cssi/SciSciGPT-SciSciNet huggingface dataset:
Measure Differential Equations

A new type of differential equations for probability measures on Euclidean spaces, called measure differential equations (briefly MDEs), is introduced. MDEs correspond to probability vector fields, which map measures on an Euclidean space to measures on its tangent bundle. Solutions are intended in weak sense and existence, uniqueness and continuous dependence results are proved under suitable conditions. The latter are expressed in terms of the Wasserstein metric on the base and fiber of the tangent bundle. MDEs represent a natural measure-theoretic generalization of ordinary differential equations via a monoid morphism mapping sums of vector fields to fiber convolution of the corresponding probability vector Fields. Various examples, including finite-speed diffusion and concentration, are shown, together with relationships to partial differential equations. Finally, MDEs are also natural mean-field limits of multi-particle systems, with convergence results extending the classical Dobrushin approach.
Generation of Entangled Photon Holes Using Quantum Interference

Entangled photon holes represent a new form of entanglement in quantum optics. Here we report on an experimental observation of entangled photon holes generated using quantum interference techniques.
Sidon sets and graphs without 4-cycles

The problem of determining the maximum number of edges in an $n$-vertex graph that does not contain a 4-cycle has a rich history in extremal graph theory. Using Sidon sets constructed by Bose and Chowla, for each odd prime power $q$ we construct a graph with $q^2 - q - 2$ vertices that does not contain a 4-cycle and has at least $\frac{1}{2}q^3 - q^2 - O(q^{3/4})$ edges. This disproves a conjecture of Abreu, Balbuena, and Labbate concerning the Tur\'{a}n number $\mathrm{ex}(q^2 - q - 2, C_4)$.
SAFFRON: an Adaptive Algorithm for Online Control of the False Discovery Rate

In the online false discovery rate (FDR) problem, one observes a possibly infinite sequence of $p$-values $P_1,P_2,\dots$, each testing a different null hypothesis, and an algorithm must pick a sequence of rejection thresholds $\alpha_1,\alpha_2,\dots$ in an online fashion, effectively rejecting the $k$-th null hypothesis whenever $P_k \leq \alpha_k$. Importantly, $\alpha_k$ must be a function of the past, and cannot depend on $P_k$ or any of the later unseen $p$-values, and must be chosen to guarantee that for any time $t$, the FDR up to time $t$ is less than some pre-determined quantity $\alpha \in (0,1)$. In this work, we present a powerful new framework for online FDR control that we refer to as SAFFRON. Like older alpha-investing (AI) algorithms, SAFFRON starts off with an error budget, called alpha-wealth, that it intelligently allocates to different tests over time, earning back some wealth on making a new discovery. However, unlike older methods, SAFFRON's threshold sequence is based on a novel estimate of the alpha fraction that it allocates to true null hypotheses. In the offline setting, algorithms that employ an estimate of the proportion of true nulls are called adaptive methods, and SAFFRON can be seen as an online analogue of the famous offline Storey-BH adaptive procedure. Just as Storey-BH is typically more powerful than the Benjamini-Hochberg (BH) procedure under independence, we demonstrate that SAFFRON is also more powerful than its non-adaptive counterparts, such as LORD and other generalized alpha-investing algorithms. Further, a monotone version of the original AI algorithm is recovered as a special case of SAFFRON, that is often more stable and powerful than the original. Lastly, the derivation of SAFFRON provides a novel template for deriving new online FDR rules.
Deep Recurrent Q-Learning for Partially Observable MDPs

Deep Reinforcement Learning has yielded proficient controllers for complex tasks. However, these controllers have limited memory and rely on being able to perceive the complete game screen at each decision point. To address these shortcomings, this article investigates the effects of adding recurrency to a Deep Q-Network (DQN) by replacing the first post-convolutional fully-connected layer with a recurrent LSTM. The resulting Deep Recurrent Q-Network (DRQN), although capable of seeing only a single frame at each timestep, successfully integrates information through time and replicates DQN's performance on standard Atari games and partially observed equivalents featuring flickering game screens. Additionally, when trained with partial observations and evaluated with incrementally more complete observations, DRQN's performance scales as a function of observability. Conversely, when trained with full observations and evaluated with partial observations, DRQN's performance degrades less than DQN's. Thus, given the same length of history, recurrency is a viable alternative to stacking a history of frames in the DQN's input layer and while recurrency confers no systematic advantage when learning to play the game, the recurrent net can better adapt at evaluation time if the quality of observations changes.
On the Aloha Throughput-Fairness Tradeoff

