cssi/SciSciGPT-SciSciNet huggingface dataset:
Homogeneous Catalytic Hydrogenation of Aromatic Hydrocarbons and Heteroaromatic Nitrogen Compounds: Synthetic and Mechanistic Aspects

The synthetic and mechanistic aspects of the homogeneous catalytic hydrogenation of mono and polynuclear aromatic hydrocarbons and the corresponding heteroaromatic nitrogen compounds will be reviewed. A comparison of the regioselectivities under various hydrogenation conditions for both classes of compounds will be discussed for a wide variety of transition-metal complexes with regard to substrate binding at the metal center and the role of free radical intermediates in metal carbonyl hydride reactions, where substrate does not bind to the metal center prior to hydrogen transfer. The polynuclear heteroaromatic nitrogen compounds appear to hydrogenate more readily, under similar reaction conditions, than the polynuclear aromatic hydrocarbons. The relative rates of hydrogenation of a variety of heteroaromatic nitrogen compounds as well as compounds that inhibit and enhance selective hydrogenation of the nitrogen-containing ring will be addressed. A relatively new spectroscopic technique, high pressure nuclear magnetic resonance spectroscopy, will be shown to be a powerful tool to elucidate the mechanisms of the regioselective hydrogenation of polynuclear heteroaromatic nitrogen compounds.
The Cytoplasmic DNA Sensor cGAS Promotes Mitotic Cell Death

Pathogenic and other cytoplasmic DNAs activate the cyclic GMP-AMP synthase (cGAS)-stimulator of interferon genes (STING) pathway to induce inflammation via transcriptional activation by IRF3 and nuclear factor κB (NF-κB), but the functional consequences of exposing cGAS to chromosomes upon mitotic nuclear envelope breakdown are unknown. Here, we show that nucleosomes competitively inhibit DNA-dependent cGAS activation and that the cGAS-STING pathway is not effectively activated during normal mitosis. However, during mitotic arrest, low level cGAS-dependent IRF3 phosphorylation slowly accumulates without triggering inflammation. Phosphorylated IRF3, independently of its DNA-binding domain, stimulates apoptosis through alleviating Bcl-xL-dependent suppression of mitochondrial outer membrane permeabilization. We propose that slow accumulation of phosphorylated IRF3, normally not sufficient for inducing inflammation, can trigger transcription-independent induction of apoptosis upon mitotic aberrations. Accordingly, expression of cGAS and IRF3 in cancer cells makes mouse xenograft tumors responsive to the anti-mitotic agent Taxol. The Cancer Genome Atlas (TCGA) datasets for non-small cell lung cancer patients also suggest an effect of cGAS expression on taxane response.
The fixed point property via dual space properties

Abstract A Banach space has the weak fixed point property if its dual space has a weak∗ sequentially compact unit ball and the dual space satisfies the weak∗ uniform Kadec–Klee property; and it has the fixed point property if there exists e > 0 such that, for every infinite subset A of the unit sphere of the dual space, A ∪ ( − A ) fails to be ( 2 − e ) -separated. In particular, E-convex Banach spaces, a class of spaces that includes the uniformly nonsquare spaces, have the fixed point property.
An Aronsson type approach to extremal quasiconformal mappings

Abstract We study C 2 extremal quasiconformal mappings in space and establish necessary and sufficient conditions for a ‘localized’ form of extremality in the spirit of the work of G. Aronsson on absolutely minimizing Lipschitz extensions. We also prove short-time existence for smooth solutions of a gradient flow of QC diffeomorphisms associated to the extremal problem.
WRS: Waiting Room Sampling for Accurate Triangle Counting in Real Graph Streams

If we cannot store all edges in a graph stream, which edges should we store to estimate the triangle count accurately?Counting triangles (i.e., cycles of length three) is a fundamental graph problem with many applications in social network analysis, web mining, anomaly detection, etc. Recently, much effort has been made to accurately estimate global and local triangle counts in streaming settings with limited space. Although existing methods use sampling techniques without considering temporal dependencies in edges, we observe temporal locality in real dynamic graphs. That is, future edges are more likely to form triangles with recent edges than with older edges. In this work, we propose a single-pass streaming algorithm called Waiting-Room Sampling (WRS) for global and local triangle counting. WRS exploits the temporal locality by always storing the most recent edges, which future edges are more likely to form triangles with, in the waiting room, while it uses reservoir sampling for the remaining edges. Our theoretical and empirical analyses show that WRS is: (a) Fast and 'any time': runs in linear time, always maintaining and updating estimates while new edges arrive, (b) Effective: yields up to 47% smaller estimation error than its best competitors, and (c) Theoretically sound: gives unbiased estimates with small variances under the temporal locality.
Coverage Control for Wire-Traversing Robots

