cssi/SciSciGPT-SciSciNet huggingface dataset:
The Globally Optimal Reparameterization Algorithm: An Alternative to Fast Dynamic Time Warping for Action Recognition in Video Sequences

Signal alignment has become a popular problem in robotics due in part to its fundamental role in action recognition. Currently, the most successful algorithms for signal alignment are Dynamic Time Warping (DTW) and its variant ‘Fast’ Dynamic Time Warping (FastDTW). Here we introduce a new framework for signal alignment, namely the Globally Optimal Reparameterization Algorithm (GORA). We review the algorithm's mathematical foundation and provide a numerical verification of its theoretical basis. We compare the performance of GORA with that of the DTW and FastDTW algorithms, in terms of computational efficiency and accuracy in matching signals. Our results show a significant improvement in both speed and accuracy over the DTW and FastDTW algorithms and suggest that GORA has the potential to provide a highly effective framework for signal alignment and action recognition.
Non-left-orderable surgeries on twisted torus knots

Boyer, Gordon, and Watson have conjectured that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental group is not left-orderable. Since large classes of L-spaces can be produced from Dehn surgery on knots in the 3-sphere, it is natural to ask what conditions on the knot group are sufficient to imply that the quotient associated to Dehn surgery is not left-orderable. Clay and Watson develop a criterion for determining the left-orderability of this quotient group and use it to verify the conjecture for surgeries on certain L-space twisted torus knots. We generalize a recent theorem of Ichihara and Temma to provide another such criterion. We then use this new criterion to generalize the results of Clay and Watson and to verify the conjecture for a much broader class of L-space twisted torus knots.
Intersections via resolutions

Abstract We investigate the viability of defining an intersection product on algebraic cycles on a singular algebraic variety by pushing forward intersection products formed on a resolution of singularities. For varieties with resolutions having a certain structure (including all varieties over a field of characteristic zero), we obtain a stratification which reflects the geometry of the centers and the exceptional divisors. This stratification is sufficiently fine that divisors can be intersected with r-cycles (for r ≥ 1 ), and 2-cycles can be intersected on a fourfold, provided their incidences with the strata are controlled. Similar pairings are defined on a variety with one-dimensional singular locus.
On sharp local turns of planar polynomials

We show that for a real polynomial of degree \(n\) in two variables \(x\) and \(y\), any local “sharp turn” must have its “size” \({\gtrsim }e^{-Cn^{2}}\). We also show that there is indeed an example that has a sharp turn of size \({\lesssim }e^{-Cn}\). This gives a quite satisfactory answer to a problem raised by Guth. The formulation of the problem was inspired by applications of the polynomial method in the study of Kakeya conjecture.
Efficient Probabilistic Performance Bounds for Inverse Reinforcement Learning

In the field of reinforcement learning there has been recent progress towards safety and high-confidence bounds on policy performance. However, to our knowledge, no practical methods exist for determining high-confidence policy performance bounds in the inverse reinforcement learning setting---where the true reward function is unknown and only samples of expert behavior are given. We propose a sampling method based on Bayesian inverse reinforcement learning that uses demonstrations to determine practical high-confidence upper bounds on the alpha-worst-case difference in expected return between any evaluation policy and the optimal policy under the expert's unknown reward function. We evaluate our proposed bound on both a standard grid navigation task and a simulated driving task and achieve tighter and more accurate bounds than a feature count-based baseline. We also give examples of how our proposed bound can be utilized to perform risk-aware policy selection and risk-aware policy improvement. Because our proposed bound requires several orders of magnitude fewer demonstrations than existing high-confidence bounds, it is the first practical method that allows agents that learn from demonstration to express confidence in the quality of their learned policy.
Scalable inference for space-time Gaussian Cox processes

The log‐Gaussian Cox process is a flexible and popular stochastic process for modeling point patterns exhibiting spatial and space‐time dependence. Model fitting requires approximation of stochastic integrals which is implemented through discretization over the domain of interest. With fine scale discretization, inference based on Markov chain Monte Carlo is computationally burdensome because of the cost of matrix decompositions and storage, such as the Cholesky, for high dimensional covariance matrices associated with latent Gaussian variables. This article addresses these computational bottlenecks by combining two recent developments: (i) a data augmentation strategy that has been proposed for space‐time Gaussian Cox processes that is based on exact Bayesian inference and does not require fine grid approximations for infinite dimensional integrals, and (ii) a recently developed family of sparsity‐inducing Gaussian processes, called nearest‐neighbor Gaussian processes, to avoid expensive matrix computations. Our inference is delivered within the fully model‐based Bayesian paradigm and does not sacrifice the richness of traditional log‐Gaussian Cox processes. We apply our method to crime event data in San Francisco and investigate the recovery of the intensity surface.
Search-based Motion Planning for Aggressive Flight in SE(3)