A well-known inner bound of the stability region of the finite-user slotted Aloha protocol (with fixed contention probabilities) on the collision channel with $n$ users assumes worst case service rates (all user queues non-empty). Using this inner bound as a feasible set of achievable rates, a characterization of the throughput–fairness tradeoff over this set is obtained, where the throughput is defined as the sum of the individual user rates, and two definitions of fairness are considered: the Jain–Chiu–Hawe function and the sum-user $\alpha $ -fair (isoelastic) utility function. This characterization is obtained using both an equality constraint and an inequality constraint on the throughput, and properties of the optimal controls, the optimal rates, and the maximum fairness as a function of the target throughput are established. A key structural property underpinning all theorems is the observation that the vector of contention probabilities that extremizes both fairness objectives has its nonzero components taking at most two distinct values.
Hadoop on HPC: Integrating Hadoop and Pilot-Based Dynamic Resource Management

High performance distributed computing environments have traditionally been designed to meet the compute demands of scientific applications, supercomputers have historically been producers and not consumers of data. The Apache Hadoop ecosystem has evolved to address many of the traditional limitations of HPC platforms. There exist a whole class of scientific applications that need the collective capabilities of traditional high-performance computing environments and the Apache Hadoop ecosystem. For example, the scientific domains of bio-molecular dynamics, genomics and high-energy physics need to couple traditional computing with Hadoop/Spark based analysis. We investigate the critical question of how to present both capabilities to such scientific applications. Whereas this questions needs answers at multiple levels, we focus on the design of middleware that might support the needs of both. We propose extensions to the Pilot-Abstraction so as to provide a unifying resource management layer. This provides an important step towards integration and thereby interoperable use of HPC and Hadoop/Spark, and allows applications to efficiently couple HPC stages (e.g. simulations) to data analytics. Many supercomputing centers have started to officially support Hadoop environments either in a dedicated environment or in hybrid deployments using tools, such as myHadoop. However, this typically involves many intrinsic, environment-specific details that need to be mastered, and often swamp conceptual questions like: How best to couple HPC and Hadoop application stages? How to explore runtime trade-offs (data localities vs. data movement)? This paper provides both conceptual understanding and practical solutions to questions central to the integrated use of HPC and Hadoop environments. Our experiments are performed on state-of-the-art production HPC environments and provide middleware for multiple domain sciences.
Observation of Bose-Einstein condensation of molecules.

We have observed Bose-Einstein condensation of molecules. When a spin mixture of fermionic $^{6}\mathrm{L}\mathrm{i}$ atoms was evaporatively cooled in an optical dipole trap near a Feshbach resonance, the atomic gas was converted into $^{6}\mathrm{L}\mathrm{i}_{2}$ molecules. Below 600 nK, a Bose-Einstein condensate of up to 900 000 molecules was identified by the sudden onset of a bimodal density distribution. This condensate realizes the limit of tightly bound fermion pairs in the crossover between BCS superfluidity and Bose-Einstein condensation.
Spin correlations: Tevatron vs. LHC

We compare theoretical expectations for the observation of spin correlations in top quark pair production and decay at the Fermilab Tevatron and the CERN Large Hadron Collider (LHC). In particular, we note that the differing top quark pair production mechanisms in the two environments test different aspects of the Standard Model and require different strategies to observe the correlations. At the Tevatron, production is dominated by q¯q → t¯t and the strategy is to construct a double-decay angle distribution where one decay angle is measured in the t rest frame and the other in the ¯t rest frame. The dominant process at the LHC is gg → t¯t, with a rich spin structure that allows for a second option in observing spin correlations. Here the strategy is to select events where the t¯t pair is produced at relatively low velocity in the zero momentum frame (ZMF). For these events, there are strong azimuthal correlations between t and ¯t decay products present. This measurement enjoys the advantage that it can be carried out in the laboratory frame.
Peckness of Edge Posets

For any graded poset P, we define a new graded poset, 𝓔(P), whose elements are the edges in the Hasse diagram of P. For any group G acting on the boolean algebra B n in a rank-preserving fashion we conjecture that 𝓔(B n /G) is Peck. We prove that the conjecture holds for “common cover transitive” actions. We give some infinite families of common cover transitive actions and show that the common cover transitive actions are closed under direct and semidirect products.
Comparison of Limited Feedback Schemes for NOMA Transmission in mmWave Drone Networks

Introducing non-orthogonal multiple access (NOMA) transmission to an unmanned aerial vehicle (UAV) based communication network is a promising solution to enhance spectral efficiency. However, for realistic deployment of such a network, identifying a practical user feedback scheme for NOMA is essential. In this paper, considering two practical feedback schemes we introduce NOMA transmission to UAVs acting as aerial base stations (BS) to provide coverage at a large stadium. In particular, a UAV-BS generates directional beams, and multiple users are served simultaneously within the same beam employing NOMA transmission. Each user is considered to have a target rate based on its quality of service (QoS) requirements. In order to relieve the burden of tracking and feeding back full channel state information, we consider two limited feedback schemes as practical alternatives: 1) user distance, and 2) user angle with respect to beamforming direction under different user region geometries. Our evaluation results show that NOMA with limited feedback can provide better sum rates compared to its orthogonal counterpart. Further, based on the geometry of user region we identify that there is an optimal feedback scheme and user ordering criteria for NOMA transmission which can maximize sum rates.
Efficient Online Relative Comparison Kernel Learning.