In this paper we consider the coverage control problem for a team of wire-traversing robots. The two-dimensional motion of robots moving in a planar environment has to be projected to one-dimensional manifolds representing the wires. Starting from Lloyd's descent algorithm for coverage control, a solution that generates continuous motion of the robots on the wires is proposed. This is realized by means of a Continuous Onto Wires (COW) map: the robots' workspace is mapped onto the wires on which the motion of the robots is constrained to be. A final projection step is introduced to ensure that the configuration of the robots on the wires is a local minimizer of the constrained locational cost. An algorithm for the continuous constrained coverage control problem is proposed and it is tested both in simulation and on a team of mobile robots.
A CYCLIC APPROACH TO THE ANNULAR TEMPERLEY–LIEB CATEGORY

In [The planar algebra of a bipartite graph, Knots in Hellas '98 (World Scientific, 2000), pp. 94–117, MR1865703], Jones found two copies of the cyclic category cΔ in the annular Temperley–Lieb category Atl. We give an abstract presentation of Atl to discuss how these two copies of cΔ generate Atl together with the coupling constants and the coupling relations. We then discuss modules over the annular category and homologies of such modules, the latter of which arises from the cyclic viewpoint.
Characteristic initial value problem for spherically symmetric barotropic flow

We study the equations of motion for a barotropic fluid in spherical symmetric flow. Making use of the Riemann invariants, we consider the characteristic form of these equations. In a first part, w...
The equivariant "K"-theory of toric varieties

Abstract This paper contains two results concerning the equivariant K -theory of toric varieties. The first is a formula for the equivariant K -groups of an arbitrary affine toric variety, generalizing the known formula for smooth ones. In fact, this result is established in a more general context, involving the K -theory of graded projective modules. The second result is a new proof of a theorem due to Vezzosi and Vistoli concerning the equivariant K -theory of smooth (not necessarily affine) toric varieties.
On the nonexistence of nontrivial involutive "n"-homomorphisms of "C*"-algebras

An n-homomorphism between algebras is a linear map Φ: A → B such that Φ(a 1 ... a n ) = Φ(a 1 ) ··· Φ(a n ) for all elements a 1 ,..., a n ∈ A. Every homomorphism is an n-homomorphism for all n > 2, but the converse is false, in general. Hejazian et al. (2005) ask: Is every *-preserving n-homomorphism between C*-algebras continuous? We answer their question in the affirmative, but the even and odd n arguments are surprisingly disjoint. We then use these results to prove stronger ones: If n > 2 is even, then Φ is just an ordinary *-homomorphism. If n > 3 is odd, then Φ is a difference of two orthogonal *-homomorphisms. Thus, there are no nontrivial *-linear n-homomorphisms between C*-algebras.
Low Degree Nullstellensatz Certificates for 3-Colorability

In a seminal paper, De Loera et. al introduce the algorithm NulLA (Nullstellensatz Linear Algebra) and use it to measure the difficulty of determining if a graph is not 3-colorable. The crux of this relies on a correspondence between 3-colorings of a graph and solutions to a certain system of polynomial equations over a field $\mathbb{k}$. In this article, we give a new direct combinatorial characterization of graphs that can be determined to be non-3-colorable in the first iteration of this algorithm when $\mathbb{k}=GF(2)$. This greatly simplifies the work of De Loera et. al, as we express the combinatorial characterization directly in terms of the graphs themselves without introducing superfluous directed graphs. Furthermore, for all graphs on at most $12$ vertices, we determine at which iteration NulLA detects a graph is not 3-colorable when $\mathbb{k}=GF(2)$.
Grid Long Short-Term Memory

Abstract: This paper introduces Grid Long Short-Term Memory, a network of LSTM cells arranged in a multidimensional grid that can be applied to vectors, sequences or higher dimensional data such as images. The network differs from existing deep LSTM architectures in that the cells are connected between network layers as well as along the spatiotemporal dimensions of the data. The network provides a unified way of using LSTM for both deep and sequential computation. We apply the model to algorithmic tasks such as 15-digit integer addition and sequence memorization, where it is able to significantly outperform the standard LSTM. We then give results for two empirical tasks. We find that 2D Grid LSTM achieves 1.47 bits per character on the Wikipedia character prediction benchmark, which is state-of-the-art among neural approaches. In addition, we use the Grid LSTM to define a novel two-dimensional translation model, the Reencoder, and show that it outperforms a phrase-based reference system on a Chinese-to-English translation task.
Sustaining the Montage image mosaic engine since 2002

