cssi/SciSciGPT-SciSciNet huggingface dataset:
Identifying interatomic potentials for the accurate modeling of interfacial segregation and structural transitions

Abstract Chemical segregation and structural transitions at interfaces are important nanoscale phenomena, making them natural targets for atomistic modeling, yet interatomic potentials must be fit to secondary physical properties. To isolate the important factors that interatomic potentials must capture in order to accurately model such behavior, the performance of four interatomic potentials was evaluated for the Cu-Zr system, with experimental observations used to provide validation. While experimental results show strong Zr segregation to grain boundary regions and the formation of nanoscale amorphous complexions at high temperatures and/or dopant compositions, a variety of disparate behaviors can be observed in hybrid Monte Carlo/molecular dynamics simulations of doping, depending on the chosen potential. The potentials that are able to recreate the correct behavior accurately reproduce the enthalpy of mixing as well as the bond energies, providing a roadmap for the exploration of interfacial phenomena with atomistic modeling. Finally, we use our observations to find a reliable potential for the Ni-Zr system and show that this alloy should also be able to sustain amorphous complexions.
Declining volatility, a general property of disparate systems: from fossils, to stocks, to the stars

: There may be structural principles pertaining to the general behaviour of systems that lead to similarities in a variety of different contexts. Classic examples include the descriptive power of fractals, the importance of surface area to volume constraints, the universality of entropy in systems, and mathematical rules of growth and form. Documenting such overarching principles may represent a rejoinder to the Neodarwinian synthesis that emphasizes adaptation and competition. Instead, these principles could indicate the importance of constraint and structure on form and evolution. Here, we document a potential example of a phenomenon suggesting congruent behaviour of very different systems. We focus on the notion that universally there has been a tendency for more volatile entities to disappear from systems such that the net volatility in these systems tends to decline. We specifically focus on origination and extinction rates in the marine animal fossil record, the performance of stocks in the stock market, and the characters of stars and stellar systems. We consider the evidence that each is experiencing declining volatility, and also consider the broader significance of this.
Relative functoriality and functional equations via trace formulas

Langlands’ functoriality principle predicts deep relations between the local and automorphic spectra of different reductive groups. This has been generalized by the relative Langlands program to include spherical varieties, among which reductive groups are special cases. In the philosophy of Langlands’ “beyond endoscopy” program, these relations should be expressed as comparisons between different trace formulas, with the insertion of appropriate L-functions. The insertion of L-functions calls for one more goal to be achieved: the study of their functional equations via trace formulas. The goal of this article is to demonstrate this program through examples, indicating a local-to-global approach as in the project of endoscopy. Here, scalar transfer factors are replaced by “transfer operators” or “Hankel transforms” which are nice enough (typically, expressible in terms of usual Fourier transforms) that they can be used, in principle, to prove global comparisons (in the form of Poisson summation formulas). Some of these examples have already appeared in the literature; for others, the proofs will appear elsewhere.
MIDI-LAB, a Powerful Visual Basic Program for Creating MIDI Music

Creating MIDI music can be a practical challenge. In the past, working with it was difficult and frustrating to all but the most accomplished and determined. Now, however, we are offering a powerful Visual Basic program called MIDI-LAB, that is easy to learn, and instantly rewarding to even the newest users. MIDILAB has been developed to give users the ability to quickly create music with a limitless variety of tunes, tempos, speeds, volumes, instruments, rhythms and major scales. This program has a simple, intuitive, and user-friendly interface, which provides a straightforward way to enter musical data with Numbered Musical Notation (NMN) and immediately create MIDI music. The key feature of this program is the digitalization of music input. It vastly simplifies creating, editing, and saving MIDI music. MIDI-LAB can be used virtually anywhere to write music for entertainment, teaching, computer games, and mobile phone ringtones.
Not-So-Random Features

We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM margin. We provide rigorous guarantees for optimality and generalization, interpreting our algorithm as online equilibrium-finding dynamics in a certain two-player min-max game. Evaluations on synthetic and real-world datasets demonstrate scalability and consistent improvements over related random features-based methods.
Modeling Sparse Deviations for Compressed Sensing using Generative Models

In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative model. A domain-specific generative model can provide a stronger prior and thus allow for recovery with far fewer measurements. However, unlike sparsity-based approaches, existing methods based on generative models guarantee exact recovery only over their support, which is typically only a small subset of the space on which the signals are defined. We propose Sparse-Gen, a framework that allows for sparse deviations from the support set, thereby achieving the best of both worlds by using a domain specific prior and allowing reconstruction over the full space of signals. Theoretically, our framework provides a new class of signals that can be acquired using compressed sensing, reducing classic sparse vector recovery to a special case and avoiding the restrictive support due to a generative model prior. Empirically, we observe consistent improvements in reconstruction accuracy over competing approaches, especially in the more practical setting of transfer compressed sensing where a generative model for a data-rich, source domain aids sensing on a data-scarce, target domain.
End-to-End Learning for the Deep Multivariate Probit Model

