cssi/SciSciGPT-SciSciNet huggingface dataset:
Global Oort groups

Abstract We study the Oort groups for a prime p, i.e. finite groups G such that every G-Galois branched cover of smooth curves over an algebraically closed field of characteristic p lifts to a G-cover of curves in characteristic 0. We prove that all Oort groups lie in a particular class of finite groups that we characterize, with equality of classes under a conjecture about local liftings. We prove this equality unconditionally if the order of G is not divisible by 2 p 2 . We also treat the local lifting problem and relate it to the global problem.
Multiplicity matrices for the affine graded Hecke algebra

In this paper we are looking at the problem of determining the composition factors for the affine graded Hecke algebra via the computation of Kazhdan–Lusztig type polynomials. We review the algorithms of [G. Lusztig, Study of perverse sheaves arising from graded Lie algebras, Adv. Math. 112 (1995) 147–217; G. Lusztig, Graded Lie algebras and intersection cohomology, preprint], and use them in particular to compute, at every real central character which admits tempered modules, the geometric parameterization, the Kazhdan–Lusztig polynomials, the composition series, and the Iwahori–Matsumoto involution for the representations with Iwahori fixed vectors of the split p-adic groups of type G2 and F4 (and by the nature of the algorithms, for their Levi subgroups).
Explicit integration with GPU acceleration for large kinetic networks

We demonstrate the first implementation of recently-developed fast explicit kinetic integration algorithms on modern graphics processing unit (GPU) accelerators. Taking as a generic test case a Type Ia supernova explosion with an extremely stiff thermonuclear network having 150 isotopic species and 1604 reactions coupled to hydrodynamics using operator splitting, we demonstrate the capability to solve of order 100 realistic kinetic networks in parallel in the same time that standard implicit methods can solve a single such network on a CPU. This orders-of-magnitude decrease in computation time for solving systems of realistic kinetic networks implies that important coupled, multiphysics problems in various scientific and technical fields that were intractable, or could be simulated only with highly schematic kinetic networks, are now computationally feasible.
The x86isa Books: Features, Usage, and Future Plans.

The x86isa library, incorporated in the ACL2 community books project, provides a formal model of the x86 instruction-set architecture and supports reasoning about x86 machine-code programs. However, analyzing x86 programs can be daunting -- even for those familiar with program verification, in part due to the complexity of the x86 ISA. Furthermore, the x86isa library is a large framework, and using and/or contributing to it may not seem straightforward. We present some typical ways of working with the x86isa library, and describe some of its salient features that can make the analysis of x86 machine-code programs less arduous. We also discuss some capabilities that are currently missing from these books -- we hope that this will encourage the community to get involved in this project.
Pluri)Potential Compactifications

Using pluricomplex Green functions we introduce a compactification of a complex manifold M invariant with respect to biholomorphisms similar to the Martin compactification in the potential theory. For this we show the existence of a norming volume form V on M such that all negative plurisubharmonic functions on M are in L1(M, V ). Moreover, the set of such functions with the norm not exceeding 1 is compact. Identifying a point w ∈ M with the normalized pluricomplex Green function with pole at w we get an imbedding of M into a compact set and the closure of M in this set is the pluripotential compactification.
Following High-level Navigation Instructions on a Simulated Quadcopter with Imitation Learning

We introduce a method for following high-level navigation instructions by mapping directly from images, instructions and pose estimates to continuous low-level velocity commands for real-time control. The Grounded Semantic Mapping Network (GSMN) is a fully-differentiable neural network architecture that builds an explicit semantic map in the world reference frame by incorporating a pinhole camera projection model within the network. The information stored in the map is learned from experience, while the local-to-world transformation is computed explicitly. We train the model using DAggerFM, a modified variant of DAgger that trades tabular convergence guarantees for improved training speed and memory use. We test GSMN in virtual environments on a realistic quadcopter simulator and show that incorporating an explicit mapping and grounding modules allows GSMN to outperform strong neural baselines and almost reach an expert policy performance. Finally, we analyze the learned map representations and show that using an explicit map leads to an interpretable instruction-following model.
The equivariant Euler characteristic of moduli spaces of curves

We derive a formula for the Sn-equivariant Euler characteristic of the moduli space Mg,n of genus g curves with n marked points.
Zero-shot Event Detection by multimodal distributional semantic embedding of videos

We propose a new zero-shot Event Detection method by Multi-modal Distributional Semantic embedding of videos. Our model embeds object and action concepts as well as other available modalities from videos into a distributional semantic space. To our knowledge, this is the first Zero-Shot event detection model that is built on top of distributional semantics and extends it in the following directions: (a) semantic embedding of multimodal information in videos (with focus on the visual modalities), (b) automatically determining relevance of concepts/attributes to a free text query, which could be useful for other applications, and (c) retrieving videos by free text event query (e.g., "changing a vehicle tire") based on their content. We embed videos into a distributional semantic space and then measure the similarity between videos and the event query in a free text form. We validated our method on the large TRECVID MED (Multimedia Event Detection) challenge. Using only the event title as a query, our method outperformed the state-of-the-art that uses big descriptions from 12.6% to 13.5% with MAP metric and 0.73 to 0.83 with ROC-AUC metric. It is also an order of magnitude faster.
Operator variational inference