This paper describes how we have sustained the Montage image mosaic engine (http://montage.ipac.caltech.edu) first released in 2002, to support the ever-growing scale and complexity of modern data sets. The key to its longevity has been its design as a toolkit written in ANSI-C, with each tool performing one distinct task, for easy integration into scripts, pipelines and workflows. The same code base now supports Windows, JavaScript and Python by taking advantage of recent advances in compilers. The design has led to applicability of Montage far beyond what was anticipated when Montage was first built, such as supporting observation planning for the JWST. Moreover, Montage is highly scalable and is in wide use within the IT community to develop advanced, fault-tolerant cyber-infrastructure, such as job schedulers for grids, workflow orchestration, and restructuring techniques for processing complex workflows and pipelines.
Quadrature Points via Heat Kernel Repulsion

We discuss the classical problem of how to pick N weighted points on a d-dimensional manifold so as to obtain a reasonable quadrature rule $$\begin{aligned} \frac{1}{|M|}\int _{M}{f(x) \mathrm{d}x} \simeq \sum _{n=1}^{N}{a_i f(x_i)}. \end{aligned}$$This problem, naturally, has a long history; the purpose of our paper is to propose selecting points and weights so as to minimize the energy functional $$\begin{aligned} \sum _{i,j =1}^{N}{ a_i a_j \exp \left( -\frac{d(x_i,x_j)^2}{4t}\right) } \rightarrow \min , \quad \text{ where }~t \sim N^{-2/d}, \end{aligned}$$d(x, y) is the geodesic distance, and d is the dimension of the manifold. This yields point sets that are theoretically guaranteed, via spectral theoretic properties of the Laplacian $$-\Delta $$, to have good properties. One nice aspect is that the energy functional is universal and independent of the underlying manifold; we show several numerical examples.
Pseudo–Anosov mapping classes from pure mapping classes

We study types of mapping classes which arise as a product of a given mapping class and powers of certain pure mapping classes. We derive an explicit constant depending only on a surface such that almost all above pure mapping classes give rise to pseudo-Anosov type whenever their powers are larger than the constant. Furthermore, the stable lengths of pseudo-Anosov mapping classes obtained by this method are directly captured from the construction.
On sums of Ramanujan sums

Let $c_q(n)$ denote the Ramanujan sum modulo $q$, and let $x$ and $y$ be large reals, with $x = o(y)$. We obtain asymptotic formulas for the sums $$\sum_{n \le y}(\sum_{q \le x} c_q(n))^k \qquad (k = 1, 2).$$
Collaboratively Learning the Best Option on Graphs, Using Bounded Local Memory

We consider multi-armed bandit problems in social groups wherein each individual has bounded memory and shares the common goal of learning the best arm/option. We say an individual learns the best option if eventually (as $t\diverge$) it pulls only the arm with the highest expected reward. While this goal is provably impossible for an isolated individual due to bounded memory, we show that, in social groups, this goal can be achieved easily with the aid of social persuasion (i.e., communication) as long as the communication networks/graphs satisfy some mild conditions. In this work, we model and analyze a type of learning dynamics which are well-observed in social groups. Specifically, under the learning dynamics of interest, an individual sequentially decides on which arm to pull next based on not only its private reward feedback but also the suggestion provided by a randomly chosen neighbor. To deal with the interplay between the randomness in the rewards and in the social interaction, we employ the \em mean-field approximation method. Considering the possibility that the individuals in the networks may not be exchangeable when the communication networks are not cliques, we go beyond the classic mean-field techniques and apply a refined version of mean-field approximation: \beginitemize \item Using coupling we show that, if the communication graph is connected and is either regular or has doubly-stochastic degree-weighted adjacency matrix, with probability $\to 1$ as the social group size $N \to \infty $, every individual in the social group learns the best option. \item If the minimum degree of the graph diverges as $N \diverge $, over an arbitrary but given finite time horizon, the sample paths describing the opinion evolutions of the individuals are asymptotically independent. In addition, the proportions of the population with different opinions converge to the unique solution of a system of ODEs. Interestingly, the obtained system of ODEs are invariant to the structures of the communication graphs. In the solution of the obtained ODEs, the proportion of the population holding the correct opinion converges to $1$ exponentially fast in time. \enditemize Notably, our results hold even if the communication graphs are highly sparse.
Is a monotone union of contractible open sets contractible