Learning a kernel matrix from relative comparison human feedback is an important problem with applications in collaborative filtering, object retrieval, and search. For learning a kernel over a large number of objects, existing methods face significant scalability issues inhibiting the application of these methods to settings where a kernel is learned in an online and timely fashion. In this paper we propose a novel framework called Efficient online Relative comparison Kernel LEarning (ERKLE), for efficiently learning the similarity of a large set of objects in an online manner. We learn a kernel from relative comparisons via stochastic gradient descent, one query response at a time, by taking advantage of the sparse and low-rank properties of the gradient to efficiently restrict the kernel to lie in the space of positive semidefinite matrices. In addition, we derive a passive-aggressive online update for minimally satisfying new relative comparisons as to not disrupt the influence of previously obtained comparisons. Experimentally, we demonstrate a considerable improvement in speed while obtaining improved or comparable accuracy compared to current methods in the online learning setting.
Using direct policy search to identify robust strategies in adapting to uncertain sea-level rise and storm surge

Abstract Sea-level rise poses considerable risks to coastal communities, ecosystems, and infrastructure. Decision makers are faced with uncertain sea-level projections when designing a strategy for coastal adaptation. The traditional methods are often silent on tradeoffs as well as the effects of tail-area events and of potential future learning. Here we reformulate a simple sea-level rise adaptation model to address these concerns. We show that Direct Policy Search yields improved solution quality, with respect to Pareto-dominance in the objectives, over the traditional approach under uncertain sea-level rise projections and storm surge. Additionally, the new formulation produces high quality solutions with less computational demands than an intertemporal optimization approach. Our results illustrate the utility of multi-objective adaptive formulations for the example of coastal adaptation and point to wider-ranging application in climate change adaptation decision problems.
Acylindrically hyperbolic groups

We say that a group $G$ is acylindrically hyperbolic if it admits a non-elementary acylindrical action on a hyperbolic space. We prove that the class of acylindrically hyperbolic groups coincides with many other classes studied in the literature, e.g., the class $C_{geom}$ introduced by Hamenstadt, the class of groups admitting a non-elementary weakly properly discontinuous action on a hyperbolic space in the sense of Bestvina and Fujiwara, and the class of groups with hyperbolically embedded subgroups studied by Dahmani, Guirardel, and the author. We also record some basic results about acylindrically hyperbolic groups for future use.
Combination Networks With or Without Secrecy Constraints: The Impact of Caching Relays

This paper considers a two-hop network architecture known as a combination network, where a layer of relay nodes connects a server to a set of end users. In particular, a new model is investigated, where the intermediate relays employ caches in addition to the end users. First, a new centralized coded caching scheme is developed that utilizes maximum distance separable coding, jointly optimizes cache placement and delivery phase, and enables decomposing the combination network into a set virtual multicast sub-network. It is shown that if the sum of the memory of an end user and its connected relay nodes is sufficient to store the database, then the server can disengage in the delivery phase and all the end users’ requests can be satisfied by the caches in the network. Lower bounds on the normalized delivery load using genie-aided cut-set arguments are presented along with second hop optimality. Next, recognizing the information security concerns of coded caching, this new model is studied under three different secrecy settings: 1) secure delivery where we require an external entity that must not gain any information about the database files by observing the transmitted signals over the network links; 2) secure caching, where we impose the constraint that end users must not be able to obtain any information about files that they did not request; and 3) both secure delivery and secure caching, simultaneously. We demonstrate how network topology affects the system performance under these secrecy requirements. Finally, we provide numerical results demonstrating the system performance in each of the settings considered.
TEACHING SYNTAX BY ADVERSARIAL DISTRACTION

A computer-implemented method and system are provided for teaching syntax for training a neural network based natural language inference model. The method includes selectively performing, by the hardware processor, person reversal on a set of hypothesis sentences, based on person reversal prevention criteria, to obtain a first training data set. The method further includes enhancing, by the hardware processor, a robustness of the neural network based natural language inference model to syntax changes by training the neural network based natural language inference model on original training data combined with the first data set.
Wave propagation in undulated structural lattices