Variational inference is an umbrella term for algorithms which cast Bayesian inference as optimization. Classically, variational inference uses the Kullback-Leibler divergence to define the optimization. Though this divergence has been widely used, the resultant posterior approximation can suffer from undesirable statistical properties. To address this, we reexamine variational inference from its roots as an optimization problem. We use operators, or functions of functions, to design variational objectives. As one example, we design a variational objective with a Langevin-Stein operator. We develop a black box algorithm, operator variational inference (OPVI), for optimizing any operator objective. Importantly, operators enable us to make explicit the statistical and computational tradeoffs for variational inference. We can characterize different properties of variational objectives, such as objectives that admit data subsampling—allowing inference to scale to massive data—as well as objectives that admit variational programs—a rich class of posterior approximations that does not require a tractable density. We illustrate the benefits of OPVI on a mixture model and a generative model of images.
Reasoning About Physical Interactions with Object-Oriented Prediction and Planning

Object-based factorizations provide a useful level of abstraction for interacting with the world. Building explicit object representations, however, often requires supervisory signals that are difficult to obtain in practice. We present a paradigm for learning object-centric representations for physical scene understanding without direct supervision of object properties. Our model, Object-Oriented Prediction and Planning (O2P2), jointly learns a perception function to map from image observations to object representations, a pairwise physics interaction function to predict the time evolution of a collection of objects, and a rendering function to map objects back to pixels. For evaluation, we consider not only the accuracy of the physical predictions of the model, but also its utility for downstream tasks that require an actionable representation of intuitive physics. After training our model on an image prediction task, we can use its learned representations to build block towers more complicated than those observed during training.
Tautological module and intersection theory on Hilbert schemes of nodal curves

This paper presents the rudiments of Hilbert-Mumford Intersection (HMI) theory: intersection theory on the relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension. We introduce an additive group of geometric cycles, called ’tautological module’, generated by diagonal loci, node scrolls, and twists thereof. We determine recursively the intersection action on this group by the discriminant (big diagonal) divisor and all its powers. We show that this suffices to determine arbitrary polynomials in Chern classes, in particular Chern numbers, for the tautological vector bundles on the Hilbert schemes, which are closely related to enumerative geometry of families of nodal curves.
Risk-Sensitive Learning and Pricing for Demand Response

We consider the setting in which an electric power utility seeks to curtail its peak electricity demand by offering a fixed group of customers a uniform price for reductions in consumption relative to their predetermined baselines. The underlying demand curve, which describes the aggregate reduction in consumption in response to the offered price, is assumed to be affine and subject to unobservable random shocks. Assuming that both the parameters of the demand curve and the distribution of the random shocks are initially unknown to the utility, we investigate the extent to which the utility might dynamically adjust its offered prices to maximize its cumulative risk-sensitive payoff over a finite number of ${T}$ days. In order to do so effectively, the utility must design its pricing policy to balance the tradeoff between the need to learn the unknown demand model (exploration) and maximize its payoff (exploitation) over time. In this paper, we propose such a pricing policy, which is shown to exhibit an expected payoff loss over ${T}$ days that is at most ${O(\sqrt {T}\log (T))}$ , relative to an oracle pricing policy that knows the underlying demand model. Moreover, the proposed pricing policy is shown to yield a sequence of prices that converge to the oracle optimal prices in the mean square sense.
On Taking Advantage of Multiple Requests in Error Correcting Codes

In most notions of locality in error correcting codes-notably locally recoverable codes (LRCs) and locally decodable codes (LDCs)-a decoder seeks to learn a single symbol of a message while looking at only a few symbols of the corresponding codeword. However, suppose that one wants to recover $r$ > 1 symbols of the message. The two extremes are repeating the single-query algorithm $r$ times (this is the intuition behind LRCs with availability, primitive multiset batch codes, and PIR codes) or simply running a global decoding algorithm to recover the whole thing. In this paper, we investigate what can happen in between these two extremes: at what value of $r$ does repetition stop being a good idea? In order to begin to study this question we introduce robust batch codes, which seek to find $r$ symbols of the message using $m$ queries to the codeword, in the presence of erasures. We focus on the case where $r$ = m, which can be seen as a generalization of the MDS property. Surprisingly, we show that for this notion of locality, repetition is optimal even up to very large values of $r$ = Ω(k).
A Syntactic Neural Model for General-Purpose Code Generation