Quadrotors with large thrust-to-weight ratios are able to track aggressive trajectories with sharp turns and high accelerations. In this letter, we develop a search-based trajectory planning algorithm that exploits the quadrotor maneuverability to generate sequences of motion primitives in cluttered environments. We model the quadrotor body as an ellipsoid and compute its flight attitude along trajectories in order to check for collisions against obstacles. The ellipsoid model allows the quadrotor to pass through gaps that are smaller than its diameter with nonzero pitch or roll angles. Without any prior information about the location of gaps and associated attitude constraints, our algorithm is able to find a safe and optimal trajectory that guides the robot to its goal as fast as possible. To accelerate planning, we first perform a lower dimensional search and use it as a heuristic to guide the generation of a final dynamically feasible trajectory. We analyze critical discretization parameters of motion primitive planning and demonstrate the feasibility of the generated trajectories in various simulations and real-world experiments.
An optimal approximation for submodular maximization under a matroid constraint in the adaptive complexity model

In this paper we study submodular maximization under a matroid constraint in the adaptive complexity model. This model was recently introduced in the context of submodular optimization to quantify the information theoretic complexity of black-box optimization in a parallel computation model. Informally, the adaptivity of an algorithm is the number of sequential rounds it makes when each round can execute polynomially-many function evaluations in parallel. Since submodular optimization is regularly applied on large datasets we seek algorithms with low adaptivity to enable speedups via parallelization. Consequently, a recent line of work has been devoted to designing constant factor approximation algorithms for maximizing submodular functions under various constraints in the adaptive complexity model. Despite the burst in work on submodular maximization in the adaptive complexity model, the fundamental problem of maximizing a monotone submodular function under a matroid constraint has remained elusive. In particular, all known techniques fail for this problem and there are no known constant factor approximation algorithms whose adaptivity is sublinear in the rank of the matroid k or in the worst case sublinear in the size of the ground set n. In this paper we present an approximation algorithm for the problem of maximizing a monotone submodular function under a matroid constraint in the adaptive complexity model. The approximation guarantee of the algorithm is arbitrarily close to the optimal 1−1/e and it has near optimal adaptivity of O(log(n)log(k)). This result is obtained using a novel technique of adaptive sequencing which departs from previous techniques for submodular maximization in the adaptive complexity model. In addition to our main result we show how to use this technique to design other approximation algorithms with strong approximation guarantees and polylogarithmic adaptivity.
Duluth at SemEval-2017 Task 7 : Puns Upon a Midnight Dreary, Lexical Semantics for the Weak and Weary

This paper describes the Duluth systems that participated in SemEval-2017 Task 7 : Detection and Interpretation of English Puns. The Duluth systems participated in all three subtasks, and relied on methods that included word sense disambiguation and measures of semantic relatedness.
Energy Scaling with Control Distance in Complex Networks

It has recently been shown that the expected energy requirements of a control action applied to a complex network scales exponentially with the number of nodes that are targeted. While the exponential scaling law provides an adequate prediction of the mean required energy, it has also been shown that the spread of energy values for a particular number of targets is large. Here, we explore more closely the effect distance between driver nodes and target nodes and the magnitude of self-regulation has on the energy of the control action. We find that the energy scaling law can be written to include information about the distance between driver nodes and target nodes to more accurately predict control energy.
Human-in-the-Loop Interpretability Prior

We often desire our models to be interpretable as well as accurate. Prior work on optimizing models for interpretability has relied on easy-to-quantify proxies for interpretability, such as sparsity or the number of operations required. In this work, we optimize for interpretability by directly including humans in the optimization loop. We develop an algorithm that minimizes the number of user studies to find models that are both predictive and interpretable and demonstrate our approach on several data sets. Our human subjects results show trends towards different proxy notions of interpretability on different datasets, which suggests that different proxies are preferred on different tasks.
Monic representations of the Cuntz algebra and Markov measures

Abstract We study representations of the Cuntz algebras O N . While, for fixed N, the set of equivalence classes of representations of O N is known not to have a Borel cross section, there are various subclasses of representations which can be classified. We study monic representations of O N , that have a cyclic vector for the canonical abelian subalgebra. We show that O N has a certain universal representation which contains all positive monic representations. A large class of examples of monic representations is based on Markov measures. We classify them and as a consequence we obtain that different parameters yield mutually singular Markov measure, extending the classical result of Kakutani. The monic representations based on the Kakutani measures are exactly the ones that have a one-dimensional cyclic S i ⁎ -invariant space.
Incentive Design and Utility Learning via Energy Disaggregation