Abstract This work investigates wave propagation in undulated square structural lattices. The undulated pattern is obtained by imposing an initial curvature to the lattice’s elements. The study considers both periodic undulated structures, in which the undulation is uniform throughout the structure as well as graded undulated patterns, in which the undulation is modulated within the lattice. Undulation is specifically considered in relation to its ability to induce anisotropy in the equivalent mechanical properties and to break the symmetry of the straight square lattice. Results show that wave motion is inhibited within specified frequency ranges owing to the generation of band gaps, and in specific directions as a result of the undulation-induced anisotropy.
Mathematical analysis and dynamic active subspaces for a long term model of HIV

a long-term model of HIV infection dynamics [8] was developed to describe the entire time course of the disease. It consists of a large system of ODEs with many parameters, and is expensive to simulate. In the current paper, this model is analyzed by determining all infection-free steady states and studying the local stability properties of the unique biologically-relevant equilibrium. Active subspace methods are then used to perform a global sensitivity analysis and study the dependence of an infected individual's T-cell count on the parameter space. Building on these results, a global-in-time approximation of the T-cell count is created by constructing dynamic active subspaces and reduced order models are generated, thereby allowing for inexpensive computation.
RepEx: A Flexible Framework for Scalable Replica Exchange Molecular Dynamics Simulations

Replica Exchange (RE) simulations have emerged as an important algorithmic tool for the molecular sciences. Typically RE functionality is integrated into the molecular simulation software package. A primary motivation of the tight integration of RE functionality with simulation codes has been performance. This is limiting at multiple levels. First, advances in the RE methodology are tied to the molecular simulation code for which they were developed. Second, it is difficult to extend or experiment with novel RE algorithms, since expertise in the molecular simulation code is required. The tight integration results in difficulty to gracefully handle failures, and other runtime fragilities. We propose the RepEx framework which is addressing aforementioned shortcomings, while striking the balance between flexibility (any RE scheme) and scalability (several thousand replicas) over a diverse range of HPC platforms. The primary contributions of the RepEx framework are: (i) its ability to support different Replica Exchange schemes independent of molecular simulation codes, (ii) provide the ability to execute different exchange schemes and replica counts independent of the specific availability of resources, (iii) provide a runtime system that has first-class support for task-level parallelism, and (iv) provide a required scalability along multiple dimensions.
The limitations of optimization from samples

In this paper we consider the following question: can we optimize objective functions from the training data we use to learn them? We formalize this question through a novel framework we call optimization from samples (OPS). In OPS, we are given sampled values of a function drawn from some distribution and the objective is to optimize the function under some constraint. While there are interesting classes of functions that can be optimized from samples, our main result is an impossibility. We show that there are classes of functions which are statistically learnable and optimizable, but for which no reasonable approximation for optimization from samples is achievable. In particular, our main result shows that there is no constant factor approximation for maximizing coverage functions under a cardinality constraint using polynomially-many samples drawn from any distribution. We also show tight approximation guarantees for maximization under a cardinality constraint of several interesting classes of functions including unit-demand, additive, and general monotone submodular functions, as well as a constant factor approximation for monotone submodular functions with bounded curvature.
Entire Solution in Cylinder-Like Domains for a Bistable Reaction–Diffusion Equation

We construct nontrivial entire solutions for a bistable reaction–diffusion equation in a class of domains that are unbounded in one direction. The motivation comes from recent results of Berestycki et al. (Calc Var Partial Differ Equ 55(3):1–32, 2016) concerning propagation and blocking phenomena in infinite domains. A key assumption in their study was the “cylinder-like” assumption: their domains are supposed to be straight cylinders in a half space. The purpose of this paper is to consider domains that tend to a straight cylinder in one direction. We need a different approach based on the long time stability of the bistable wave in heterogeneous media. We also prove the existence of an entire solution for a one-dimensional problem with a non-homogeneous linear term.
On irreducible divisor graphs in commutative rings with zero-divisors

In this paper, we continue the program initiated by I. Beck's now classical paper concerning zero-divisor graphs of commutative rings. After the success of much research regarding zero-divisor graphs, many authors have turned their attention to studying divisor graphs of non-zero elements in integral domains. This inspired the so called irreducible divisor graph of an integral domain studied by J. Coykendall and J. Maney. Factorization in rings with zero-divisors is considerably more complicated than integral domains and has been widely studied recently. We find that many of the same techniques can be extended to rings with zero-divisors. In this article, we construct several distinct irreducible divisor graphs of a commutative ring with zero-divisors. This allows us to use graph theoretic properties to help characterize finite factorization properties of commutative rings, and conversely.
A note on the DP-chromatic number of complete bipartite graphs

Abstract DP-coloring (also called correspondence coloring) is a generalization of list coloring recently introduced by Dvořak and Postle. Several known bounds for the list chromatic number of a graph G , χ l ( G ) , also hold for the DP-chromatic number of G , χ D P ( G ) . On the other hand, there are several properties of the DP-chromatic number that show that it differs with the list chromatic number. In this note we show one such property. It is well known that χ l ( K k , t ) = k + 1 if and only if t ≥ k k . We show that χ D P ( K k , t ) = k + 1 if t ≥ 1 + ( k k ∕ k ! ) ( log ( k ! ) + 1 ) , and we show that χ D P ( K k , t ) k + 1 if t k k ∕ k ! .
A sharp lower bound for choosing the maximum of an independent sequence