Abstract This paper presents some partial answers to the following question. Question If a normal space X is the union of an increasing sequence of open sets U 1 ⊂ U 2 ⊂ U 3 ⊂ … such that each U n contracts to a point in X, must X be contractible? The main results of the paper are: Theorem 1 If a normal space X is the union of a sequence of open subsets { U n } such that c l ( U n ) ⊂ U n + 1 and U n contracts to a point in U n + 1 for each n ≥ 1 , then X is contractible. Corollary 2 If a locally compact σ-compact normal space X is the union of an increasing sequence of open sets U 1 ⊂ U 2 ⊂ U 3 ⊂ … such that each U n contracts to a point in X, then X is contractible.
A KNOTTED MINIMAL TREE

There is a finite set of points on the boundary of the three-dimensional unit ball whose minimal tree is knotted. This example answers a problem posed by Michael Freedman.
Structure of One-Phase Free Boundaries in the Plane

We study classical solutions to the one-phase free boundary problem in which the free boundary consists of smooth curves and the components of the positive phase are simply-connected. We show that if two components of the free boundary are close, then the solution locally resembles an entire solution discovered by Hauswirth, Helein and Pacard, whose free boundary has the shape of a double hairpin. Our results are analogous to theorems of Colding and Minicozzi characterizing embedded minimal annuli, and a direct connection between our theorems and theirs can be made using a correspondence due to Traizet.
ZigZag: A New Approach to Adaptive Online Learning

We develop a novel family of algorithms for the online learning setting with regret against any data sequence bounded by the empirical Rademacher complexity of that sequence. To develop a general theory of when this type of adaptive regret bound is achievable we establish a connection to the theory of decoupling inequalities for martingales in Banach spaces. When the hypothesis class is a set of linear functions bounded in some norm, such a regret bound is achievable if and only if the norm satisfies certain decoupling inequalities for martingales. Donald Burkholder's celebrated geometric characterization of decoupling inequalities (1984) states that such an inequality holds if and only if there exists a special function called a Burkholder function satisfying certain restricted concavity properties. Our online learning algorithms are efficient in terms of queries to this function. We realize our general theory by giving novel efficient algorithms for classes including lp norms, Schatten p-norms, group norms, and reproducing kernel Hilbert spaces. The empirical Rademacher complexity regret bound implies --- when used in the i.i.d. setting --- a data-dependent complexity bound for excess risk after online-to-batch conversion. To showcase the power of the empirical Rademacher complexity regret bound, we derive improved rates for a supervised learning generalization of the online learning with low rank experts task and for the online matrix prediction task. In addition to obtaining tight data-dependent regret bounds, our algorithms enjoy improved efficiency over previous techniques based on Rademacher complexity, automatically work in the infinite horizon setting, and are scale-free. To obtain such adaptive methods, we introduce novel machinery, and the resulting algorithms are not based on the standard tools of online convex optimization.
Distribution of the Periodic Points of the Farey Map

We expand the cross section of the geodesic flow in the tangent bundle of the modular surface given by Series to produce another section whose return map under the geodesic flow is a double cover of the natural extension of the Farey map. We use this cross section to extend the correspondence between the closed geodesics on the modular surface and the periodic points of the Gauss map to include the periodic points of the Farey map. Then, analogous to the work of Pollicott, we prove an equidistribution result for the periodic points of the Farey map when they are ordered according to the length of their corresponding closed geodesics.
Secure Broadcasting over Fading Channels with Statistical QoS Constraints

In this paper, the fading broadcast channel with confidential messages is studied in the presence of statistical quality of service (QoS) constraints in the form of limitations on the buffer length. We employ the effective capacity formulation to measure the throughput of the confidential and common messages. We assume that the channel side information (CSI) is available at both the transmitter and the receivers. Considering average power constraints at the transmitter side, we first define the effective secure throughput region, and prove that the throughput region is convex. Then, we obtain the optimal power control policies that achieve the boundary points of the effective secure throughput region.
A Unified Computational and Statistical Framework for Nonconvex Low-rank Matrix Estimation

