in short intervals and prove "equivalence" result on odd moments. We also provide numerical evidence in support of these results.
Model Selection for High-Dimensional Regression under the Generalized Irrepresentability Condition

In the high-dimensional regression model a response variable is linearly related to p covariates, but the sample size n is smaller than p. We assume that only a small subset of covariates is 'active' (i.e., the corresponding coefficients are non-zero), and consider the model-selection problem of identifying the active covariates. A popular approach is to estimate the regression coefficients through the Lasso (l1-regularized least squares). This is known to correctly identify the active set only if the irrelevant covariates are roughly orthogonal to the relevant ones, as quantified through the so called 'irrepresentability' condition. In this paper we study the 'Gauss-Lasso' selector, a simple two-stage method that first solves the Lasso, and then performs ordinary least squares restricted to the Lasso active set. We formulate 'generalized irrepresentability condition' (GIC), an assumption that is substantially weaker than irrepresentability. We prove that, under GIC, the Gauss-Lasso correctly recovers the active set.
Mathematical deep learning for pose and binding affinity prediction and ranking in D3R Grand Challenges

Advanced mathematics, such as multiscale weighted colored subgraph and element specific persistent homology, and machine learning including deep neural networks were integrated to construct mathematical deep learning models for pose and binding affinity prediction and ranking in the last two D3R Grand Challenges in computer-aided drug design and discovery. D3R Grand Challenge 2 focused on the pose prediction, binding affinity ranking and free energy prediction for Farnesoid X receptor ligands. Our models obtained the top place in absolute free energy prediction for free energy set 1 in stage 2. The latest competition, D3R Grand Challenge 3 (GC3), is considered as the most difficult challenge so far. It has five subchallenges involving Cathepsin S and five other kinase targets, namely VEGFR2, JAK2, p38-α, TIE2, and ABL1. There is a total of 26 official competitive tasks for GC3. Our predictions were ranked 1st in 10 out of these 26 tasks.
Efficient Computation of Moments in Sum-Product Networks

Bayesian online algorithms for Sum-Product Networks (SPNs) need to update their posterior distribution after seeing one single additional instance. To do so, they must compute moments of the model parameters under this distribution. The best existing method for computing such moments scales quadratically in the size of the SPN, although it scales linearly for trees. This unfortunate scaling makes Bayesian online algorithms prohibitively expensive, except for small or tree-structured SPNs. We propose a linear-time algorithm that works even when the SPN is a general directed acyclic graph (DAG). Our algorithm significantly broadens the applicability of Bayesian online algorithms for SPNs. We achieve our goal by reducing the moment computation problem to a joint inference problem in SPNs and by taking advantage of a special structure of the updated posterior distribution: it is a multilinear polynomial with exponentially many positive monomials, and we can evaluate moments by differentiation. We demonstrate the usefulness of our linear time moment computation algorithm by applying it to develop a linear time assume density filter (ADF) for SPNs.
On Non-Interactive Simulation of Joint Distributions

We consider the following non-interactive simulation problem: Alice and Bob observe sequences $X^{n}$ and $Y^{n}$ , respectively, where $\{(X_{i}, Y_{i})\}_{i=1}^{n}$ are drawn independent identically distributed from $P(x,y)$ , and they output $U$ and $V$ , respectively, which is required to have a joint law that is close in total variation to a specified $Q(u,v)$ . It is known that the maximal correlation of $U$ and $V$ must necessarily be no bigger than that of $X$ and $Y$ if this is to be possible. Our main contribution is to bring hypercontractivity to bear as a tool on this problem. In particular, we show that if $P(x,y)$ is the doubly symmetric binary source, then hypercontractivity provides stronger impossibility results than maximal correlation. Finally, we extend these tools to provide impossibility results for the $k$ -agent version of this problem.
Fast Amortized Inference and Learning in Log-linear Models with Randomly Perturbed Nearest Neighbor Search

Inference in log-linear models scales linearly in the size of output space in the worst-case. This is often a bottleneck in natural language processing and computer vision tasks when the output space is feasibly enumerable but very large. We propose a method to perform inference in log-linear models with sublinear amortized cost. Our idea hinges on using Gumbel random variable perturbations and a pre-computed Maximum Inner Product Search data structure to access the most-likely elements in sublinear amortized time. Our method yields provable runtime and accuracy guarantees. Further, we present empirical experiments on ImageNet and Word Embeddings showing significant speedups for sampling, inference, and learning in log-linear models.
On the expressive power of deep neural networks