Abstract The utility company has many motivations for modifying energy consumption patterns of consumers such as revenue decoupling and demand response programs. We model the utility company–consumer interaction as a reverse Stackelberg game and present an iterative algorithm to design incentives for consumers while estimating their utility functions. Incentives are designed using the aggregated as well as the disaggregated (device level) consumption data. We simulate the iterative control (incentive design) and estimation (utility learning and disaggregation) process for examples.
Anomalous transport effects and possible environmental symmetry ‘violation’ in heavy-ion collisions

The heavy-ion collision provides a unique many-body environment where local domains of strongly interacting chiral medium may occur and in a sense allow environmental symmetry ‘violation’ phenomena. For example, certain anomalous transport processes, forbidden in usual medium, become possible in such domains. We briefly review recent progress in both the theoretical understanding and experimental search of various anomalous transport effects (such as the chiral magnetic effect, chiral separation effect, chiral electric separation effect, chiral electric /magnetic waves, etc.) in the hot QCD fluid formed by such collisions.
The truth about torsion in the CM case

Abstract Let T CM ( d ) be the maximum size of the torsion subgroup of an elliptic curve with complex multiplication over a degree d number field. We show there is an absolute, effective constant C such that T CM ( d ) ≤ C d log ⁡ log ⁡ d for all d ≥ 3 .
Workspace Aware Online Grasp Planning

This work provides a framework for a workspace aware online grasp planner. This framework greatly improves the performance of standard online grasp planning algorithms by incorporating a notion of reachability into the online grasp planning process. Offline, a database of hundreds of thousands of unique end-effector poses were queried for feasibility. At runtime, our grasp planner uses this database to bias the hand towards reachable end-effector configurations. The bias keeps the grasp planner in accessible regions of the planning scene so that the resulting grasps are tailored to the situation at hand. This results in a higher percentage of reachable grasps, a higher percentage of successful grasp executions, and a reduced planning time. We also present experimental results using simulated and real environments.
A randomized approach to efficient kernel clustering

Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory requirement since memory scales as the square of the number of data points. We provide a new analysis of a class of approximate kernel methods that have more modest memory requirements, and propose a specific one-pass randomized kernel approximation followed by standard K-means on the transformed data. The analysis and experiments suggest the method is accurate, while requiring drastically less memory than standard kernel K-means and significantly less memory than Nystrom based approximations.
On the Consequences of the Detection of an Interstellar Asteroid

The robustly hyperbolic asteroid A/2017 U1's arrival (IAU Minor Planet Center 2017a) seems fortuitously timed to coincide with the revival of the AAS Research Notes. Both the sparse facts surrounding A/2017 U1's properties and trajectory, as well as its apparently startling ramifications for the planet-formation process, are readily summarized with N_(words) < 1000.
The IBM 2015 English Conversational Telephone Speech Recognition System

We describe the latest improvements to the IBM English conversational telephone speech recognition system. Some of the techniques that were found beneficial are: maxout networks with annealed dropout rates; networks with a very large number of outputs trained on 2000 hours of data; joint modeling of partially unfolded recurrent neural networks and convolutional nets by combining the bottleneck and output layers and retraining the resulting model; and lastly, sophisticated language model rescoring with exponential and neural network LMs. These techniques result in an 8.0% word error rate on the Switchboard part of the Hub5-2000 evaluation test set which is 23% relative better than our previous best published result. Index Terms: recurrent neural networks, convolutional neural networks, conversational speech recognition
On the Capacity of Secure Distributed Matrix Multiplication

Matrix multiplication is one of the key operations in various engineering applications. Outsourcing large-scale matrix multiplication tasks to multiple distributed servers or cloud is desirable to speed up computation. However, security becomes an issue when these servers are untrustworthy. In this paper, we study the problem of secure distributed matrix multiplication from distributed untrustworthy servers. This problem falls in the category of secure function computation and has received significant attention in the cryptography community. However, characterizing the fundamental limits of information-theoretically secure matrix multiplication remain an open problem. We focus on information-theoretically secure distributed matrix multiplication with the goal of characterizing the minimum communication overhead. The capacity of secure matrix multiplication is defined as the maximum possible ratio of the desired information and the total communication received from $N$ distributed servers. In particular, we study the following two models where we want to multiply two matrices $A\in \mathbb{F}^{m\times \mathrm{n}}$ and $B\in \mathbb{F}^{n\times p}$ : (a) one-sided secure matrix multiplication with $\ell$ colluding servers, in which $B$ is a public matrix available at all servers and $A$ is a private matrix. (b) fully secure matrix multiplication with $\ell$ colluding servers, in which both $A$ and $B$ are private matrices. The goal is to securely multiply $A$ and $B$ when any $\ell$ servers can collude. For model (a), we characterize the capacity as $C_{\mathbf{one}-\mathbf{sided}}^{(\ell)}= (N-\ell)/N$ by providing a secure matrix multiplication scheme and a matching converse. For model (b), we propose a novel scheme that lower bounds the capacity, i.e., $C_{\mathrm{fuly}}\geq(\lceil\sqrt{N}-\ell\rceil)^{2}/(\lceil\sqrt{N}-\ell\rceil+\ell)^{2}$ .
Boundary continuity of complete proper holomorphic maps