We consider the problem of parsing natural language descriptions into source code written in a general-purpose programming language like Python. Existing data-driven methods treat this problem as a language generation task without considering the underlying syntax of the target programming language. Informed by previous work in semantic parsing, in this paper we propose a novel neural architecture powered by a grammar model to explicitly capture the target syntax as prior knowledge. Experiments find this an effective way to scale up to generation of complex programs from natural language descriptions, achieving state-of-the-art results that well outperform previous code generation and semantic parsing approaches.
The derived Picard group of an affine Azumaya algebra

We describe the derived Picard group of an Azumaya algebra A on an affine scheme X in terms of global sections of the constant sheaf of integers on X, the Picard group of X, and the stabilizer of the Brauer class of A under the action of $$\mathrm {Aut}(X)$$ . In particular, we find that the derived Picard group of an Azumaya algebra is generally not isomorphic to that of the underlying scheme. In the case of the trivial Azumaya algebra, our result refines Yekutieli’s description of the derived Picard group of a commutative algebra. We also get, as a corollary, an alternate proof of a result of Antieau which relates derived equivalences to Brauer equivalences for affine Azumaya algebras. The example of a Weyl algebra in finite characteristic is examined in some detail.
Sequential Joint Detection and Estimation: Optimum Tests and Applications

We treat the statistical inference problems in which one needs to detect the correct signal model among multiple hypotheses and estimate a parameter simultaneously using as small number of samples as possible. Conventional methods treat the detection and estimation subproblems separately, ignoring the intrinsic coupling between them. However, a joint detection and estimation problem should be solved to maximize the overall performance. We address the sample size concern through a sequential and Bayesian setup. Specifically, we seek the optimum triplet of stopping time, detector, and estimator(s) that minimizes the number of samples subject to a constraint on the combined detection and estimation cost. A general framework for optimum sequential joint detection and estimation is developed. The resulting optimum detector and estimator(s) are strongly coupled with each other, proving that the separate treatment is strictly suboptimum. The theoretical results derived for a quite general model are then applied to several problems with linear quadratic Gaussian (LQG) models, including dynamic spectrum access in cognitive radio, and state estimation in smart grid with topological uncertainty. Numerical results corroborate the superior overall detection and estimation performance of the proposed schemes over the conventional methods that handle the subproblems separately.
First eigenvalue of the $p$-Laplacian under integral curvature condition

Abstract We give various estimates of the first eigenvalue of the p -Laplace operator on closed Riemannian manifold with integral curvature conditions.
BISTRO: an efficient relaxation-based method for contextual bandits

We present efficient algorithms for the problem of contextual bandits with i.i.d. covariates, an arbitrary sequence of rewards, and an arbitrary class of policies. Our algorithm BISTRO requires d calls to the empirical risk minimization (ERM) oracle per round, where d is the number of actions. The method uses unlabeled data to make the problem computationally simple. When the ERM problem itself is computationally hard, we extend the approach by employing multiplicative approximation algorithms for the ERM. The integrality gap of the relaxation only enters in the regret bound rather than the benchmark. Finally, we show that the adversarial version of the contextual bandit problem is learnable (and efficient) whenever the full-information supervised online learning problem has a non-trivial regret guarantee (and efficient).
Convex normality of rational polytopes with long edges

Abstract We introduce the property of convex normality of rational polytopes and give a dimensionally uniform lower bound for the edge lattice lengths, guaranteeing the property. As an application, we show that if every edge of a lattice d -polytope P has lattice length ⩾ 4 d ( d + 1 ) then P is normal. This answers in the positive a question raised in 2007. If P is a lattice simplex whose edges have lattice lengths ⩾ d ( d + 1 ) then P is even covered by lattice parallelepipeds. For the approach developed here, it is necessary to involve rational polytopes even for the application to lattice polytopes.
Consensus ranking under the exponential model

We analyze the generalized Mallows model, a popular exponential model over rankings. Estimating the central (or consensus) ranking from data is NP-hard. We obtain the following new results: (1) We show that search methods can estimate both the central ranking π0 and the model parameters θ exactly. The search is n! in the worst case, but is tractable when the true distribution is concentrated around its mode; (2) We show that the generalized Mallows model is jointly exponential in (π0, θ), and introduce the conjugate prior for this model class; (3) The sufficient statistics are the pairwise marginal probabilities that item i is preferred to item j. Preliminary experiments confirm the theoretical predictions and compare the new algorithm and existing heuristics.
Joint Transmission Map Estimation and Dehazing Using Deep Networks