We propose a new approach to the problem of neural network expressivity, which seeks to characterize how structural properties of a neural network family affect the functions it is able to compute. Our approach is based on an interrelated set of measures of expressivity, unified by the novel notion of trajectory length, which measures how the output of a network changes as the input sweeps along a one-dimensional path. Our findings can be summarized as follows: (1) The complexity of the computed function grows exponentially with depth. (2) All weights are not equal: trained networks are more sensitive to their lower (initial) layer weights. (3) Regularizing on trajectory length (trajectory regularization) is a simpler alternative to batch normalization, with the same performance.
One-Bit Compressed Sensing by Linear Programming

ONE-BIT COMPRESSED SENSING BY LINEAR PROGRAMMING arXiv:1109.4299v5 [cs.IT] 16 Mar 2012 YANIV PLAN AND ROMAN VERSHYNIN Abstract. We give the first computationally tractable and almost optimal solution to the problem of one-bit compressed sensing, showing how to accurately recover an s-sparse vector x ∈ R n from the signs of O(s log 2 (n/s)) random linear measurements of x. The recovery is achieved by a simple linear program. This result extends to approximately sparse vectors x. Our result is universal in the sense that with high probability, one measurement scheme will successfully recover all sparse vectors simultaneously. The argument is based on solving an equivalent geometric problem on random hyperplane tessellations. 1. Introduction Compressed sensing is a modern paradigm of data acquisition, which is having an impact on several disciplines, see [21]. The scientist has access to a measurement vector v ∈ R m obtained as v = Ax, where A is a given m × n measurement matrix and x ∈ R n is an unknown signal that one needs to recover from v. One would like to take m n, rendering A non-invertible; the key ingredient to successful recovery of x is take into account its assumed structure – sparsity. Thus one assumes that x has at most s nonzero entries, although the support pattern is unknown. The strongest known results are for random measurement matrices A. In particular, if A has Gaussian i.i.d. entries, then we may take m = O(s log(n/s)) and still recover x exactly with high probability [10, 7]; see [26] for an overview. Furthermore, this recovery may be achieved in polynomial time by solving the convex minimization program min x 0 1 subject to Ax 0 = v. Stability results are also available when noise is added to the problem [9, 8, 3, 27]. However, while the focus of compressed sensing is signal recovery with minimal information, the classical set-up (1.1), (1.2) assumes infinite bit precision of the measurements. This disaccord raises an important question: how many bits per measurement (i.e. per coordinate of v) are sufficient for tractable and accurate sparse recovery? This paper shows that one bit per measurement is enough. There are many applications where such severe quantization may be inherent or preferred — analog-to-digital conversion [20, 18], binomial regression in statistical modeling and threshold group testing [12], to name a few. 1.1. Main results. This paper demonstrates that a simple modification of the convex program (1.2) is able to accurately estimate x from extremely quantized measurement vector y = sign(Ax). Date: September 19, 2011. 2000 Mathematics Subject Classification. 94A12; 60D05; 90C25. Y.P. is supported by an NSF Postdoctoral Research Fellowship under award No. 1103909. R.V. is supported by NSF grants DMS 0918623 and 1001829.
Homotopy Analysis for Tensor PCA

Author(s): Anandkumar, Anima; Deng, Yuan; Ge, Rong; Mobahi, Hossein | Editor(s): Kale, Satyen; Shamir, Ohad | Abstract: Developing efficient and guaranteed nonconvex algorithms has been an important challenge in modern machine learning. Algorithms with good empirical performance such as stochastic gradient descent often lack theoretical guarantees. In this paper, we analyze the class of homotopy or continuation methods for global optimization of nonconvex functions. These methods start from an objective function that is efficient to optimize (e.g. convex), and progressively modify it to obtain the required objective, and the solutions are passed along the homotopy path. For the challenging problem of tensor PCA, we prove global convergence of the homotopy method in the "high noise" regime. The signal-to-noise requirement for our algorithm is tight in the sense that it matches the recovery guarantee for the best degree-4 sum-of-squares algorithm. In addition, we prove a phase transition along the homotopy path for tensor PCA. This allows to simplify the homotopy method to a local search algorithm, viz., tensor power iterations, with a specific initialization and a noise injection procedure, while retaining the theoretical guarantees.
Large deviations of empirical measures of zeros on riemann surfaces