In this paper we consider a variation of the full-information secretary problem where the random variables to be observed are independent but not necessary identically distributed. The main result is a sharp lower bound for the optimal win probability. Precisely, if X1,...,Xn are independent random variables with known continuous distributions and Vn(X1,...,Xn):=supτℙ(Xτ=Mn), where Mn≔max{X1,...,Xn} and the supremum is over all stopping times adapted to X1,...,Xn then Vn(X1,...,Xn)≥(1-1/n)n-1, and this bound is attained. The method of proof consists in reducing the problem to that of a sequence of random variables taking at most two possible values, and then applying Bruss' sum-the-odds theorem, Bruss (2000). In order to obtain a sharp bound for each n, we improve Bruss' lower bound, Bruss (2003), for the sum-the-odds problem.
Push-Pull Block Puzzles are Hard

This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question [19]. Push-pull block puzzles are a type of recreational motion planning problem, similar to Sokoban, that involve moving a ‘robot’ on a square grid with \(1 \times 1\) obstacles. The obstacles cannot be traversed by the robot, but some can be pushed and pulled by the robot into adjacent squares. Thin walls prevent movement between two adjacent squares. This work follows in a long line of algorithms and complexity work on similar problems [3, 4, 5, 6, 7, 8, 9, 14, 16, 18]. The 2D push-pull block puzzle shows up in the video games Pukoban as well as The Legend of Zelda: A Link to the Past, giving another proof of hardness for the latter [2]. This variant of block-pushing puzzles is of particular interest because of its connections to reversibility, since any action (e.g., push or pull) can be inverted by another valid action (e.g., pull or push).
Directional Emphasis in Ambisonics

We describe an ambisonics enhancement method that increases the signal strength in specified directions at a low-computational cost. The method can be used in a static setup to emphasize the signal arriving from a particular direction or set of directions. It can also be used in an adaptive arrangement where it sharpens directionality and reduces the distortion in timbre associated with low-degree ambisonics representations. The emphasis operator has a very low-computational complexity and can be applied to time domain as well as time–frequency ambisonics representations. The operator upscales a low-degree ambisonics representation to a higher degree representation.
Controlled Islanding via Weak Submodularity

Cascading failures typically occur following a large disturbance in power systems, such as tripping of a generating unit or a transmission line. Such failures can propagate and destabilize the entire power system, potentially leading to widespread outages. One approach to mitigate impending cascading failures is through controlled islanding, in which a set of transmission lines is deliberately tripped to partition the unstable system into several disjoint, internally stable islands. Selecting such a set of transmission lines is inherently a combinatorial optimization problem. Current approaches address this problem in two steps: first, classify coherent generators into groups and then separate generator groups into different islands with minimal load-generation imbalance. These methods, however, are based on computationally expensive heuristics that do not provide optimality guarantees. This paper proposes a novel approach to controlled islanding based on weak submodularity. The new formulation jointly captures the minimal generator non-coherency and minimal load-generation imbalance in one objective function. The islanding problem is then relaxed to a formulation with bounded submodularity ratio and a matroid constraint. An approximation algorithm is proposed which achieves a provable optimality bound on non-coherency and load-generation imbalance. The proposed framework is tested on IEEE 39-bus and 118-bus power systems.
Automatic action annotation in weakly labeled videos

Abstract Manual spatio-temporal annotation of human actions in videos is laborious, requires several annotators and contains human biases. In this paper, we present a weakly supervised approach to automatically obtain spatio-temporal annotations of an actor in action videos. We first obtain a large number of action proposals in each video. To capture a few most representative action proposals in each video and evade processing thousands of them, we rank them using optical flow and saliency in a 3D-MRF based framework and select a few proposals using MAP based proposal subset selection method. We demonstrate that this ranking preserves the high quality action proposals. Several such proposals are generated for each video of the same action. Our next challenge is to iteratively select one proposal from each video so that all proposals are globally consistent. We formulate this as Generalized Maximum Clique Graph problem using shape, global and fine-grained similarity of proposals across the videos. The output of our method is the most action representative proposals from each video. Our method can also annotate multiple instances of the same action in a video. We have validated our approach on three challenging action datasets: UCF-Sport, sub-JHMDB and THUMOS13 and have obtained promising results compared to several baseline methods. Moreover, action detection experiments using annotations obtained by our method and several baselines demonstrate the superiority of our approach.
Quantitative Control Approach for Wind Turbine Generators to Provide Fast Frequency Response with Guarantee of Rotor Security