The multivariate probit model (MVP) is a popular classic model for studying binary responses of multiple entities. Nevertheless, the computational challenge of learning the MVP model, given that its likelihood involves integrating over a multidimensional constrained space of latent variables, significantly limits its application in practice. We propose a flexible deep generalization of the classic MVP, the Deep Multivariate Probit Model (DMVP), which is an end-to-end learning scheme that uses an efficient parallel sampling process of the multivariate probit model to exploit GPU-boosted deep neural networks. We present both theoretical and empirical analysis of the convergence behavior of DMVP's sampling process with respect to the resolution of the correlation structure. We provide convergence guarantees for DMVP and our empirical analysis demonstrates the advantages of DMVP's sampling compared with standard MCMC-based methods. We also show that when applied to multi-entity modelling problems, which are natural DMVP applications, DMVP trains faster than classical MVP, by at least an order of magnitude, captures rich correlations among entities, and further improves the joint likelihood of entities compared with several competitive models.
Maximal decay inequalities for trilinear oscillatory integrals of convolution type

Abstract In this paper we prove sharp L ∞ – L ∞ – L ∞ decay for certain trilinear oscillatory integral forms of convolution type on R 2 . These estimates imply earlier L 2 – L 2 – L 2 results obtained by the second author as well as corresponding sharp, stable sublevel set estimates of the form studied by Christ [3] and Christ, Li, Tao, and Thiele [5] . New connections to the multilinear results of Phong, Stein, and Sturm [13] are also considered.
The Composition Theorem for Differential Privacy

Sequential querying of differentially private mechanisms degrades the overall privacy level. In this paper, we answer the fundamental question of characterizing the level of overall privacy degradation as a function of the number of queries and the privacy levels maintained by each privatization mechanism. Our solution is complete: we prove an upper bound on the overall privacy level and construct a sequence of privatization mechanisms that achieves this bound. The key innovation is the introduction of an operational interpretation of differential privacy (involving hypothesis testing) and the use of a data processing inequality along with its converse. Our result improves over the state of the art, and has immediate connections to several problems studied in the literature.
Interactive Launch of 16,000 Microsoft Windows Instances on a Supercomputer

Simulation, machine learning, and data analysis require a wide range of software which can be dependent upon specific operating systems, such as Microsoft Windows. Running this software interactively on massively parallel supercomputers can present many challenges. Traditional methods of scaling Microsoft Windows applications to run on thousands of processors have typically relied on heavyweight virtual machines that can be inefficient and slow to launch on modern manycore processors. This paper describes a unique approach using the Lincoln Laboratory LLMapReduce technology in combination with the Wine Windows compatibility layer to rapidly and simultaneously launch and run Microsoft Windows applications on thousands of cores on a supercomputer. Specifically, this work demonstrates launching 16,000 Microsoft Windows applications in 5 minutes running on 16,000 processor cores. This capability significantly broadens the range of applications that can be run at large scale on a supercomputer.
T-duality for Langlands dual groups

This article addresses the question of whether Langlands duality for complex reductive Lie groups may be implemented by T-dualization. We prove that for reductive groups whose simple factors are of Dynkin type A, D, or E, the answer is yes.
Unrolling Residues to Avoid Progressions

SummaryWe look at the problem of coloring 1, 2, …, n with r colors to minimize the portion of monochromatic k-term arithmetic progressions. By using residues to color Zm and then unrolling, we produce the best-known colorings for several small values of r and k.
BP-STDP: Approximating backpropagation using spike timing dependent plasticity

Abstract The problem of training spiking neural networks (SNNs) is a necessary precondition to understanding computations within the brain, a field still in its infancy. Previous work has shown that supervised learning in multi-layer SNNs enables bio-inspired networks to recognize patterns of stimuli through hierarchical feature acquisition. Although gradient descent has shown impressive performance in multi-layer (and deep) SNNs, it is generally not considered biologically plausible and is also computationally expensive. This paper proposes a novel supervised learning approach based on an event-based spike-timing-dependent plasticity (STDP) rule embedded in a network of integrate-and-fire (IF) neurons. The proposed temporally local learning rule follows the backpropagation weight change updates applied at each time step. This approach enjoys benefits of both accurate gradient descent and temporally local, efficient STDP. The experimental results on the XOR problem, the Iris data, and the MNIST dataset demonstrate that the proposed SNN performs as successfully as the traditional NNs. Our approach also compares favorably with the state-of-the-art multi-layer SNNs. Thus, this method can be applied to develop deep SNNs with end-to-end STDP-based learning rules in future studies.
Controlling for Unobserved Confounds in Classification Using Correlational Constraints.