This is a continuation of a project on large deviations for the empirical measures of zeros of random holomorphic sections of random line bundles over a Riemann surface X. In a previous article with O. Zeitouni (arXiv:0904.4271), we proved an LDP for random polynomials in the genus zero case. In higher genus, there is a Picard variety of line bundles and so the line bundle L is a random variable as well as the section s. The space of pairs (L, s) is known as the "vortex moduli space". The zeros of (L, s) fill out the configuration space $X^{(N)}$ of $N$ points of $X$. The LDP shows that the configurations concentrate at one equilibrium measure exponentially fast. The new features of the proof involve Abel-Jacobi theory, the prime form and bosonization.
Dark energy and the refined de sitter conjecture

We revisit the phenomenology of quintessence models in light of the recently refined version of the de Sitter Swampland conjecture, which includes the possibility of unstable de Sitter critical points. We show that models of quintessence can evade previously derived lower bounds on (1 + w), albeit with very finely-tuned initial conditions. In the absence of such tuning or other rolling quintessence fields, a field with mass close to Hubble is required, which has a generic prediction for (1+ w). Slow-roll single field inflation models remain in tension. Other phenomenological constraints arising from the coupling of the quintessence field with the Higgs or the QCD axion are significantly relaxed.
Resonant clocking circuits for reversible computation

A mechanism for the reduction of dynamic energy dissipation in the computing circuit is described. The resonant circuit with controlled switches conserves the stored energy by recovering upto 90% of energy that would be otherwise lost during logic state transitions. This energy-conserving approach preserves thermodynamic entropy, ideally preventing heat generation in the system. This approach is used in a proposed resonant clocking and logic application without dynamic energy dissipation.
Coded State Machine -- Scaling State Machine Execution under Byzantine Faults

We introduce Coded State Machine (CSM), an information-theoretic framework to securely and efficiently execute multiple state machines on Byzantine nodes. The standard method of solving this problem is using State Machine Replication, which achieves high security at the cost of low efficiency. CSM simultaneously achieves the optimal linear scaling in storage, throughput, and security with increasing network size. The storage is scaled via the design of Lagrange coded states and coded input commands that require the same storage size as their origins. The computational efficiency is scaled using a novel delegation algorithm, called INTERMIX, which is an information-theoretically verifiable matrix-vector multiplication algorithm of independent interest.
Properties of DH Type II Radio Bursts and Their Space Weather Implications

We report on the properties of type II radio bursts observed by the Radio and Plasma Wave Experiment (WAVES) on board the Wind spacecraft over the past two solar cycles. We confirm that the associated coronal mass ejections (CMEs) are fast and wide, more than half the CMEs being halos. About half of the type II bursts extend down to 0.5 MHz, corresponding to a heliocentric distance of tens of solar radii. The DH type II bursts are mostly confined to the active region belt and their occurrence rate follows the solar activity cycle. Type II burst occurring on the western hemisphere of the Sun and extending to lower frequencies are good indicators of a solar energetic particle event.
Informational bottlenecks in two-unicast wireless networks with delayed CSIT

We study the impact of delayed channel state information at the transmitters (CSIT) in two-unicast wireless networks with a layered topology and arbitrary connectivity. We introduce a technique to obtain outer bounds to the degrees-of-freedom (DoF) region through the new graph-theoretic notion of bottleneck nodes. Such nodes act as informational bottlenecks only under the assumption of delayed CSIT, and imply asymmetric DoF bounds of the form mD1 + D2 ≤ m. Combining this outer-bound technique with new achievability schemes, we characterize the sum DoF of a class of two-unicast wireless networks, which shows that, unlike in the case of instantaneous CSIT, the DoF of two-unicast networks with delayed CSIT can take an infinite set of values.
Does Managerial Ability Drive Firm Innovativeness