Abstract We show that there is no complete proper holomorphic map from the disc Δ to the bidisc Δ 2 which extends continuously through Δ ¯ .
A subsequence-histogram method for generic vocabulary recognition over deletion channels

We consider the problem of recognizing a vocabulary-a collection of words (sequences) over a finite alphabet-from a potential subsequence of one of its words. We assume the given subsequence is received through a deletion channel as a result of transmission of a random word from one of the two generic underlying vocabularies. An exact maximum a posterior (MAP) solution for this problem counts the number of ways a given subsequence can be derived from particular subsets of candidate vocabularies, requiring exponential time or space.
Compactness methods for doubly nonlinear parabolic systems

We study solutions of the system of PDE $D\psi({\bf v}_t)=\text{div}DF(D{\bf v})$, where $\psi$ and $F$ are convex functions. This type of system arises in various physical models for phase transitions. We establish compactness properties of solutions that allow us to verify partial regularity when $F$ is quadratic and characterize the large time limits of weak solutions. Special consideration is also given to systems that are homogeneous and their connections with nonlinear eigenvalue problems. While the uniqueness of weak solutions of such systems of PDE remains an open problem, we show scalar equations always have a preferred solution that is also unique as a viscosity solution.
Apprentice: Using Knowledge Distillation Techniques To Improve Low-Precision Network Accuracy

Deep learning networks have achieved state-of-the-art accuracies on computer vision workloads like image classification and object detection. The performant systems, however, typically involve big models with numerous parameters. Once trained, a challenging aspect for such top performing models is deployment on resource constrained inference systems - the models (often deep networks or wide networks or both) are compute and memory intensive. Low-precision numerics and model compression using knowledge distillation are popular techniques to lower both the compute requirements and memory footprint of these deployed models. In this paper, we study the combination of these two techniques and show that the performance of low-precision networks can be significantly improved by using knowledge distillation techniques. Our approach, Apprentice, achieves state-of-the-art accuracies using ternary precision and 4-bit precision for variants of ResNet architecture on ImageNet dataset. We present three schemes using which one can apply knowledge distillation techniques to various stages of the train-and-deploy pipeline.
Lagrangian systems on hyperbolic manifolds

This paper gives two results that show that the dynamics of a time-periodic Lagrangian system on a hyperbolic manifold are at least as complicated as the geodesic flow of a hyperbolic metric. Given a hyperbolic geodesic in the Poincare ball, Theorem A asserts that there are minimizers of the lift of the Lagrangian system that are a bounded distance away and have a variety of approximate speeds. Theorem B gives the existence of a collection of compact invariant sets of the Euler–Lagrange flow that are semiconjugate to the geodesic flow of a hyperbolic metric. These results can be viewed as a generalization of the Aubry–Mather theory of twist maps and the Hedlund–Morse–Gromov theory of minimal geodesics on closed surfaces and hyperbolic manifolds.
Linear Convergence of the Primal-Dual Gradient Method for Convex-Concave Saddle Point Problems without Strong Convexity

We consider the convex-concave saddle point problem $\min_{x}\max_{y} f(x)+y^\top A x-g(y)$ where $f$ is smooth and convex and $g$ is smooth and strongly convex. We prove that if the coupling matrix $A$ has full column rank, the vanilla primal-dual gradient method can achieve linear convergence even if $f$ is not strongly convex. Our result generalizes previous work which either requires $f$ and $g$ to be quadratic functions or requires proximal mappings for both $f$ and $g$. We adopt a novel analysis technique that in each iteration uses a "ghost" update as a reference, and show that the iterates in the primal-dual gradient method converge to this "ghost" sequence. Using the same technique we further give an analysis for the primal-dual stochastic variance reduced gradient method for convex-concave saddle point problems with a finite-sum structure.
Sequential Testing for Sparse Recovery

This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared with fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples needed for reliable signal support recovery. Starting with a lower bound, we show any coordinate-wise sequential sampling procedure fails in the high dimensional limit provided the average number of measurements per dimension is less then log(s)/D(P 0 ||P 1 ), where s is the level of sparsity and D(P 0 ||P 1 ) is the Kullback-Leibler divergence between the underlying distributions. A series of sequential probability ratio tests, which require complete knowledge of the underlying distributions is shown to achieve this bound. Motivated by real-world experiments and recent work in adaptive sensing, we introduce a simple procedure termed sequential thresholding, which can be implemented when the underlying testing problem satisfies a monotone likelihood ratio assumption. Sequential thresholding guarantees exact support recovery provided the average number of measurements per dimension grows faster than log(s)/D(P 0 ||P 1 ), achieving the lower bound. For comparison, we show any nonsequential procedure fails provided the number of measurements grows at a rate less than log(n)/D(P 1 ||P 0 ), where n is the total dimension of the problem.
Posterior sampling for reinforcement learning: worst-case regret bounds