Wind generation is expected to reach substantially higher levels of penetration in the near future. With the converter interface, the rotor inertia of doubly-fed induction generator (DFIG) based wind turbine generator is effectively decoupled from the system, causing a reduction in inertial response. This can be compensated by enabling the DFIG to provide fast frequency response. This paper proposes a quantitative control approach for DFIG to deliver fast frequency response in the inertial response time scale. A supplementary power surge function is added to the active power reference of DFIG. The exact amount of power surge that is available from DFIG-based wind turbine is quantified based on estimation of maximum extractable energy. Moreover, the operational constraints such as rotor limits and converter over-load limit are considered at the same time. Thus, the proposed approach not only provides adequate inertial response but also ensures the rotor speed is kept within a specified operating range. Rotor safety is guaranteed without the need for an additional rotor speed protection scheme.
SPRINGER ISOMORPHISMS IN CHARACTERISTIC p

Let G be a simple algebraic group over an algebraically closed field of characteristic p, and assume that p is a separably good prime for G. Let P be a parabolic subgroup whose unipotent radical UP has nilpotence class less than p. We show that there exists a particularly nice Springer isomorphism for G which restricts to a certain canonical isomorphism Lie \( \left({U}_P\right)\overset{\sim }{\to }{U}_P \) defined by J.-P. Serre. This answers a question raised both by G. McNinch in [M2], and by J. Carlson et. al in [CLN]. For the groups SLn; SOn, and Sp2n, viewed in the usual way as subgroups of GLn or GL2n, such a Springer isomorphism can be given explicitly by the Artin–Hasse exponential series.
Benchmarking deep reinforcement learning for continuous control

Recently, researchers have made significant progress combining the advances in deep learning for learning feature representations with reinforcement learning. Some notable examples include training agents to play Atari games based on raw pixel data and to acquire advanced manipulation skills using raw sensory inputs. However, it has been difficult to quantify progress in the domain of continuous control due to the lack of a commonly adopted benchmark. In this work, we present a benchmark suite of continuous control tasks, including classic tasks like cart-pole swing-up, tasks with very high state and action dimensionality such as 3D humanoid locomotion, tasks with partial observations, and tasks with hierarchical structure. We report novel findings based on the systematic evaluation of a range of implemented reinforcement learning algorithms. Both the benchmark and reference implementations are released at https://github.com/rllab/rllab in order to facilitate experimental reproducibility and to encourage adoption by other researchers.
Cooperative Holistic Scene Understanding: Unifying 3D Object, Layout, and Camera Pose Estimation

Holistic 3D indoor scene understanding refers to jointly recovering the i) object bounding boxes, ii) room layout, and iii) camera pose, all in 3D. The existing methods either are ineffective or only tackle the problem partially. In this paper, we propose an end-to-end model that simultaneously solves all three tasks in real-time given only a single RGB image. The essence of the proposed method is to improve the prediction by i) parametrizing the targets (e.g., 3D boxes) instead of directly estimating the targets, and ii) cooperative training across different modules in contrast to training these modules individually. Specifically, we parametrize the 3D object bounding boxes by the predictions from several modules, i.e., 3D camera pose and object attributes. The proposed method provides two major advantages: i) The parametrization helps maintain the consistency between the 2D image and the 3D world, thus largely reducing the prediction variances in 3D coordinates. ii) Constraints can be imposed on the parametrization to train different modules simultaneously. We call these constraints "cooperative losses" as they enable the joint training and inference. We employ three cooperative losses for 3D bounding boxes, 2D projections, and physical constraints to estimate a geometrically consistent and physically plausible 3D scene. Experiments on the SUN RGB-D dataset shows that the proposed method significantly outperforms prior approaches on 3D layout estimation, 3D object detection, 3D camera pose estimation, and holistic scene understanding.
An Interpreter for Quantum Circuits

This paper describes an ACL2 interpreter for "netlists" describing quantum circuits. Several quantum gates are implemented, including the Hadamard gate H, which rotates vectors by 45 degrees, necessitating the use of irrational numbers, at least at the logical level. Quantum measurement presents an especially difficult challenge, because it requires precise comparisons of irrational numbers and the use of random numbers. This paper does not address computation with irrational numbers or the generation of random numbers, although future work includes the development of pseudo-random generators for ACL2.
Bernoulli identities, zeta relations, determinant expressions, Mellin transforms, and representation of the Hurwitz numbers

Abstract The Riemann zeta identity at even integers of Lettington, along with his other Bernoulli and zeta relations, is generalized. Other corresponding recurrences and determinant relations are illustrated. Another consequence is the application to sums of double zeta values. A set of identities for the Ramanujan and generalized Ramanujan polynomials is presented. An alternative proof of Lettington's identity is provided, together with its generalizations to the Hurwitz and Lerch zeta functions, hence to Dirichlet L series, to Eisenstein series, and to general Mellin transforms. The Hurwitz numbers H ˜ n occur in the Laurent expansion about the origin of a certain Weierstrass ℘ function for a square lattice, and are highly analogous to the Bernoulli numbers. An integral representation of the Laurent coefficients about the origin for general ℘ functions, and for these numbers in particular, is presented. As a Corollary, the asymptotic form of the Hurwitz numbers is determined. In addition, a series representation of the Hurwitz numbers is given, as well as a new recurrence. Other results concern the Matter numbers of the equianharmonic case of the ℘ function.
Unexpected distribution phenomenon resulting from Cantor series expansions