In this paper, we investigate the impact of managerial ability on firm innovativeness. We further investigate how managerial ability impacts the association between firm innovativeness and competitive advantage. We employ two measures of managerial ability, namely strategic managerial ability and operational managerial ability. We find that firm innovativeness rises with strategic ability at an increasing rate. However, firm innovativeness initially falls and then rises with an increase in operational ability. Our results are consistent with the notion that a firm's innovation activity is a tradeoff between opportunity exploration and exploitation in that explorative and exploitative activities compete for manager's fixed attention. The greater the strategic ability of management, the more opportunity-focused they are, the greater is their risk tolerance, and the greater is the investment in research and development. Strategic managers seek and cultivate growth opportunities to resolve the uncertainty associated with the growth opportunities in the firm's favor, which enhances the firm's competitive advantage.
Multistage Campaigning in Social Networks

We consider control problems for multi-stage campaigning over social networks. The dynamic programming framework is employed to balance the high present reward and large penalty on low future outcome in the presence of extensive uncertainties. In particular, we establish theoretical foundations of optimal campaigning over social networks where the user activities are modeled as a multivariate Hawkes process, and we derive a time dependent linear relation between the intensity of exogenous events and several commonly used objective functions of campaigning. We further develop a convex dynamic programming framework for determining the optimal intervention policy that prescribes the required level of external drive at each stage for the desired campaigning result. Experiments on both synthetic data and the real-world MemeTracker dataset show that our algorithm can steer the user activities for optimal campaigning much more accurately than baselines.
Stability criteria and turbulence paradox problem for type II 3D shears

There are two types of 3D shears in channel flows: (U(y, z), 0, 0) and (U(y), 0, W(y)). Both are important in organizing the phase-space structures of the channel flows. Stability criteria of type I 3D shears were studied in Li (2011 Q. Appl. Math. 69 379–87). Here we study the stability criteria of type II 3D shears. We also provide more support to the idea of resolution of a turbulence paradox, introduced in Li and Lin (2011 SIAM J. Math. Anal. 43 1923–54) by studying a sequence of type II 3D shears.
The bulk-edge correspondence for continuous honeycomb lattices

AbstractWe study bulk/edge aspects of continuous honeycomb lattices in a magnetic field. We compute the bulk index of Bloch eigenbundles: it equals 2 or –2, with sign depending on nearby Dirac poin...
Using Location-Based Social Networks to Validate Human Mobility and Relationships Models

We propose to use social networking data to validate mobility models for pervasive mobile ad-hoc networks (MANETs) and delay tolerant networks (DTNs). The Random Waypoint (RWP) and Erdos-Renyi (ER) models have been a popular choice among researchers for generating mobility traces of nodes and relationships between them. Not only RWP and ER are useful in evaluating networking protocols in a simulation environment, but they are also used for theoretical analysis of such dynamic networks. However, it has been observed that neither relationships among people nor their movements are random. Instead, human movements frequently contain repeated patterns and friendship is bounded by distance. We used social networking site Go Walla to collect, create and validate models of human mobility and relationships for analysis and evaluations of applications in opportunistic networks such as sensor networks and transportation models in civil engineering. In doing so, we hope to provide more human-like movements and social relationship models to researchers to study problems in complex and mobile networks.
Regularity of the Eikonal equation with two vanishing entropies