We present an algorithm based on posterior sampling (aka Thompson sampling) that achieves near-optimal worst-case regret bounds when the underlying Markov Decision Process (MDP) is communicating with a finite, though unknown, diameter. Our main result is a high probability regret upper bound of $\tilde{O}(D\sqrt{SAT})$ for any communicating MDP with $S$ states, $A$ actions and diameter $D$, when $T\ge S^5A$. Here, regret compares the total reward achieved by the algorithm to the total expected reward of an optimal infinite-horizon undiscounted average reward policy, in time horizon $T$. This result improves over the best previously known upper bound of $\tilde{O}(DS\sqrt{AT})$ achieved by any algorithm in this setting, and matches the dependence on $S$ in the established lower bound of $\Omega(\sqrt{DSAT})$ for this problem.
Point-based POMDP algorithms: improved analysis and implementation

Existing complexity bounds for point-based POMDP value iteration algorithms focus either on the curse of dimensionality or the curse of history. We derive a new bound that relies on both and uses the concept of discounted reachability; our conclusions may help guide future algorithm design. We also discuss recent improvements to our (point-based) heuristic search value iteration algorithm. Our new implementation calculates tighter initial bounds, avoids solving linear programs, and makes more effective use of sparsity. Empirical results show speedups of more than two orders of magnitude.
Reactive trajectory generation in an unknown environment

Autonomous trajectory generation for unmanned aerial vehicles (UAVs) in unknown environments continues to be an important research area as UAVs become more prolific. In this paper, we develop a trajectory generation algorithm for a vehicle in an unknown environment with wind disturbances, that relies only on the vehicle's on-board distance sensors and communication with other vehicles within a finite region to generate a smooth, collision-free trajectory. The proposed trajectory generation algorithm can be used in conjunction with high-level planners and low-level motion controllers, as demonstrated. The algorithm provides guarantees that the trajectory does not violate the vehicle's thrust limitation, sensor constraints, or a user-defined clearance radius around other vehicles and obstacles. Simulation results of two quadrotors moving through an unknown building environment with obstacles demonstrates the trajectory generation performance.
Higher Bruhat Orders in Type B

Motivated by the geometry of hyperplane arrangements, Manin and Schechtman defined for each integer $n \geq 1$ a hierarchy of finite partially ordered sets $B(n, k),$ indexed by positive integers $k$, called the higher Bruhat orders. The poset $B(n, 1)$ is naturally identified with the weak left Bruhat order on the symmetric group $S_n$, each $B(n, k)$ has a unique maximal and a unique minimal element, and the poset $B(n, k + 1)$ can be constructed from the set of maximal chains in $B(n, k)$. Ben Elias has demonstrated a striking connection between the posets $B(n, k)$ for $k = 2$ and the diagrammatics of Bott-Samelson bimodules in type A, providing significant motivation for the development of an analogous theory of higher Bruhat orders in other Cartan-Killing types, particularly for $k = 2$. In this paper we present a partial generalization to type B, complete up to $k = 2$, prove a direct analogue of the main theorem of Manin and Schechtman, and relate our construction to the weak Bruhat order and reduced expression graph for Weyl group $B_n$.
Neural Programmer-Interpreters

Abstract: We propose the neural programmer-interpreter (NPI): a recurrent and compositional neural network that learns to represent and execute programs. NPI has three learnable components: a task-agnostic recurrent core, a persistent key-value program memory, and domain-specific encoders that enable a single NPI to operate in multiple perceptually diverse environments with distinct affordances. By learning to compose lower-level programs to express higher-level programs, NPI reduces sample complexity and increases generalization ability compared to sequence-to-sequence LSTMs. The program memory allows efficient learning of additional tasks by building on existing programs. NPI can also harness the environment (e.g. a scratch pad with read-write pointers) to cache intermediate results of computation, lessening the long-term memory burden on recurrent hidden units. In this work we train the NPI with fully-supervised execution traces; each program has example sequences of calls to the immediate subprograms conditioned on the input. Rather than training on a huge number of relatively weak labels, NPI learns from a small number of rich examples. We demonstrate the capability of our model to learn several types of compositional programs: addition, sorting, and canonicalizing 3D models. Furthermore, a single NPI learns to execute these programs and all 21 associated subprograms.
Cyber Defense as a Complex Adaptive System: A model-based approach to strategic policy design