Abstract We explore in depth the number theoretic and statistical properties of certain sets of numbers arising from their Cantor series expansions. As a direct consequence of our main theorem we deduce numerous new results as well as strengthen the known ones.
Error resilience in distributed storage via rank-metric codes

This paper presents a novel coding scheme for distributed storage systems containing nodes with adversarial errors. The key challenge in such systems is the propagation of erroneous data from a single corrupted node to the rest of the system during a node repair process. This paper presents a concatenated coding scheme which is based on two types of codes: maximum rank distance (MRD) code as an outer code and optimal repair maximal distance separable (MDS) array code as an inner code. Given this, two different types of adversarial errors are considered: the first type considers an adversary that can replace the content of an affected node only once; while the second attack-type considers an adversary that can pollute data an unbounded number of times. This paper proves that the proposed coding scheme attains an upper bound on resilience capacity for the first type of error. Further, the paper presents mechanisms that combine this code with subspace signatures to achieve error resilience for the second type of errors. Finally, the paper concludes by presenting a construction based on MRD codes for optimal locally repairable scalar codes that can tolerate adversarial errors.
Learning ReLUs via Gradient Descent

In this paper we study the problem of learning Rectified Linear Units (ReLUs) which are functions of the form $\vct{x}\mapsto \max(0,\langle \vct{w},\vct{x}\rangle)$ with $\vct{w}\in\R^d$ denoting the weight vector. We study this problem in the high-dimensional regime where the number of observations are fewer than the dimension of the weight vector. We assume that the weight vector belongs to some closed set (convex or nonconvex) which captures known side-information about its structure. We focus on the realizable model where the inputs are chosen i.i.d.~from a Gaussian distribution and the labels are generated according to a planted weight vector. We show that projected gradient descent, when initialized at $\vct{0}$, converges at a linear rate to the planted model with a number of samples that is optimal up to numerical constants. Our results on the dynamics of convergence of these very shallow neural nets may provide some insights towards understanding the dynamics of deeper architectures.
Overcoming Language Variation in Sentiment Analysis with Social Attention

Variation in language is ubiquitous, particularly in newer forms of writing such as social media. Fortunately, variation is not random; it is often linked to social properties of the author. In this paper, we show how to exploit social networks to make sentiment analysis more robust to social language variation. The key idea is \emph{linguistic homophily}: the tendency of socially linked individuals to use language in similar ways. We formalize this idea in a novel attention-based neural network architecture, in which attention is divided among several basis models, depending on the author's position in the social network. This has the effect of smoothing the classification function across the social network, and makes it possible to induce personalized classifiers even for authors for whom there is no labeled data or demographic metadata. This model significantly improves the accuracies of sentiment analysis on Twitter and review data.
Ocean Plume Tracking with Unmanned Surface Vessels: Algorithms and Experiments

Pollution plume monitoring using autonomous vehicles is important due to the adverse effect of pollution plumes on the environment and associated monetary losses. Using the advection-diffusion plume dispersion model, we present a control law design to track dynamic concentration level curves. We also present a gradient and divergence estimation method to enable this control law from concentration measurement only. We then present the field testing results of the control law to track concentration level curves in a plume generated using Rhodamine dye as a pollution surrogate in a near-shore marine environment. These plumes are then autonomously tracked using an unmanned surface vessel equipped with fluorometer sensors. Field experimental results are shown to evaluate the performance of the controller, and complexities of field experiments in real-world marine environments are discussed in the paper.
Classifying (almost)-Belyi maps with five exceptional points

Abstract We classify all rational functions f : P 1 → P 1 whose branching pattern above 0 , 1 , ∞ satisfy a certain regularity condition with precisely d = 5 exceptions. This work is motivated by solving second order linear differential equations, with d = 5 true singularities, in terms of hypergeometric functions. A similar problem was solved for d = 4 in Vidunas and Filipuk (2013).
Unipotent elements and generalized exponential maps