As statistical classifiers become integrated into real-world applications, it is important to consider not only their accuracy but also their robustness to changes in the data distribution. In this paper, we consider the case where there is an unobserved confounding variable $z$ that influences both the features $\mathbf{x}$ and the class variable $y$. When the influence of $z$ changes from training to testing data, we find that the classifier accuracy can degrade rapidly. In our approach, we assume that we can predict the value of $z$ at training time with some error. The prediction for $z$ is then fed to Pearl's back-door adjustment to build our model. Because of the attenuation bias caused by measurement error in $z$, standard approaches to controlling for $z$ are ineffective. In response, we propose a method to properly control for the influence of $z$ by first estimating its relationship with the class variable $y$, then updating predictions for $z$ to match that estimated relationship. By adjusting the influence of $z$, we show that we can build a model that exceeds competing baselines on accuracy as well as on robustness over a range of confounding relationships.
C*-Algebras of inverse semigroups: Amenability and weak containment

We argue that weak containment is an appropriate notion of amenability for inverse semigroups. Given an inverse semigroup $S$ and a homomorphism $\phi$ of $S$ onto a group $G$, we show, under an assumption on $\ker(\phi)$, that $S$ has weak containment if and only if $G$ is amenable and $\ker(\phi)$ has weak containment. Using Fell bundle amenability, we find a related result for inverse semigroups with zero. We show that all graph inverse semigroups have weak containment and that Nica's inverse semigroup $\mcT_{G,P}$ of a quasi-lattice ordered group $(G,P)$ has weak containment if and only if $(G,P)$ is amenable.
Learning-Aided Optimization for Energy-Harvesting Devices With Outdated State Information

This paper considers utility optimal power control for energy-harvesting wireless devices with a finite capacity battery. The distribution information of the underlying wireless environment and harvestable energy is unknown, and only outdated system state information is known at the device controller. This scenario shares similarity with Lyapunov opportunistic optimization and online learning but is different from both. By a novel combination of Zinkevich’s online gradient learning technique and the drift-plus-penalty technique from Lyapunov opportunistic optimization, this paper proposes a learning-aided algorithm that achieves utility within $O(\epsilon)$ of the optimal, for any desired $\epsilon >0$ , by using a battery with an $O(1/\epsilon)$ capacity. The proposed algorithm has low complexity and makes power investment decisions based on system history, without requiring knowledge of the system state or its probability distribution.
Commuting planar polynomial vector fields for conservative Newton systems

We study the problem of characterizing polynomial vector fields that commute with a given polynomial vector field on a plane. It is a classical result that one can write down solution formulas for ...
Residual networks behave like ensembles of relatively shallow networks

In this work we propose a novel interpretation of residual networks showing that they can be seen as a collection of many paths of differing length. Moreover, residual networks seem to enable very deep networks by leveraging only the short paths during training. To support this observation, we rewrite residual networks as an explicit collection of paths. Unlike traditional models, paths through residual networks vary in length. Further, a lesion study reveals that these paths show ensemble-like behavior in the sense that they do not strongly depend on each other. Finally, and most surprising, most paths are shorter than one might expect, and only the short paths are needed during training, as longer paths do not contribute any gradient. For example, most of the gradient in a residual network with 110 layers comes from paths that are only 10-34 layers deep. Our results reveal one of the key characteristics that seem to enable the training of very deep networks: Residual networks avoid the vanishing gradient problem by introducing short paths which can carry gradient throughout the extent of very deep networks.
Enhancing Heralding Efficiency and Biphoton Rate in Type-I Spontaneous Parametric Down-Conversion

The nonlinear optical process of spontaneous parametric down-conversion (SPDC) is widely studied for applications in quantum information science due to its ability to produce two photons that can be entangled in many degrees of freedom. For applications in quantum communication, two metrics of this process are particularly important: heralding efficiency and total joint rate. Here, we derive expressions for both quantities for a variety of different beam geometries and frequencies. We pay specific attention to the spectrum of both biphotons and individual photons. We reveal the underlying mechanisms responsible for the spectral shape and show they differ for different geometries and frequencies. We then use these spectra to calculate heralding efficiency and joint count rate and examine how each of these metrics changes with different geometries, frequencies, spectral filtering, and beam parameters. Interestingly, we find very high heralding efficiencies are achievable for collinear geometries without spectral filtering, while noncollinear geometries require spectral filtering to achieve the same values. We also find that the spectrum is narrower for nondegenerate SPDC than for degenerate SPDC, leading to lower joint count rates and higher heralding efficiency in the former. In addition to the theory, we verify selected predictions with experimental results.
Differencing methods for Korobov-type exponential sums