Single image haze removal is an extremely challenging problem due to its inherent ill-posed nature. Several prior-based and learning-based methods have been proposed in the literature to solve this problem and they have achieved visually appealing results. However, most of the existing methods assume constant atmospheric light model and tend to follow a two-step procedure involving prior-based methods for estimating transmission map followed by calculation of dehazed image using the closed form solution. In this paper, we relax the constant atmospheric light assumption and propose a novel unified single image dehazing network that jointly estimates the transmission map and performs dehazing. In other words, our new approach provides an end-to-end learning framework, where the inherent transmission map and dehazed result are learned jointly from the loss function. The extensive experiments evaluated on synthetic and real datasets with challenging hazy images demonstrate that the proposed method achieves significant improvements over the state-of-the-art methods.
Inner radius of nodal domains of quantum ergodic eigenfunctions

In this short note we show that the lower bounds of Mangoubi on the inner radius of nodal domains can be improved for quantum ergodic sequences of eigenfunctions, according to a certain power of the radius of shrinking balls on which the eigenfunctions equidistribute. We prove such improvements using a quick application of our recent results (arXiv:1606.02057), which give modified growth estimates for eigenfunctions that equidistribute on small balls. Since by the results of Han and Hezari-Riviere small scale QE holds for negatively curved manifolds on logarithmically shrinking balls, we get logarithmic improvements on the inner radius of such manifolds. We also get improvements for manifolds with ergodic geodesic flows. In addition using the small scale equidistribution results of Lester-Rudnick, one gets polynomial betterments of for toral eigenfunctions in dimensions $n \geq 3$. The results work only for a full density subsequence of eigenfunctions.
On opinion dynamics in heterogeneous networks

This paper studies the opinion dynamics model recently introduced by Hegselmann and Krause: each agent in a group maintains a real number describing its opinion; and each agent updates its opinion by averaging all other opinions that are within some given confidence range. The confidence ranges are distinct for each agent. This heterogeneity and state-dependent topology leads to poorly-understood complex dynamic behavior. We classify the agents via their interconnection topology and, accordingly, compute the equilibria of the system. We conjecture that any trajectory of this model eventually converges to a steady state under fixed topology. To establish this conjecture, we derive two novel sufficient conditions: both conditions guarantee convergence and constant topology for infinite time, while one condition also guarantees monotonicity of the convergence. In the evolution under fixed topology for infinite time, we define leader groups that determine the followers' rate and direction of convergence.
Hierarchical Capacity Provisioning for Fog Computing

The concept of fog computing is centered around providing computation resources at the edge of the network, thereby reducing the latency and improving the quality of service. However, it is still desirable to investigate how and where at the edge of the network the computation capacity should be provisioned. To this end, we propose a hierarchical capacity provisioning scheme. In particular, we consider a two-tier network architecture consisting of shallow and deep cloudlets and explore the benefits of hierarchical capacity provisioning based on queuing analysis. Moreover, we explore two different network scenarios in which the network delay between the two tiers is negligible and the case that the deep cloudlet is located somewhere deeper in the network and thus the delay is significant. More importantly, we model the first network delay scenario with bufferless shallow cloudlets and the second scenario with finite-size buffer shallow cloudlets, and formulate an optimization problem for each model. We also use stochastic ordering to solve the optimization problem formulated for the first model and an upper bound-based technique is proposed for the second model. The performance of the proposed scheme is evaluated via simulations in which we show the accuracy of the proposed upper bound technique and the queue length estimation approach for both randomly generated input and real trace data.
Visual task: a collaborative cognitive aid for acute care resuscitation

Preventable medical errors are a severe problem in healthcare, causing over 400,000 deaths per year in the US in hospitals alone. In acute care, the branch of medicine encompassing the emergency department (ED) and intensive care units (ICU), error rates may be higher to due low situational awareness among clinicians performing resuscitation on patients. To support cognition, novice team leaders may rely on reference guides to direct and anticipate future steps. However, guides often act as a fixation point, diverting the leader's attention away from the team. To address this issue, we conducted a qualitative study that evaluates a collaborative cognitive aid co-designed with clinicians called Visual TASK. Our study explored the use of Visual TASK in three simulations employing a projected shared display with two different interaction modalities: the Microsoft Kinect and a touchscreen. Our results suggest that tools like the Kinect, while useful in other areas of acute care like the OR, are unsuitable for use in high-stress situations like resuscitation. We also observed that fixation may not be constrained to reference guides alone, and may extend to other objects in the room. We present our findings, and a discussion regarding future avenues in which collaborative cognitive aids may help in improving situational awareness in resuscitation.
RF-PUF: Enhancing IoT Security Through Authentication of Wireless Nodes Using In-Situ Machine Learning