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general case with noisy observations, we show that our algorithm is guaranteed to linearly converge to the unknown low-rank matrix up to minimax optimal statistical error, provided an appropriate initial estimator. While in the generic noiseless setting, our algorithm converges to the unknown low-rank matrix at a linear rate and enables exact recovery with optimal sample complexity. In addition, we develop a new initialization algorithm to provide a desired initial estimator, which outperforms existing initialization algorithms for nonconvex low-rank matrix estimation. We illustrate the superiority of our framework through three examples: matrix regression, matrix completion, and one-bit matrix completion. We also corroborate our theory through extensive experiments on synthetic data.
Downlink Performance Analysis for a Generalized Shotgun Cellular System

In this paper, we analyze the signal-to-interference-plus-noise ratio (SINR) performance at a mobile station (MS) in a random cellular network. The cellular network is formed by base stations (BSs) placed in a one-, two-, or three-dimensional space according to a possibly non-homogeneous Poisson point process, which is a generalization of the so-called shotgun cellular system. We develop a sequence of equivalence relations for the SCSs and use them to derive semi-analytical expressions for the coverage probability at the MS when the transmissions from each BS may be affected by random fading with arbitrary distributions as well as attenuation following arbitrary path-loss models. For homogeneous Poisson point processes in the interference-limited case with power-law path-loss model, we show that the SINR distribution is the same for all fading distributions and is not a function of the base station density. In addition, the influence of random transmission power, power control, and multiple channel reuse groups on the downlink performance is also discussed. The techniques developed for the analysis of SINR have applications beyond cellular networks and can be used in similar studies for cognitive radio networks, femtocell networks, and other heterogeneous and multi-tier networks.
Maps of degree 1 and Lusternik–Schnirelmann category

Abstract Given a map f : M → N of degree 1 of closed manifolds, is it true that the Lusternik–Schnirelmann category of the range of the map is not more than the category of the domain? We discuss this and some related questions.
Prioritized Experience Replay

Abstract: Experience replay lets online reinforcement learning agents remember and reuse experiences from the past. In prior work, experience transitions were uniformly sampled from a replay memory. However, this approach simply replays transitions at the same frequency that they were originally experienced, regardless of their significance. In this paper we develop a framework for prioritizing experience, so as to replay important transitions more frequently, and therefore learn more efficiently. We use prioritized experience replay in Deep Q-Networks (DQN), a reinforcement learning algorithm that achieved human-level performance across many Atari games. DQN with prioritized experience replay achieves a new state-of-the-art, outperforming DQN with uniform replay on 41 out of 49 games.
Anderson Localization for Radial Tree Graphs With Random Branching Numbers

Abstract We prove Anderson localization for the discrete Laplace operator on radial tree graphs with random branching numbers. Our method relies on the representation of the Laplace operator as the direct sum of half-line Jacobi matrices whose entries are non-degenerate, independent, identically distributed random variables with singular distributions.
Review of Multi-Agent Algorithms for Collective Behavior: a Structural Taxonomy

Abstract In this paper, we review multi-agent collective behavior algorithms in the literature and classify them according to their underlying mathematical structure. For each mathematical technique, we identify the multi-agent coordination tasks it can be applied to, and we analyze its scalability, bandwidth use, and demonstrated maturity. We highlight how versatile techniques such as artificial potential functions can be used for applications ranging from low-level position control to high-level coordination and task allocation, we discuss possible reasons for the slow adoption of complex distributed coordination algorithms in the field, and we highlight areas for further research and development.
Ergodicity and conservativity of products of infinite transformations and their inverses

We construct a class of rank-one infinite measure-preserving transformations such that for each transformation $T$ in the class, the cartesian product $T\times T$ of the transformation with itself is ergodic, but the product $T\times T^{-1}$ of the transformation with its inverse is not ergodic. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.
BRILL-NOETHER LOCI WITH FIXED DETERMINANT IN RANK 2

In the 1990s, Bertram, Feinberg and Mukai examined Brill–Noether loci for vector bundles of rank 2 with fixed canonical determinant, noting that the dimension was always bigger in this case than the naive expectation. We generalize their results to treat a much broader range of fixed-determinant Brill–Noether loci. The main technique is a careful study of symplectic Grassmannians and related concepts.
Nearly linear-time packing and covering LP solvers