We study exponential sums of the form $$\Sigma_{n=1}^N\;e^{{2\pi}iab^{n}/m}$$ for nonzero integers a, b, m. Classically, non-trivial bounds were known for N ≥ √m by Korobov, and this range has been extended significantly by Bourgain as a result of his and others’ work on the sum-product phenomenon. Let P be a finite set of primes and let m be a large integer whose primes factors all belong to P. We use a variant of the Weyl-van der Corput method of differencing to give more explicit bounds that become non-trivial around the time when exp(log m/ log2 logm) ≤ N. We include applications to the digits of rational numbers and constructions of normal numbers.
Regge trajectories in \( \mathcal{N} \) = 2 supersymmetric Yang-Mills theory

We demonstrate that $$ \mathcal{N} $$ = 2 supersymmetric non-Abelian gauge theories have towers of BPS particles obeying a Regge relation, J ∼ m 2, between their angular momenta, J, and their masses, m. For SU(N) Yang-Mills theories, we estimate the slope of these Regge trajectories using a non-relativistic quiver quantum mechanics model. Along the way, we also prove various structure theorems for the quiver moduli spaces that appear in the calculation.
Hecke algebras with independent parameters

We study the Hecke algebra $${\mathcal {H}}({\mathbf {q}})$$H(q) over an arbitrary field $${\mathbb {F}}$$F of a Coxeter system (W, S) with independent parameters $${\mathbf {q}}=(q_s\in {\mathbb {F}}:s\in S)$$q=(qs?F:s?S) for all generators. This algebra always has a spanning set indexed by the Coxeter group W, which is indeed a basis if and only if every pair of generators joined by an odd edge in the Coxeter diagram receives the same parameter. In general, the dimension of $${\mathcal {H}}({\mathbf {q}})$$H(q) could be as small as 1. We construct a basis for $${\mathcal {H}}({\mathbf {q}})$$H(q) when (W, S) is simply laced. We also characterize when $${\mathcal {H}}({\mathbf {q}})$$H(q) is commutative, which happens only if the Coxeter diagram of (W, S) is simply laced and bipartite. In particular, for type A, we obtain a tower of semisimple commutative algebras whose dimensions are the Fibonacci numbers. We show that the representation theory of these algebras has some features in analogy/connection with the representation theory of the symmetric groups and the 0-Hecke algebras.
Uniform bounds for sums of Kloosterman sums of half integral weight

For $$m,n>0$$ or $$mn<0$$ we estimate the sums $$\begin{aligned} \sum _{c \le x} \frac{S(m,n,c,\chi )}{c}, \end{aligned}$$ where the $$S(m,n,c,\chi )$$ are Kloosterman sums attached to a multiplier $$\chi $$ of weight 1 / 2 on the full modular group. Our estimates are uniform in m, n and x in analogy with the bounds for the case $$mn<0$$ due to Ahlgren–Andersen, and those of Sarnak–Tsimerman for the trivial multiplier when $$m,n>0$$ . In the case $$mn<0$$ , our estimates are stronger in the mn-aspect than those of Ahlgren–Andersen. We also obtain a refinement whose quality depends on the factorization of $$24m-23$$ and $$24n-23$$ as well as the best known exponent for the Ramanujan–Petersson conjecture.
Spectrally Optimized Pointset Configurations

The search for optimal configurations of pointsets, the most notable examples being the problems of Kepler and Thompson, have an extremely rich history with diverse applications in physics, chemistry, communication theory, and scientific computing. In this paper, we introduce and study a new optimality criteria for pointset configurations. Namely, we consider a certain weighted graph associated with a pointset configuration and seek configurations that minimize certain spectral properties of the adjacency matrix or graph Laplacian defined on this graph, subject to geometric constraints on the pointset configuration. This problem can be motivated by solar cell design and swarming models, and we consider several spectral functions with interesting interpretations such as spectral radius, algebraic connectivity, effective resistance, and condition number. We prove that the regular simplex extremizes several spectral invariants on the sphere. We also consider pointset configurations on flat tori via (i) the analogous problem on lattices and (ii) through a variety of computational experiments. For many of the objectives considered (but not all), the triangular lattice is extremal.
Beyond L2-loss functions for learning sparse models

In sparse learning, the squared Euclidean distance is a popular choice for measuring the approximation quality. However, the use of other forms of parametrized loss functions, including asymmetric losses, has generated research interest. In this paper, we perform sparse learning using a broad class of smooth piecewise linear quadratic (PLQ) loss functions, including robust and asymmetric losses that are adaptable to many real-world scenarios. The proposed framework also supports heterogeneous data modeling by allowing different PLQ penalties for different blocks of residual vectors (split-PLQ). We demonstrate the impact of the proposed sparse learning in image recovery, and apply the proposed split-PLQ loss approach to tag refinement for image annotation and retrieval.
Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds

"Concentrated differential privacy" was recently introduced by Dwork and Rothblum as a relaxation of differential privacy, which permits sharper analyses of many privacy-preserving computations. We present an alternative formulation of the concept of concentrated differential privacy in terms of the Renyi divergence between the distributions obtained by running an algorithm on neighboring inputs. With this reformulation in hand, we prove sharper quantitative results, establish lower bounds, and raise a few new questions. We also unify this approach with approximate differential privacy by giving an appropriate definition of "approximate concentrated differential privacy".
A theoretical study of Y structures for causal discovery

Causal discovery from observational data in the presence of unobserved variables is challenging. Identification of so-called Y substructures is a sufficient condition for ascertaining some causal relations in the large sample limit, without the assumption of no hidden common causes. An example of a Y substructure is A → C, B → C, C → D. This paper describes the first asymptotically reliable and computationally feasible score-based search for discrete Y structures that does not assume that there are no unobserved common causes. For any parameterization of a directed acyclic graph (DAG) that has scores with the property that any DAG that can represent the distribution beats any DAG that can't, and for two DAGs that represent the distribution, if one has fewer parameters than the other, the one with the fewest parameter wins. In this framework there is no need to assign scores to causal structures with unobserved common causes. The paper also describes how the existence of a Y structure shows the presence of an unconfounded causal relation, without assuming that there are no hidden common causes.
Evidence for longitudinal variability of ethane ice on the surface of Pluto

Abstract We present the results of an investigation using near-infrared spectra of Pluto taken on 72 separate nights using SpeX/IRTF. These data were obtained between 2001 and 2013 at various sub-observer longitudes. The aim of this work was to confirm the presence of ethane ice and to determine any longitudinal trends on the surface of Pluto. We computed models of the continuum near the 2.405 μm band using Hapke theory and calculated an equivalent width of the ethane absorption feature for six evenly-spaced longitude bins and a grand average spectrum. The 2.405 μm band on Pluto was detected at the 7.5-σ level from the grand average spectrum. Additionally, the band was found to vary longitudinally with the highest absorption occurring in the N2-rich region and the lowest absorption occurring in the visibly dark region. The longitudinal variability of 12CO does not match that of the 2.405 μm band, suggesting a minimal contribution to the band by 13CO. We argue for ethane production in the atmosphere and present a theory of volatile transport to explain the observed longitudinal trend.
Parallel local graph clustering

Graph clustering has many important applications in computing, but due to growing sizes of graph, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest. Motivated partly by this, so-called local algorithms for graph clustering have received significant interest due to the fact that they can find good clusters in a graph with work proportional to the size of the cluster rather than that of the entire graph. This feature has proven to be crucial in making such graph clustering and many of its downstream applications efficient in practice. While local clustering algorithms are already faster than traditional algorithms that touch the entire graph, they are sequential and there is an opportunity to make them even more efficient via parallelization. In this paper, we show how to parallelize many of these algorithms in the shared-memory multicore setting, and we analyze the parallel complexity of these algorithms. We present comprehensive experiments on large-scale graphs showing that our parallel algorithms achieve good parallel speedups on a modern multicore machine, thus significantly speeding up the analysis of local graph clusters in the very large-scale setting.
A study of Landau damping with random initial inputs

Abstract For the Vlasov–Poisson equation with random uncertain initial data, we prove that the Landau damping solution given by the deterministic counterpart (Caglioti and Maffei (1998) [3] ) depends smoothly on the random variable if the time asymptotic profile does, under the smoothness and smallness assumptions similar to the deterministic case. The main idea is to generalize the deterministic contraction argument to more complicated function spaces to estimate derivatives in space, velocity and random variables. This result suggests that the random space regularity can persist in long-time even in time-reversible nonlinear kinetic equations.
On Gaussian Lipschitz spaces and the boundedness of fractional integrals and fractional derivatives on them

AbstractThe main purpose of this paper is to study the boundedness of Gaussian fractional integrals and derivatives associated to Hermite polynomial expansions on Gaussian Lipschitz spaces Lipα (γ). To get these results we introduce formulas for these operators in terms of the Hermite-Poisson semigroup as well as the Gaussian Lipschitz spaces. This approach was originally developed for the classical Poisson integral. These proofs can also be extended to the case of Laguerre and Jacobi expansions. In subsequent papers we will study the same operators on Gaussian Besov-Lipschitz and Triebel-Lizorkin spaces.
Network design with probabilistic capacities

We consider a network design problem with random arc capacities and give a formulation with a probabilistic capacity constraint on each cut of the network. To handle the exponentially-many probabilistic constraints a separation procedure that solves a nonlinear minimum cut problem is introduced. For the case with independent arc capacities, we exploit the supermodularity of the set function defining the constraints and generate cutting planes based on the supermodular covering knapsack polytope. For the general correlated case, we give a reformulation of the constraints that allows to uncover and utilize the submodularity of a related function. The computational results indicate that exploiting the underlying submodularity and supermodularity arising with the probabilistic constraints provides significant advantages over the classical approaches. © 2017 Wiley Periodicals, Inc. NETWORKS, 2017
Online Active Linear Regression via Thresholding.