In a world of ever-increasing systems interdependence, effective cybersecurity policy design seems to be one of the most critically understudied elements of our national security strategy. Enterprise cyber technologies are often implemented without much regard to the interactions that occur between humans and the new technology. Furthermore, the interactions that occur between individuals can often have an impact on the newly employed technology as well. Without a rigorous, evidence-based approach to ground an employment strategy and elucidate the emergent organizational needs that will come with the fielding of new cyber capabilities, one is left to speculate on the impact that novel technologies will have on the aggregate functioning of the enterprise. In this paper, we will explore a scenario in which a hypothetical government agency applies a complexity science perspective, supported by agent-based modeling, to more fully understand the impacts of strategic policy decisions. We present a model to explore the socio-technical dynamics of these systems, discuss lessons using this platform, and suggest further research and development.
Selmer ranks of twists of hyperelliptic curves and superelliptic curves

Abstract We study the variation of Selmer ranks of Jacobians of twists of hyperelliptic curves and superelliptic curves. We find sufficient conditions for such curves to have infinitely many twists whose Jacobians have Selmer ranks equal to r, for any given nonnegative integer r. This generalizes earlier results of Mazur–Rubin on elliptic curves.
Multiple zeta values and ideles

In this paper we give two idelic representations of the multiple zeta values—one using iterated integrals over the finite ideles and the other using iterated integrals over the idele class group. The two representations lead to stuffle and shuffle relations, respectively. Using iterated integrals over the ideles, we recover in a unified way the double shuffle relations for multiple zeta values.
The Khovanov homology of infinite braids

We show that the limiting Khovanov chain complex of any infinite positive braid categorifies the Jones-Wenzl projector. This result extends Lev Rozansky's categorification of the Jones-Wenzl projectors using the limiting complex of infinite torus braids. We also show a similar result for the limiting Lipshitz-Sarkar-Khovanov homotopy types of the closures of such braids. Extensions to more general infinite braids are also considered.
Reconfigurable Antenna Multiple Access for 5G mmWave Systems

This paper aims to realize a new multiple access technique based on recently proposed millimeter- wave reconfigurable antenna architectures. To this end, first we show that integration of the existing reconfigurable antenna systems with the well-known non-orthogonal multiple access (NOMA) technique causes a significant degradation in sum rate due to the inevitable power division in reconfigurable antennas. To circumvent this fundamental limit, a new multiple access technique is proposed. The technique which is called reconfigurable antenna multiple access (RAMA) transmits only each user's intended signal at the same time/frequency/code, which makes RAMA an inter-user interference-free technique. Two different cases are considered, i.e., RAMA with partial and full channel state information (CSI). In the first case, CSI is not required and only the direction of arrival for a specific user is used. Our analytical results indicate that with partial CSI and for symmetric channels, RAMA outperforms NOMA in terms of sum rate. Further, the analytical result indicates that RAMA for asymmetric channels achieves better sum rate than NOMA when less power is assigned to users that experience better channel quality. In the second case, RAMA with full CSI allocates optimal power to each user which leads to higher achievable rates compared to NOMA for both symmetric and asymmetric channels. The numerical computations demonstrate the analytical findings.
Synthesis of Insertion Functions to Enforce Decentralized and Joint Opacity Properties of Discrete-event Systems

Opacity is a confidentiality property that characterizes the non-disclosure of specified secret information of a system to an outside observer. In this paper, we consider the enforcement of opacity within the discrete-event system formalism in the presence of multiple intruders. We study two cases, one without coordination among the intruders and the other with coordination. We propose appropriate notions of opacity corresponding to the two cases, respectively, and propose enforcement mechanisms based on the implementation of insertion functions, which manipulates the output of the system by inserting fictitious observable events whenever necessary. The effectiveness of the proposed opacity-enforcement approaches is validated through illustrative examples.
DER Allocation and Line Repair Scheduling for Storm-induced Failures in Distribution Networks

Electricity distribution networks (DNs) in many regions are increasingly subjected to disruptions caused by tropical storms. Distributed Energy Resources (DERs) can act as temporary supply sources to sustain “microgrids” resulting from disruptions. In this paper, we investigate the problem of suitable DER allocation to facilitate more efficient repair operations and faster recovery. First, we estimate the failure probabilities of DN components (lines) using a stochastic model of line failures which parametrically depends on the location-specific storm wind field. Next, we formulate a two-stage stochastic mixed integer program, which models the distribution utility’s decision to allocate DERs in the DN (pre-storm stage); and accounts for multi-period decisions on optimal dispatch and line repair scheduling (post-storm stage). A key feature of this formulation is that it jointly optimizes electricity dispatch within the individual microgrids and the line repair schedules to minimize the sum of the cost of DER allocation and cost due to lost load. To illustrate our approach, we use the sample average approximation method to solve our problem for a small-size DN under different storm intensities and DER/crew constraints.
Efficient Dictionary Learning with Gradient Descent

Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of poor objective value. For some highly structured nonconvex problems however, the success of gradient descent can be understood by studying the geometry of the objective. We study one such problem -- complete orthogonal dictionary learning, and provide converge guarantees for randomly initialized gradient descent to the neighborhood of a global optimum. The resulting rates scale as low order polynomials in the dimension even though the objective possesses an exponential number of saddle points. This efficient convergence can be viewed as a consequence of negative curvature normal to the stable manifolds associated with saddle points, and we provide evidence that this feature is shared by other nonconvex problems of importance as well.
Completely integrally closed Prüfer v-multiplication domains

ABSTRACTWe study the effects on D of assuming that the power series ring D[[X]] is a v-domain or a Prufer v-multiplication domain (PVMD). We show that a PVMD D is completely integrally closed if and only if ⋂n=1∞(In)v=(0) for every proper t-invertible t-ideal I of D. Using this, we show that if D is an almost GCD domain, then D[[X]] is integrally closed if and only if D is a completely integrally closed PVMD with torsion t-class group. We also determine several classes of PVMDs for which being Archimedean is equivalent to being completely integrally closed and give some new characterizations of integral domains related to Krull domains.
SOME GROUP THEORY PROBLEMS

This is a survey of some problems in geometric group theory that I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some necessary definitions and motivations, problems and some discussions of them. For each problem, I try to mention the author. If the author is not given, the problem, to the best of my knowledge, was formulated by me first.
Using semi-supervised learning for predicting metamorphic relations

Software testing is difficult to automate, especially in programs which have no oracle, or method of determining which output is correct. Metamorphic testing is a solution this problem. Metamorphic testing uses metamorphic relations to define test cases and expected outputs. A large amount of time is needed for a domain expert to determine which metamorphic relations can be used to test a given program. Metamorphic relation prediction removes this need for such an expert. We propose a method using semi-supervised machine learning to detect which metamorphic relations are applicable to a given code base. We compare this semi-supervised model with a supervised model, and show that the addition of unlabeled data improves the classification accuracy of the MR prediction model.
Implications of a Stop Sector Signal at the LHC

Naturalness arguments suggest that the stop sector is within reach of the Large Hadron Collider (LHC). We investigate how the observation of a third generation squark signal could predict masses and discovery modes of other supersymmetric particles, or potentially test the Higgs boson mass relation and the validity of the Minimal Supersymmetric Standard Model (MSSM) at the high luminosity LHC. We illustrate these ideas in three distinct scenarios: discovery of a light stop, a sbottom signal in multileptons, and a signal of the second (heavier) stop in boosted dibosons.
ENGEL RELATIONS IN 4-MANIFOLD TOPOLOGY

We give two applications of the 2-Engel relation, classically studied in finite and Lie groups, to the 4-dimensional (4D) topological surgery conjecture. The A–B slice problem, a reformulation of the surgery conjecture for free groups, is shown to admit a homotopy solution. We also exhibit a new collection of universal surgery problems, defined using ramifications of homotopically trivial links. More generally we show how $n$ -Engel relations arise from higher-order double points of surfaces in 4-space.
Dynamic High Resolution Deformable Articulated Tracking

The last several years have seen significant progress in using depth cameras for tracking articulated objects such as human bodies, hands, and robotic manipulators. Most approaches focus on tracking skeletal parameters of a fixed shape model, which makes them insufficient for applications that require accurate estimates of deformable object surfaces. To overcome this limitation, we present a 3D model-based tracking system for articulated deformable objects. Our system is able to track human body pose and high resolution surface contours in real time using a commodity depth sensor and GPU hardware. We implement this as a joint optimization over a skeleton to account for changes in pose, and over the vertices of a high resolution mesh to track the subject's shape. Through experimental results we show that we are able to capture dynamic sub-centimeter surface detail such as folds and wrinkles in clothing. We also show that this shape estimation aids kinematic pose estimation by providing a more accurate target to match against the point cloud. The end result is highly accurate spatiotemporal and semantic information which is well suited for physical human robot interaction as well as virtual and augmented reality systems.
Kronecker Determinantal Point Processes

Determinantal Point Processes (DPPs) are probabilistic models over all subsets a ground set of N items. They have recently gained prominence in several applications that rely on diverse subsets. However, their applicability to large problems is still limited due to O(N^3) complexity of core tasks such as sampling and learning. We enable efficient sampling and learning for DPPs by introducing KronDPP, a DPP model whose kernel matrix decomposes as a tensor product of multiple smaller kernel matrices. This decomposition immediately enables fast exact sampling. But contrary to what one may expect, leveraging the Kronecker product structure for speeding up DPP learning turns out to be more difficult. We overcome this challenge, and derive batch and stochastic optimization algorithms for efficiently learning the parameters of a KronDPP.
Adaptive nonparametric empirical Bayes estimation via wavelet series: The minimax study