Traditional authentication in radio-frequency (RF) systems enable secure data communication within a network through techniques such as digital signatures and hash-based message authentication codes (HMAC), which suffer from key-recovery attacks. State-of-the-art Internet of Things networks such as Nest also use open authentication (OAuth 2.0) protocols that are vulnerable to cross-site-recovery forgery (CSRF), which shows that these techniques may not prevent an adversary from copying or modeling the secret IDs or encryption keys using invasive, side channel, learning or software attacks. Physical unclonable functions (PUFs), on the other hand, can exploit manufacturing process variations to uniquely identify silicon chips which makes a PUF-based system extremely robust and secure at low cost, as it is practically impossible to replicate the same silicon characteristics across dies. Taking inspiration from human communication, which utilizes inherent variations in the voice signatures to identify a certain speaker, we present RF-PUF: a deep neural network-based framework that allows real-time authentication of wireless nodes, using the effects of inherent process variation on RF properties of the wireless transmitters (Tx), detected through in-situ machine learning at the receiver (Rx) end. The proposed method utilizes the already-existing asymmetric RF communication framework and does not require any additional circuitry for PUF generation or feature extraction. The burden of device identification is completely shifted to the gateway Rx, similar to the operation of a human listener’s brain. Simulation results involving the process variations in a standard 65-nm technology node, and features such as local oscillator offset and ${I}$ – ${Q}$ imbalance detected with a neural network having 50 neurons in the hidden layer indicate that the framework can distinguish up to 4800 Tx(s) with an accuracy of 99.9% [≈99% for 10000 Tx(s)] under varying channel conditions, and without the need for traditional preambles. The proposed scheme can be used as a stand-alone security feature, or as a part of traditional multifactor authentication.
Differential Algebras with Banach-Algebra Coefficients I: from C*-Algebras to the K-Theory of the Spectral Curve

We present an operator-coefficient version of Sato’s infinite-dimensional Grassmann manifold, and τ-function. In this setting the classical Burchnall–Chaundy ring of commuting differential operators can be shown to determine a C*-algebra. For this C*-algebra topological invariants of the spectral ring become readily available, and further, the Brown–Douglas–Fillmore theory of extensions can be applied. We construct KK classes of the spectral curve of the ring and, motivated by the fact that all isospectral Burchnall–Chaundy rings make up the Jacobian of the curve, we compare the (degree-1) K-homology of the curve with that of its Jacobian. We show how the Burchnall–Chaundy C*-algebra extension by the compact operators provides a family of operator τ-functions.
Remarks on compactifications of pseudofinite groups

We discuss the Bohr compactification of a pseudofinite group, motivated by a question of Boris Zilber. Basically referring to results in the literature we point out that (i) the Bohr compactification of an ultraproduct of finite simple groups is trivial, and (ii) the “definable” Bohr compactification of any pseudofinite group G, relative to an ambient nonstandard model of set theory in which it is definable, is commutative-by-profinite.
Hardness of approximate nearest neighbor search

We prove conditional near-quadratic running time lower bounds for approximate Bichromatic Closest Pair with Euclidean, Manhattan, Hamming, or edit distance. Specifically, unless the Strong Exponential Time Hypothesis (SETH) is false, for every δ>0 there exists a constant e>0 such that computing a (1+e)-approximation to the Bichromatic Closest Pair requires Ω(n2−δ) time. In particular, this implies a near-linear query time for Approximate Nearest Neighbor search with polynomial preprocessing time. Our reduction uses the recently introduced Distributed PCP framework, but obtains improved efficiency using Algebraic Geometry (AG) codes. Efficient PCPs from AG codes have been constructed in other settings before, but our construction is the first to yield new hardness results.
Stochastic variance reduction for nonconvex optimization

We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient descent (SGD); but their theoretical analysis almost exclusively assumes convexity. In contrast, we obtain nonasymptotic rates of convergence of SVRG for nonconvex optimization, showing that it is provably faster than SGD and gradient descent. We also analyze a subclass of nonconvex problems on which SVRG attains linear convergence to the global optimum. We extend our analysis to mini-batch variants, showing (theoretical) linear speedup due to minibatching in parallel settings.
Capacity and Achievable Rate Regions for Linear Network Coding Over Ring Alphabets

The rate of a network code is the ratio of the block size of the network’s messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general cases of arbitrary ring and module alphabets. For non-commutative rings, two-sided linearity is allowed. Specifically, we prove the following for directed acyclic networks. First, the linear rate region and the linear capacity of any network over a finite field depend only on the characteristic of the field. Furthermore, any two fields with different characteristics yield different linear capacities for at least one network. Second, whenever the characteristic of a given finite field divides the size of a given finite ring, each network’s linear rate region over the ring is contained in its linear rate region over the field. Thus, any network’s linear capacity over a field is at least its linear capacity over any other ring of the same size. An analogous result also holds for linear network codes over module alphabets. Third, whenever the characteristic of a given finite field does not divide the size of a given finite ring, there is some network whose linear capacity over the ring is strictly greater than its linear capacity over the field. Thus, for any finite field, there always exist rings over which some networks have higher linear capacities than over the field.
Cluster Ensembles and Kac-Moody Groups