We consider the problem of online active learning to collect data for regression modeling. Specifically, we consider a decision maker with a limited experimentation budget who must efficiently learn an underlying linear population model. Our main contribution is a novel threshold-based algorithm for selection of most informative observations; we characterize its performance and fundamental lower bounds. We extend the algorithm and its guarantees to sparse linear regression in high-dimensional settings. Simulations suggest the algorithm is remarkably robust: it provides significant benefits over passive random sampling in real-world datasets that exhibit high nonlinearity and high dimensionality --- significantly reducing both the mean and variance of the squared error.
Coordinates Adapted to Vector Fields: Canonical Coordinates

Given a finite collection of C1 vector fields on aC2 manifold which span the tangent space at every point, we consider the question of when there is locally a coordinate system in which these vector fields have a higher level of smoothness. For example, when is there a coordinate system in which the vector fields are smooth, or real analytic, or have Zygmund regularity of some finite order? We address this question in a quantitative way, which strengthens and generalizes previous works on the quantitative theory of sub-Riemannian (aka Carnot–Caratheodory) geometry due to Nagel, Stein, and Wainger, Tao and Wright, the second author, and others. Furthermore, we provide a diffeomorphism invariant version of these theories. This is the first part in a three part series of papers. In this paper, we study a particular coordinate system adapted to a collection of vector fields (sometimes called canonical coordinates) and present results related to the above questions which are not quite sharp; these results form the backbone of the series. The methods of this paper are based on techniques from ODEs. In the second paper, we use additional methods from PDEs to obtain the sharp results. In the third paper, we prove results concerning real analyticity and use methods from ODEs.
RADIO EMISSION AND ORBITAL MOTION FROM THE CLOSE-ENCOUNTER STAR–BROWN DWARF BINARY WISE J072003.20–084651.2*

We report the detection of radio emission and orbital motion from the nearby star–brown dwarf binary WISE J072003.20–084651.2AB. Radio observations across the 4.5–6.5 GHz band with the Very Large Array identify at the position of the system quiescent emission with a flux density of 15 ± 3 μJy, and a highly polarized radio source that underwent a 2–3 minute burst with peak flux density 300 ± 90 μJy. The latter emission is likely a low-level magnetic flare similar to optical flares previously observed for this source. No outbursts were detected in separate narrow-band Hα monitoring observations. We report new high-resolution imaging and spectroscopic observations that confirm the presence of a co-moving T5.5 secondary and provide the first indications of three-dimensional orbital motion. We used these data to revise our estimates for the orbital period (4.1_(-1.3)^(+2.7) year) and tightly constrain the orbital inclination to be nearly edge-on (93o6^(+1o6)_(−1o4)), although robust measures of the component and system masses will require further monitoring. The inferred orbital motion does not change the high likelihood that this radio-emitting very low-mass binary made a close pass to the Sun in the past 100 kyr.
Representation Theory in Complex Rank, I

P. Deligne defined interpolations of the tensor category of representations of the symmetric group S n to complex values of n. Namely, he defined tensor categories Rep(S t ) for any complex t. This construction was generalized by F. Knop to the case of wreath products of S n with a finite group. Generalizing these results, we propose a method of interpolating representation categories of various algebras containing S n (such as degenerate affine Hecke algebras, symplectic reflection algebras, rational Cherednik algebras, etc.) to complex values of n. We also define the group algebra of S n for complex n, study its properties, and propose a Schur-Weyl duality for Rep(S t ).
DCCast: Efficient Point to Multipoint Transfers Across Datacenters

Using multiple datacenters allows for higher availability, load balancing and reduced latency to customers of cloud services. To distribute multiple copies of data, cloud providers depend on inter-datacenter WANs that ought to be used efficiently considering their limited capacity and the ever-increasing data demands. In this paper, we focus on applications that transfer objects from one datacen-ter to several datacenters over dedicated inter-datacenter networks. We present DCCast, a centralized Point to Multi-Point (P2MP) algorithm that uses forwarding trees to efficiently deliver an object from a source datacenter to required destination datacenters. With low computational overhead, DCCast selects forwarding trees that minimize bandwidth usage and balance load across all links. With simulation experiments on Google's GScale network, we show that DCCast can reduce total band-width usage and tail Transfer Completion Times (TCT) by up to 50% compared to delivering the same objects via independent point-to-point (P2P) transfers.
AutoSeM: Automatic Task Selection and Mixing in Multi-Task Learning.