Abstract In the present paper, we derive lower bounds for the risk of the nonparametric empirical Bayes estimators. In order to attain the optimal convergence rate, we propose generalization of the linear empirical Bayes estimation method which takes advantage of the flexibility of the wavelet techniques. We present an empirical Bayes estimator as a wavelet series expansion and estimate coefficients by minimizing the prior risk of the estimator. As a result, estimation of wavelet coefficients requires solution of a well-posed low-dimensional sparse system of linear equations. The dimension of the system depends on the size of wavelet support and smoothness of the Bayes estimator. An adaptive choice of the resolution level is carried out using Lepski et al. (1997) method. The method is computationally efficient and provides asymptotically optimal adaptive EB estimators. The theory is supplemented by numerous examples.
On the multiplicity of tangent cones of monomial curves

Let S be a numerical semigroup, R the local ring of the monomial curve singularity associated to S, and G its associated graded ring. In this paper we provide a sharp upper bound for the least positive integer in S in terms of the codimension and the maximum degree of the equations of G, when G is not a complete intersection. A special case of this result settles a question of J. Herzog and D. Stamate.
Quantitative Simplification of Filtered Simplicial Complexes

We introduce a new invariant defined on the vertices of a given filtered simplicial complex, called codensity, which controls the impact of removing vertices on the persistent homology of this filtered complex. We achieve this control through the use of an interleaving type of distance between filtered simplicial complexes. We study the special case of Vietoris–Rips filtrations and show that our bounds offer a significant improvement over the immediate bounds coming from considerations related to the Gromov–Hausdorff distance. Based on these ideas we give an iterative method for the practical simplification of filtered simplicial complexes. As a byproduct of our analysis we identify a notion of core of a filtered simplicial complex which admits the interpretation as a minimalistic simplicial filtration which retains all the persistent homology information.
Online multiclass boosting

Recent work has extended the theoretical analysis of boosting algorithms to multiclass problems and to online settings. However, the multiclass extension is in the batch setting and the online extensions only consider binary classification. We fill this gap in the literature by defining, and justifying, a weak learning condition for online multiclass boosting. This condition leads to an optimal boosting algorithm that requires the minimal number of weak learners to achieve a certain accuracy. Additionally, we propose an adaptive algorithm which is near optimal and enjoys an excellent performance on real data due to its adaptive property.
Coarse coherence of metric spaces and groups and its permanence properties

We introduce properties of metric spaces and, specifically, finitely generated groups with word metrics which we call coarse coherence and coarse regular coherence. They are geometric counterparts of the classical algebraic notion of coherence and the regular coherence property of groups defined and studied by F. Waldhausen. The new properties can be defined in the general context of coarse metric geometry and are coarse invariants. In particular, they are quasi-isometry invariants of spaces and groups. We show that coarse regular coherence implies weak regular coherence, a weakening of regular coherence by G. Carlsson and the first author. The latter was introduced with the same goal as Waldhausen's, in order to perform computations of algebraic K-theory of group rings. However, all groups known to be weakly regular coherent are also coarsely regular coherent. The new framework allows us to prove structural results by developing permanence properties, including the particularly important fibering permanence property, for coarse regular coherence.
Batched Large-scale Bayesian Optimization in High-dimensional Spaces

Bayesian optimization (BO) has become an effective approach for black-box function optimization problems when function evaluations are expensive and the optimum can be achieved within a relatively small number of queries. However, many cases, such as the ones with high-dimensional inputs, may require a much larger number of observations for optimization. Despite an abundance of observations thanks to parallel experiments, current BO techniques have been limited to merely a few thousand observations. In this paper, we propose ensemble Bayesian optimization (EBO) to address three current challenges in BO simultaneously: (1) large-scale observations; (2) high dimensional input spaces; and (3) selections of batch queries that balance quality and diversity. The key idea of EBO is to operate on an ensemble of additive Gaussian process models, each of which possesses a randomized strategy to divide and conquer. We show unprecedented, previously impossible results of scaling up BO to tens of thousands of observations within minutes of computation.
Leaf space isometries of singular Riemannian foliations and their spectral properties

In this note, the authors show by example that an isometry between leaf spaces of singular Riemannian foliations need not induce an equality of the basic spectra. If the leaf space isometry preserves the mean curvature vector fields, then it is proved that the basic spectra are equivalent, i.e. that the leaf spaces are isospectral. As a corollary to the main result, the authors identify geometric conditions that ensure preservation of the mean curvature vector fields, and therefore isospectrality of the leaf spaces.