Abstract We study the relationship between two sets of coordinates on a double Bruhat cell, the cluster variables introduced by Berenstein, Fomin, and Zelevinsky and the X -coordinates defined by the coweight parametrization of Fock and Goncharov. In these coordinates, we show that the generalized Chamber Ansatz of Fomin and Zelevinsky coincides with the cluster ensemble map, a canonical monomial transformation between the cluster variables and X -coordinates defined by a common exchange matrix. We prove this in the setting of an arbitrary symmetrizable Kac–Moody group, generalizing along the way many previous results on the double Bruhat cells of a semisimple algebraic group. In particular, we construct an upper cluster algebra structure on the coordinate ring of any double Bruhat cell in a symmetrizable Kac–Moody group, proving a conjecture of Berenstein, Fomin, and Zelevinsky.
Rotationally Invariant Singular Solutions to the Kapustin-Witten Equations

In the present paper, we find a system of non-linear ODEs that gives rotationally invariant solutions to the Kapustin-Witten equations in 4-dimensional Euclidean space. We explicitly solve these ODEs in some special cases and find decaying rational solutions, which provide solutions to the Kapustin-Witten equations. The imaginary parts of the solutions are singular. By rescaling, we find some limit behavior for these singular solutions. In addition, for any integer $k$, we can construct a 5$|k|$ dimensional family of $C^1$ solutions to the Kapustin-Witten equations on Euclidean space, again with singular imaginary parts. Moreover, we find solutions to the Kapustin-Witten equations over $S^3\times (0,+\infty)$ with the Nahm pole boundary condition.
Approximate Low-Weight Check Codes and Circuit Lower Bounds for Noisy Ground States

The No Low-Energy Trivial States (NLTS) conjecture of Freedman and Hastings (Quantum Information and Computation 2014), which asserts the existence of local Hamiltonians whose low-energy states cannot be generated by constant-depth quantum circuits, identifies a fundamental obstacle to resolving the quantum PCP conjecture. Progress towards the NLTS conjecture was made by Eldar and Harrow (Foundations of Computer Science 2017), who proved a closely related theorem called No Low-Error Trivial States (NLETS). In this paper, we give a much simpler proof of the NLETS theorem and use the same technique to establish superpolynomial circuit size lower bounds for noisy ground states of local Hamiltonians (assuming QCMA != QMA), resolving an open question of Eldar and Harrow. We discuss the new light our results cast on the relationship between NLTS and NLETS. Finally, our techniques imply the existence of approximate quantum low-weight check (qLWC) codes with linear rate, linear distance, and constant weight checks. These codes are similar to quantum LDPC codes except (1) each particle may participate in a large number of checks, and (2) errors only need to be corrected up to fidelity 1 - 1/poly(n). This stands in contrast to the best-known stabilizer LDPC codes due to Freedman, Meyer, and Luo which achieve a distance of O(sqrt{n log n}). The principal technique used in our results is to leverage the Feynman-Kitaev clock construction to approximately embed a subspace of states defined by a circuit as the ground space of a local Hamiltonian.
Finding your Lookalike: Measuring Face Similarity Rather than Face Identity

Face images are one of the main areas of focus for computer vision, receiving on a wide variety of tasks. Although face recognition is probably the most widely researched, many other tasks such as kinship detection, facial expression classification and facial aging have been examined. In this work we propose the new, subjective task of quantifying perceived face similarity between a pair of faces. That is, we predict the perceived similarity between facial images, given that they are not of the same person. Although this task is clearly correlated with face recognition, it is different and therefore justifies a separate investigation. Humans often remark that two persons look alike, even in cases where the persons are not actually confused with one another. In addition, because face similarity is different than traditional image similarity, there are challenges in data collection and labeling, and dealing with diverging subjective opinions between human labelers. We present evidence that finding facial look-alikes and recognizing faces are two distinct tasks. We propose a new dataset for facial similarity and introduce the Lookalike network, directed towards similar face classification, which outperforms the ad hoc usage of a face recognition network directed at the same task
Generalizations of maximal inequalities to arbitrary selection rules

Abstract We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of n jointly distributed random variables. We control the expectation of a randomly selected random variable from n jointly distributed random variables, and present bounds that are at least as tight as the classical maximal inequalities, and much tighter when the distribution of selection index is near deterministic. A new family of information theoretic measures was introduced in the process, which may be of independent interest.
Kasner Meets Poncelet

Given a planar pentagon, construct two new pentagons: the vertices of the first one are the intersection points of the diagonals of the original pentagon, and the vertices of the second one are the tangency points of the conic inscribed in the original pentagon. E. Kasner theorem, published in 1928, asserts that these two operations on pentagons commute. We extend Kasner's result to Poncelet polygons, that is, the polygons inscribed into a conic and circumscribed about a conic.
Binary log-linear learning with stochastic communication links