Multi-task learning (MTL) has achieved success over a wide range of problems, where the goal is to improve the performance of a primary task using a set of relevant auxiliary tasks. However, when the usefulness of the auxiliary tasks w.r.t. the primary task is not known a priori, the success of MTL models depends on the correct choice of these auxiliary tasks and also a balanced mixing ratio of these tasks during alternate training. These two problems could be resolved via manual intuition or hyper-parameter tuning over all combinatorial task choices, but this introduces inductive bias or is not scalable when the number of candidate auxiliary tasks is very large. To address these issues, we present AutoSeM, a two-stage MTL pipeline, where the first stage automatically selects the most useful auxiliary tasks via a Beta-Bernoulli multi-armed bandit with Thompson Sampling, and the second stage learns the training mixing ratio of these selected auxiliary tasks via a Gaussian Process based Bayesian optimization framework. We conduct several MTL experiments on the GLUE language understanding tasks, and show that our AutoSeM framework can successfully find relevant auxiliary tasks and automatically learn their mixing ratio, achieving significant performance boosts on several primary tasks. Finally, we present ablations for each stage of AutoSeM and analyze the learned auxiliary task choices.
Near linear time approximation schemes for uncapacitated and capacitated b-matching problems in nonbipartite graphs

We present the first fully polynomial approximation schemes for the maximum weighted (uncapacitated or capacitated) b-Matching problem for nonbipartite graphs that run in time (near) linear in the number of edges, that is, given any δ > 0 the algorithm produces a (1 -- δ) approximation in O(m poly(δ-1, log n)) time. We provide fractional solutions for the standard linear programming formulations for these problems and subsequently also provide fully polynomial (near) linear time approximation schemes for rounding the fractional solutions.Through these problems as a vehicle, we also present several ideas in the context of solving linear programs approximately using fast primal-dual algorithms. First, we show that approximation algorithms can be used to reduce the width of the formulation, and as a consequence we induce faster convergence. Second, even though the dual of these problems have exponentially many variables and an efficient exact computation of dual weights is infeasible, we can efficiently compute and use a sparse approximation of the dual weights using a combination of (i) adding perturbation to the constraints of the polytope and (ii) amplification followed by thresholding of the dual weights.These algorithms also have the advantage that they use O(n poly(δ-1, log n)) storage space and only make O(δ-4 log2(1/δ) log n) (or better) passes over a read only list of edges. These algorithms therefore can be run in the semi-streaming model and serve as exemplars where algorithms and ideas developed for the streaming model gives us algorithms for combinatorial optimization problems that were not known in absence of the streaming constraints.
Optimal Thresholds for Anomaly-Based Intrusion Detection in Dynamical Environments

In cyber-physical systems, malicious and resourceful attackers could penetrate a system through cyber means and cause significant physical damage. Consequently, early detection of such attacks becomes integral towards making these systems resilient to attacks. To achieve this objective, intrusion detection systems IDS that are able to detect malicious behavior early enough can be deployed. However, practical IDS are imperfect and sometimes they may produce false alarms even for normal system behavior. Since alarms need to be investigated for any potential damage, a large number of false alarms may increase the operational costs significantly. Thus, IDS need to be configured properly, as oversensitive IDS could detect attacks very early but at the cost of a higher number of false alarms. Similarly, IDS with very low sensitivity could reduce the false alarms while increasing the time to detect the attacks. The configuration of IDS to strike the right balance between time to detecting attacks and the rate of false positives is a challenging task, especially in dynamic environments, in which the damage caused by a successful attack is time-varying. In this paper, using a game-theoretic setup, we study the problem of finding optimal detection thresholds for anomaly-based detectors implemented in dynamical systems in the face of strategic attacks. We formulate the problem as an attacker-defender security game, and determine thresholds for the detector to achieve an optimal trade-off between the detection delay and the false positive rates. In this direction, we first provide an algorithm that computes an optimal fixed threshold that remains fixed throughout. Second, we allow the detector's threshold to change with time to further minimize the defender's loss, and we provide a polynomial-time algorithm to compute time-varying thresholds, which we call adaptive thresholds. Finally, we numerically evaluate our results using a water-distribution network as a case study.
Graphical Markov models for infinitely many variables

Representing the conditional independences present in a multivariate random vector via graphs has found widespread use in applications, and such representations are popularly known as graphical models or Markov random fields. These models have many useful properties, but their fundamental attractive feature is their ability to reflect conditional independences between blocks of variables through graph separation, a consequence of the equivalence of the pairwise, local and global Markov properties demonstrated by Pearl and Paz (1985). Modern day applications often necessitate working with either an infinite collection of variables (such as in a spatial-temporal field) or approximating a large high-dimensional finite stochastic system with an infinite-dimensional system. However, it is unclear whether the conditional independences present in an infinite-dimensional random vector or stochastic process can still be represented by separation criteria in an infinite graph. In light of the advantages of using graphs as tools to represent stochastic relationships, we undertake in this paper a general study of infinite graphical models. First, we demonstrate that naive extensions of the assumptions required for the finite case results do not yield equivalence of the Markov properties in the infinite-dimensional setting, thus calling for a more in-depth analysis. To this end, we proceed to derive general conditions which do allow representing the conditional independence in an infinite-dimensional random system by means of graphs, and our results render the result of Pearl and Paz as a special case of a more general phenomenon. We conclude by demonstrating the applicability of our theory through concrete examples of infinite-dimensional graphical models.
Deep learning for identifying radiogenomic associations in breast cancer