Abstract Let G be a simple and simply connected algebraic group over an algebraically closed field k of characteristic p > 0 . Assume that p is good for the root system of G and that the covering map G s c → G is separable. In previous work we proved the existence of a (not necessarily unique) Springer isomorphism for G that behaved like the exponential map on the restricted nullcone of G. In the present paper we give a formal definition of these maps, which we call ‘generalized exponential maps.’ We provide an explicit and uniform construction of such maps for all root systems, demonstrate their existence over Z ( p ) , and give a complete parameterization of all such maps. One application is that this gives a uniform approach to dealing with the “saturation problem” for a unipotent element u in G, providing a new proof of the known result that u lies inside a subgroup of C G ( u ) that is isomorphic to a truncated Witt group. We also develop a number of other explicit and new computations for g and for G. This paper grew out of an attempt to answer a series of questions posed to us by P. Deligne, who also contributed several of the new ideas that appear here.
A Switched Systems Approach to Path Following With Intermittent State Feedback

Autonomous agents are often tasked with operating in an area where feedback is unavailable. Inspired by such applications, this paper develops a novel switched system-based control method for uncertain nonlinear systems with temporary loss-of-state feedback. To compensate for intermittent feedback, an observer is used while state feedback is available to reduce the estimation error, and a predictor is utilized to propagate the estimates while state feedback is unavailable. Based on the resulting subsystems, maximum and minimum dwell time conditions are developed via a Lyapunov-based switched systems analysis to relax the constraint of maintaining constant feedback. Using the dwell time conditions, a switching trajectory is developed to enter and exit the feedback denied region in a manner that ensures that the overall switched system remains stable. A scheme for designing a switching trajectory with a smooth transition function is provided. Simulation and experimental results are presented to demonstrate the performance of control design.
Spectral Asymptotics Revisited

We discuss two heuristic ideas concerning the spectrum of a Laplacian, and we give theorems and conjectures from the realms of manifolds, graphs and fractals that validate these heuristics. The first heuristic concerns Laplacians that do not have discrete spectra: here we discuss the notion of “spectral mass” closely related to the “integrated density of states”, an average of the diagonal of the kernel of the spectral projection operator, and show that this can serve as a substitute for the eigenvalue counting function. The second heuristic is an “asymptotic splitting law” that describes the proportions of the spectrum that transforms according to the irreducible representations of a finite group that acts as a symmetry group of the Laplacian. For this to be valid we require the existence of a fundamental domain with relatively small boundary. We also give a version in the case that the symmetry group is a compact Lie group. Many of our results are reformulations of known results, and some are merely conjectures, but there is something to be gained by looking at them together with a unified perspective.
Ordinal definability and combinatorics of equivalence relations

Assume ZF + AD+ + V = L(&#x1d4ab;(ℝ)). Let E be a Σ11 equivalence relation coded in HOD. E has an ordinal definable equivalence class without any ordinal definable elements if and only if HOD⊧E is unpinned...
Probabilistic consequences of some polynomial recurrences

In this paper, we consider sequences of polynomials that satisfy differential--difference recurrences. Our interest is motivated by the fact that polynomials satisfying such recurrences frequently appear as generating polynomials of integer valued random variables that are of interest in discrete mathematics. It is, therefore, of interest to understand the properties of such polynomials and their probabilistic consequences. As an illustration we analyze probabilistic properties of tree--like tableaux, combinatorial objects that are connected to asymmetric exclusion processes. In particular, we show that the number of diagonal boxes in symmetric tree--like tableaux is asymptotically normal and that the number of occupied corners in a random tree--like tableau is asymptotically Poisson. This extends earlier results of Aval, Boussicault, Nadeau, and Laborde Zubieta, respectively.
Bias Reduction via End-to-End Shift Learning: Application to Citizen Science

Citizen science projects are successful at gathering rich datasets for various applications. However, the data collected by citizen scientists are often biased — in particular, aligned more with the citizens’ preferences than with scientific objectives. We propose the Shift Compensation Network (SCN), an end-to-end learning scheme which learns the shift from the scientific objectives to the biased data while compensating for the shift by re-weighting the training data. Applied to bird observational data from the citizen science project eBird, we demonstrate how SCN quantifies the data distribution shift and outperforms supervised learning models that do not address the data bias. Compared with competing models in the context of covariate shift, we further demonstrate the advantage of SCN in both its effectiveness and its capability of handling massive high-dimensional data.
Ideals and idempotents in the uniform ultrafilters

Abstract For every discrete semigroup S , the space βS (the Stone–Cech compactification of S ) has a natural, right-topological semigroup structure extending S . Under some mild conditions, U ( S ) , the set of uniform ultrafilters on S , is a two-sided ideal of βS , and therefore contains all of its minimal left ideals and minimal idempotents. Our main theorem states that, if S satisfies some mild distributivity conditions, U ( S ) contains prime minimal left ideals and left-maximal idempotents. If S is countable, then U ( S ) = S ⁎ , and a special case of our main theorem is that if a countable discrete semigroup S is weakly cancellative and left-cancellative, then S ⁎ = β S ∖ S contains prime minimal left ideals and left-maximal idempotents. We will provide examples of weakly cancellative semigroups where these conclusions fail, thus showing that this result is fairly sharp.