Abstract Let Ω ⊂ R 2 be a bounded simply-connected domain. The Eikonal equation | ∇ u | = 1 for a function u : Ω ⊂ R 2 → R has very little regularity, examples with singularities of the gradient existing on a set of positive H 1 measure are trivial to construct. With the mild additional condition of two vanishing entropies we show ∇ u is locally Lipschitz outside a locally finite set. Our condition is motivated by a well known problem in Calculus of Variations known as the Aviles–Giga problem. The two entropies we consider were introduced by Jin, Kohn [26] , Ambrosio, DeLellis, Mantegazza [2] to study the Γ-limit of the Aviles–Giga functional. Formally if u satisfies the Eikonal equation and if (1) ∇ ⋅ ( Σ ˜ e 1 e 2 ( ∇ u ⊥ ) ) = 0 and ∇ ⋅ ( Σ ˜ ϵ 1 ϵ 2 ( ∇ u ⊥ ) ) = 0 distributionally in Ω , where Σ ˜ e 1 e 2 and Σ ˜ ϵ 1 ϵ 2 are the entropies introduced by Jin, Kohn [26] , and Ambrosio, DeLellis, Mantegazza [2] , then ∇ u is locally Lipschitz continuous outside a locally finite set. Condition (1) is motivated by the zero energy states of the Aviles–Giga functional. The zero energy states of the Aviles–Giga functional have been characterized by Jabin, Otto, Perthame [25] . Among other results they showed that if lim n → ∞ ⁡ I ϵ n ( u n ) = 0 for some sequence u n ∈ W 0 2 , 2 ( Ω ) and u = lim n → ∞ ⁡ u n then ∇ u is Lipschitz continuous outside a finite set. This is essentially a corollary to their theorem that if u is a solution to the Eikonal equation | ∇ u | = 1 a.e. and if for every “entropy” Φ (in the sense of [18] , Definition 1) function u satisfies ∇ ⋅ [ Φ ( ∇ u ⊥ ) ] = 0 distributionally in Ω then ∇ u is locally Lipschitz continuous outside a locally finite set. In this paper we generalize this result in that we require only two entropies to vanish. The method of proof is to transform any solution of the Eikonal equation satisfying (1) into a differential inclusion D F ∈ K where K ⊂ M 2 × 2 is a connected compact set of matrices without Rank-1 connections. Equivalently this differential inclusion can be written as a constrained non-linear Beltrami equation. The set K is also non-elliptic in the sense of Sverak [32] . By use of this transformation and by utilizing ideas from the work on regularity of solutions of the Eikonal equation in fractional Sobolev space by Ignat [23] , DeLellis, Ignat [15] as well as methods of Sverak [32] , regularity is established.
Asymptotics of the translation flow on holomorphic maps out of the poly-plane

We study the family of holomorphic maps from the polydisk to the disk which restrict to the identity on the diagonal. In particular, we analyze the asymptotics of the orbit of such a map under the conjugation action of a unipotent subgroup of $\text{PSL}_2(\mathbb{R})$. We discuss an application our results to the study of the Caratheodory metric on Teichmuller space.
Translocation of Dense Granule Effectors across the Parasitophorous Vacuole Membrane in Toxoplasma-Infected Cells Requires the Activity of ROP17, a Rhoptry Protein Kinase.

ABSTRACT Toxoplasma gondii tachyzoites co-opt host cell functions through introduction of a large set of rhoptry- and dense granule-derived effector proteins. These effectors reach the host cytosol through different means: direct injection for rhoptry effectors and translocation across the parasitophorous vacuolar membrane (PVM) for dense granule (GRA) effectors. The machinery that translocates these GRA effectors has recently been partially elucidated, revealing three components, MYR1, MYR2, and MYR3. To determine whether other proteins might be involved, we returned to a library of mutants defective in GRA translocation and selected one with a partial defect, suggesting it might be in a gene encoding a new component of the machinery. Surprisingly, whole-genome sequencing revealed a missense mutation in a gene encoding a known rhoptry protein, a serine/threonine protein kinase known as ROP17. ROP17 resides on the host cytosol side of the PVM in infected cells and has previously been known for its activity in phosphorylating and thereby inactivating host immunity-related GTPases. Here, we show that null or catalytically dead mutants of ROP17 are defective in GRA translocation across the PVM but that translocation can be rescued “in trans” by ROP17 delivered by other tachyzoites infecting the same host cell. This strongly argues that ROP17’s role in regulating GRA translocation is carried out on the host cytosolic side of the PVM, not within the parasites or lumen of the parasitophorous vacuole. This represents an entirely new way in which the different secretory compartments of Toxoplasma tachyzoites collaborate to modulate the host-parasite interaction. IMPORTANCE When Toxoplasma infects a cell, it establishes a protective parasitophorous vacuole surrounding it. While this vacuole provides protection, it also serves as a barrier to the export of parasite effector proteins that impact and take control of the host cell. Our discovery here that the parasite rhoptry protein ROP17 is necessary for export of these effector proteins provides a distinct, novel function for ROP17 apart from its known role in protecting the vacuole. This will enable future research into ways in which we can prevent the export of effector proteins, thereby preventing Toxoplasma from productively infecting its animal and human hosts.
Heterogeneous Gaussian mechanism: Preserving differential privacy in deep learning with provable robustness