In this paper, we consider distributed decision-making over stochastic communication links in multi-agent systems. We show how to extend the current literature on potential games with binary log-linear learning (which mainly focuses on ideal communication links) to consider the impact of stochastic communication channels. More specifically, we derive conditions on the probability of link connectivity to achieve a target probability for the set of potential maximizers (in the stationary distribution). Furthermore, our toy example demonstrates a transition phenomenon for achieving any target probability for the set of potential maximizers.
Building a RAPPOR with the Unknown: Privacy-Preserving Learning of Associations and Data Dictionaries

Techniques based on randomized response enable the collection of potentially sensitive data from clients in a privacy-preserving manner with strong local differential privacy guarantees. One of the latest such technologies, RAPPOR, allows the marginal frequencies of an arbitrary set of strings to be estimated via privacy-preserving crowdsourcing. However, this original estimation process requires a known set of possible strings; in practice, this dictionary can often be extremely large and sometimes completely unknown. In this paper, we propose a novel decoding algorithm for the RAPPOR mechanism that enables the estimation of "unknown unknowns," i.e., strings we do not even know we should be estimating. To enable learning without explicit knowledge of the dictionary, we develop methodology for estimating the joint distribution of two or more variables collected with RAPPOR. This is a critical step towards understanding relationships between multiple variables collected in a privacy-preserving manner.
Language modeling with highway LSTM

Language models (LMs) based on Long Short Term Memory (LSTM) have shown good gains in many automatic speech recognition tasks. In this paper, we extend an LSTM by adding highway networks inside an LSTM and use the resulting Highway LSTM (HW-LSTM) model for language modeling. The added highway networks increase the depth in the time dimension. Since a typical LSTM has two internal states, a memory cell and a hidden state, we compare various types of HW-LSTM by adding highway networks onto the memory cell and/or the hidden state. Experimental results on English broadcast news and conversational telephone speech recognition show that the proposed HW-LSTM LM improves speech recognition accuracy on top of a strong LSTM LM baseline. We report 5.1% and 9.9% on the Switchboard and CallHome subsets of the Hub5 2000 evaluation, which reaches the best performance numbers reported on these tasks to date.
Portfolio choice with small temporary and transient price impact

We study portfolio selection in a model with both temporary and transient price impact introduced by Garleanu and Pedersen (2016). In the large-liquidity limit where both frictions are small, we derive explicit formulas for the asymptotically optimal trading rate and the corresponding minimal leading-order performance loss. We find that the losses are governed by the volatility of the frictionless target strategy, like in models with only temporary price impact. In contrast, the corresponding optimal portfolio not only tracks the frictionless optimizer, but also exploits the displacement of the market price from its unaffected level.
Learning network of multivariate Hawkes processes: a time series approach

Learning the influence structure of multiple time series data is of great interest to many disciplines. This paper studies the problem of recovering the causal structure in network of multivariate linear Hawkes processes. In such processes, the occurrence of an event in one process affects the probability of occurrence of new events in some other processes. Thus, a natural notion of causality exists between such processes captured by the support of the excitation matrix. We show that the resulting causal influence network is equivalent to the Directed Information graph (DIG) of the processes, which encodes the causal factorization of the joint distribution of the processes. Furthermore, we present an algorithm for learning the support of excitation matrix of a class of multivariate Hawkes processes with exponential exciting functions (or equivalently the DIG). The performance of the algorithm is evaluated on synthesized multivariate Hawkes networks as well as a stock market and MemeTracker real-world dataset.
From the weak Bruhat order to crystal posets

We investigate the ways in which fundamental properties of the weak Bruhat order on a Weyl group can be lifted (or not) to a corresponding highest weight crystal graph, viewed as a partially ordered set; the latter projects to the weak order via the key map. First, a crystal theoretic analogue of the statement that any two reduced expressions for the same Coxeter group element are related by Coxeter moves is proven for all lower intervals $$[\hat{0},v]$$ in a simply or doubly laced crystal. On the other hand, it is shown that no finite set of moves exists, even in type A, for arbitrary crystal graph intervals. In fact, it is shown that there are relations of arbitrarily high degree amongst crystal operators that are not implied by lower degree relations. Second, for crystals associated to Kac–Moody algebras it is shown for lower intervals that the Mobius function is always 0 or ±1, and in finite type this is also proven for upper intervals, with a precise formula given in each case. Moreover, the order complex for each of these intervals is proven to be homotopy equivalent to a ball or to a sphere of some dimension, despite often not being shellable. For general intervals, examples are constructed with arbitrarily large Mobius function, again even in type A. Any interval having Mobius function other than 0 or ±1 is shown to contain within it a relation amongst crystal operators that is not implied by the relations giving rise to the local structure of the crystal, making precise a tight relationship between the Mobius function and these somewhat unexpected relations appearing in crystals. New properties of the key map are also derived. The key is shown to be determined entirely by the edge-colored poset-theoretic structure of the crystal, and a recursive algorithm is given for calculating it. In finite types, the fiber of the longest element of any parabolic subgroup of the Weyl group is also proven to have a unique minimal and a unique maximal element; this property fails for more general elements of the Weyl group.
Rortex and comparison with eigenvalue-based vortex identification criteria