Abstract Rationale and objectives To determine whether deep learning models can distinguish between breast cancer molecular subtypes based on dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). Materials and methods In this institutional review board–approved single-center study, we analyzed DCE-MR images of 270 patients at our institution. Lesions of interest were identified by radiologists. The task was to automatically determine whether the tumor is of the Luminal A subtype or of another subtype based on the MR image patches representing the tumor. Three different deep learning approaches were used to classify the tumor according to their molecular subtypes: learning from scratch where only tumor patches were used for training, transfer learning where networks pre-trained on natural images were fine-tuned using tumor patches, and off-the-shelf deep features where the features extracted by neural networks trained on natural images were used for classification with a support vector machine. Network architectures utilized in our experiments were GoogleNet, VGG, and CIFAR. We used 10-fold crossvalidation method for validation and area under the receiver operating characteristic (AUC) as the measure of performance. Results The best AUC performance for distinguishing molecular subtypes was 0.65 (95% CI:[0.57,0.71]) and was achieved by the off-the-shelf deep features approach. The highest AUC performance for training from scratch was 0.58 (95% CI:[0.51,0.64]) and the best AUC performance for transfer learning was 0.60 (95% CI:[0.52,0.65]) respectively. For the off-the-shelf approach, the features extracted from the fully connected layer performed the best. Conclusion Deep learning may play a role in discovering radiogenomic associations in breast cancer.
Max k-cut and the smallest eigenvalue

Abstract Let G be a graph of order n and size m , and let mc k ( G ) be the maximum size of a k -cut of G . It is shown that mc k ( G ) ≤ k − 1 k ( m − μ min ( G ) n 2 ) , where μ min ( G ) is the smallest eigenvalue of the adjacency matrix of G . An infinite class of graphs forcing equality in this bound is constructed.
Bayesian regression tree ensembles that adapt to smoothness and sparsity

Ensembles of decision trees are a useful tool for obtaining flexible estimates of regression functions. Examples of these methods include gradient‐boosted decision trees, random forests and Bayesian classification and regression trees. Two potential shortcomings of tree ensembles are their lack of smoothness and their vulnerability to the curse of dimensionality. We show that these issues can be overcome by instead considering sparsity inducing soft decision trees in which the decisions are treated as probabilistic. We implement this in the context of the Bayesian additive regression trees framework and illustrate its promising performance through testing on benchmark data sets. We provide strong theoretical support for our methodology by showing that the posterior distribution concentrates at the minimax rate (up to a logarithmic factor) for sparse functions and functions with additive structures in the high dimensional regime where the dimensionality of the covariate space is allowed to grow nearly exponentially in the sample size. Our method also adapts to the unknown smoothness and sparsity levels, and can be implemented by making minimal modifications to existing Bayesian additive regression tree algorithms.
In-Line Post-Process Scribing for Reducing Cell to Module Efficiency Gap in Monolithic Thin-Film Photovoltaics

The gap between cell and module efficiency is a major challenge for all photovoltaic (PV) technologies. For monolithic thin-film PV modules, a significant fraction of this gap has been attributed to parasitic shunts and other defects, distributed across the module. In this paper, we show that it is possible to contain or isolate these shunts using state-of-the-art laser scribing processes, after the fabrication of the series-connected module is finished. We discuss three alternatives, and quantify the performance gains for each technique. We demonstrate that using these techniques, it is possible to recover up to 50% of the power lost to parasitic shunts, which results in 1-2% (absolute) increase in module efficiencies for typical thin-film PV technologies.
Many closed symplectic manifolds have infinite Hofer-Zehnder capacity

We exhibit many examples of closed symplectic manifolds on which there is an autonomous Hamiltonian whose associated flow has no nonconstant periodic orbits (the only previous explicit example in the literature was the torus T2n (n ≥ 2) with an irrational symplectic structure). The underlying smooth manifolds of our examples include, for instance: the K3 surface and also infinitely many smooth manifolds homeomorphic but not diffeomorphic to it; infinitely many minimal four-manifolds having any given finitely-presented group as their fundamental group; and simply connected minimal four-manifolds realizing all but finitely many points in the first quadrant of the geography plane below the line corresponding to signature 3. The examples are constructed by performing symplectic sums along suitable tori and then perturbing the symplectic form in such a way that hypersurfaces near the “neck” in the symplectic sum have no closed characteristics. We conjecture that any closed symplectic four-manifold with b > 1 admits symplectic forms with a similar property.