In this paper, we propose a novel Heterogeneous Gaussian Mechanism (HGM) to preserve differential privacy in deep neural networks, with provable robustness against adversarial examples. We first relax the constraint of the privacy budget in the traditional Gaussian Mechanism from (0, 1] to (0, \infty), with a new bound of the noise scale to preserve differential privacy. The noise in our mechanism can be arbitrarily redistributed, offering a distinctive ability to address the trade-off between model utility and privacy loss. To derive provable robustness, our HGM is applied to inject Gaussian noise into the first hidden layer. Then, a tighter robustness bound is proposed. Theoretical analysis and thorough evaluations show that our mechanism notably improves the robustness of differentially private deep neural networks, compared with baseline approaches, under a variety of model attacks.
Lattice models that realize Z n -1 symmetry-protected topological states for even n

Higher symmetries can emerge at low energies in a topologically ordered state with no symmetry, when some topological excitations have very high-energy scales while other topological excitations have low energies. The low-energy properties of topological orders in this limit, with the emergent higher symmetries, may be described by higher symmetry-protected topological order. This motivates us, as a simplest example, to study a lattice model of ${\mathbb{Z}}_{n}$-1 symmetry-protected topological (1-SPT) states in $3+1$ dimensions for even $n$. We write an exactly solvable lattice model and study its boundary transformation. On the boundary, we show the existence of anyons with nontrivial self-statistics. For the $n=2$ case, where the bulk classification is given by an integer $m$ mod 4, we show that the boundary can be gapped with double-semion topological order for $m=1$ and toric code for $m=2$. The bulk ground-state wave-function amplitude is given in terms of the linking numbers of loops in the dual lattice. Our construction can be generalized to arbitrary 1-SPT protected by finite unitary symmetry.
Robust and Adaptive Planning under Model Uncertainty

Planning under model uncertainty is a fundamental problem across many applications of decision making and learning. In this paper, we propose the Robust Adaptive Monte Carlo Planning (RAMCP) algorithm, which allows computation of risk-sensitive Bayes-adaptive policies that optimally trade off exploration, exploitation, and robustness. RAMCP formulates the risk-sensitive planning problem as a two-player zero-sum game, in which an adversary perturbs the agent’s belief over the models. We introduce two versions of the RAMCP algorithm. The first, RAMCP-F, converges to an optimal risksensitive policy without having to rebuild the search tree as the underlying belief over models is perturbed. The second version, RAMCP-I, improves computational efficiency at the cost of losing theoretical guarantees, but is shown to yield empirical results comparable to RAMCP-F. RAMCP is demonstrated on an n-pull multi-armed bandit problem, as well as a patient treatment scenario.
A quantitative risk assessment method for synthetic biology products in the environment.

Abstract The need to prevent possible adverse environmental health impacts resulting from synthetic biology (SynBio) products is widely acknowledged in both the SynBio risk literature and the global regulatory community. To-date, however, discussions of potential risks of SynBio products have been largely speculative, and the limited attempts to characterize the risks of SynBio products have been non-uniform and entirely qualitative. As the SynBio discipline continues to accelerate and bring forth novel, highly-engineered life forms, a standardized risk assessment framework will become critical for ensuring that the environmental risks of these products are characterized in a consistent, reliable, and objective manner that incorporates all SynBio-unique risk factors. In their current forms, established risk assessment frameworks – including those that address traditional genetically modified organisms – fall short of the features required of this standard framework. To address this gap, we propose the Quantitative Risk Assessment Method for Synthetic Biology Products (QRA-SynBio) – an incremental build on established risk assessment methodologies that supplements traditional paradigms with the SynBio risk factors that are currently absent, and necessitates quantitative analysis for more transparent and objective risk characterizations. We demonstrate through a hypothetical case study that the proposed framework facilitates defensible quantification of the environmental risks of SynBio products in both foreseeable and hypothetical use scenarios. Additionally, we show how the quantitative nature of the proposed method can promote increased experimental investigation into the true likelihood of hazard and exposure parameters and highlight the most sensitive parameters where uncertainty should be reduced, ultimately leading to more targeted SynBio risk research and yielding more precise characterizations of risk.
The clauses of exception in “domestic law” and in Hague Conventions

The present work is proposed after a necessary preliminary examination on the terminology and classification level to analyze the clauses (in comparative mode) in question under EU legislation and jurisprudence at a conventional level. In this reconstruction it will be necessary to identify not only the content and scope of the normative data but also to understand with examples where possible supported by practical references, the hypotheses that can concretely justify and concretize the non-application of the conflict rule destined to operate in general as well as the use of the exception clause.