Most of the current Eulerian vortex identification criteria, including the Q criterion and the λci criterion, are exclusively determined by the eigenvalues of the velocity gradient tensor or the related invariants and thereby can be regarded as eigenvalue-based criteria. However, these criteria will be plagued with two shortcomings: (1) these criteria fail to identify the swirl axis or orientation; (2) these criteria are prone to severe contamination by shearing. To address these issues, a new vector named Rortex which represents the local fluid rotation was proposed in our previous work. In this paper, an alternative eigenvector-based definition of Rortex is introduced. The direction of Rortex, which represents the possible axis of the local rotation, is determined by the real eigenvector of the velocity gradient tensor. And then the rotational strength obtained in the plane perpendicular to the possible axis is used to define the magnitude of Rortex. This new equivalent definition allows a much more efficient implementation. Furthermore, a systematic interpretation of scalar, vector, and tensor versions of Rortex is presented. By relying on the tensor interpretation, the velocity gradient tensor is decomposed to a rigid rotation part and a non-rotational part including shearing, stretching, and compression, different from the traditional symmetric and anti-symmetric tensor decomposition. It can be observed that shearing always manifests its effect on the imaginary part of the complex eigenvalues and consequently contaminates eigenvalue-based criteria, while Rortex can exclude the shearing contamination and accurately quantify the local rotational strength. In addition, in contrast to eigenvalue-based criteria, not only the iso-surface of Rortex but also the Rortex vectors and the Rortex lines can be applied to investigate vortical structures. Several comparative studies on simple examples and realistic flows are studied to confirm the superiority of Rortex.
Error-correcting dynamics in visual working memory

Working memory is critical to cognition, decoupling behavior from the immediate world. Yet, it is imperfect; internal noise introduces errors into memory representations. Such errors have been shown to accumulate over time and increase with the number of items simultaneously held in working memory. Here, we show that discrete attractor dynamics mitigate the impact of noise on working memory. These dynamics pull memories towards a few stable representations in mnemonic space, inducing a bias in memory representations but reducing the effect of random diffusion. Model-based and model-free analyses of human and monkey behavior show that discrete attractor dynamics account for the distribution, bias, and precision of working memory reports. Furthermore, attractor dynamics are adaptive. They increase in strength as noise increases with memory load and experiments in humans show these dynamics adapt to the statistics of the environment, such that memories drift towards contextually-predicted values. Together, our results suggest attractor dynamics mitigate errors in working memory by counteracting noise and integrating contextual information into memories.
Can we trust teaching evaluations when response rates are not high? Implications from a Monte Carlo simulation

ABSTRACTOnline teaching evaluations have replaced in-class teaching evaluations as the new norm for assessing teaching performance. Faculty raise concerns regarding lower response rates compared to...
Conservation genomic analysis reveals ancient introgression and declining levels of genetic diversity in Madagascar’s hibernating dwarf lemurs

Madagascar's biodiversity is notoriously threatened by deforestation and climate change. Many of these organisms are rare, cryptic, and severely threatened, making population-level sampling unrealistic. Such is the case with Madagascar's dwarf lemurs (genus Cheirogaleus), the only obligate hibernating primate. We here apply comparative genomic approaches to generate the first genome-wide estimates of genetic diversity within dwarf lemurs. We generate a reference genome for the fat-tailed dwarf lemur, Cheirogaleus medius, and use this resource to facilitate analyses of high-coverage (~30×) genome sequences for wild-caught individuals representing species: C. sp. cf. medius, C. major, C. crossleyi, and C. sibreei. This study represents the largest contribution to date of novel genomic resources for Madagascar's lemurs. We find concordant phylogenetic relationships among the four lineages of Cheirogaleus across most of the genome, and yet detect a number of discordant genomic regions consistent with ancient admixture. We hypothesized that these regions could have resulted from adaptive introgression related to hibernation, indeed finding that genes associated with hibernation are present, though most significantly, that gene ontology categories relating to transcription are over-represented. We estimate levels of heterozygosity and find particularly low levels in an individual sampled from an isolated population of C. medius that we refer to as C. sp. cf. medius. Results are consistent with a recent decline in effective population size, which is evident across species. Our study highlights the power of comparative genomic analysis for identifying species and populations of conservation concern, as well as for illuminating possible mechanisms of adaptive phenotypic evolution.