Packing and covering linear programs (PC-LP s) form an important class of linear programs (LPs) across computer science, operations research, and optimization. Luby and Nisan (in: STOC, ACM Press, New York, 1993) constructed an iterative algorithm for approximately solving PC-LP s in nearly linear time, where the time complexity scales nearly linearly in N, the number of nonzero entries of the matrix, and polynomially in $$\varepsilon $$ , the (multiplicative) approximation error. Unfortunately, existing nearly linear-time algorithms (Plotkin et al. in Math Oper Res 20(2):257–301, 1995; Bartal et al., in: Proceedings 38th annual symposium on foundations of computer science, IEEE Computer Society, 1997; Young, in: 42nd annual IEEE symposium on foundations of computer science (FOCS’01), IEEE Computer Society, 2001; Koufogiannakis and Young in Algorithmica 70:494–506, 2013; Young in Nearly linear-time approximation schemes for mixed packing/covering and facility-location linear programs, 2014. arXiv:1407.3015 ; Allen-Zhu and Orecchia, in: SODA, 2015) for solving PC-LP s require time at least proportional to $$\varepsilon ^{-2}$$ . In this paper, we break this longstanding barrier by designing a packing solver that runs in time $$\widetilde{O}(N \varepsilon ^{-1})$$ and covering LP solver that runs in time $$\widetilde{O}(N \varepsilon ^{-1.5})$$ . Our packing solver can be extended to run in time $$\widetilde{O}(N \varepsilon ^{-1})$$ for a class of well-behaved covering programs. In a follow-up work, Wang et al. (in: ICALP, 2016) showed that all covering LPs can be converted into well-behaved ones by a reduction that blows up the problem size only logarithmically.
ALGEBRAIC STRUCTURES ON THE TOPOLOGY OF MODULI SPACES OF CURVES AND MAPS

We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relation with GromovnWitten the- ory and integrable systems.
Split orders and convex polytopes in buildings

Abstract As part of his work to develop an explicit trace formula for Hecke operators on congruence subgroups of SL 2 ( Z ) , Hijikata (1974) [13] defines and characterizes the notion of a split order in M 2 ( k ) , where k is a local field. In this paper, we generalize the notion of a split order to M n ( k ) for n > 2 and give a natural geometric characterization in terms of the affine building for SL n ( k ) . In particular, we show that there is a one-to-one correspondence between split orders in M n ( k ) and a collection of convex polytopes in apartments of the building such that the split order is the intersection of all the maximal orders representing the vertices in the polytope. This generalizes the geometric interpretation in the n = 2 case in which split orders correspond to geodesics in the tree for SL 2 ( k ) with the split order given as the intersection of the endpoints of the geodesic.
Computational performance of a projection and rescaling algorithm

This paper documents a computational implementation of a projection and rescaling algorithm for finding most interior solutions to the pair of feasibility problems find x∈L∩R+nandfind xˆ∈L⊥∩R+n, wh...
Chern–Simons Forms and Higher Character Maps of Lie Representations

This paper is a sequel to our earlier work [BFPRW], where we study the derived representation scheme DRep_{g}(A) parametrizing the representations of a Lie algebra A in a finite-dimensional reductive Lie algebra g. In [BFPRW], we defined two canonical maps Tr_{g}(A): HC^{(r)}(A) \to \H[\DRep_{g}(A)]^G and \Phi_{g}(A): H[\DRep_{g}(A)]^G \to H[\DRep_{h}(A)]^W called the Drinfeld trace and the derived Harish-Chandra homomorphism, respectively. In this paper, we give an explicit formula for the Drinfeld trace in terms of Chern-Simons classes of a canonical g-torsor associated to the pair (A, g). Our construction is inspired by (and, in a sense, dual to) the classical construction of `additive regulator maps' due to Beilinson and Feigin. As a consequence, we show that, if A is an abelian Lie algebra, the composite map Phi_{g}(A) Tr_{g}(A) is represented by a canonical differential operator acting on differential forms on Sym(A) and depending only on the Cartan data (h, W, P), where P is a W-invariant polynomial on h. We derive a combinatorial formula for this operator that plays an important role in the study of derived commuting schemes in [BFPRW].
Unsupervised Visuomotor Control through Distributional Planning Networks

While reinforcement learning (RL) has the potential to enable robots to autonomously acquire a wide range of skills, in practice, RL usually requires manual, per-task engineering of reward functions, especially in real world settings where aspects of the environment needed to compute progress are not directly accessible. To enable robots to autonomously learn skills, we instead consider the problem of reinforcement learning without access to rewards. We aim to learn an unsupervised embedding space under which the robot can measure progress towards a goal for itself. Our approach explicitly optimizes for a metric space under which action sequences that reach a particular state are optimal when the goal is the final state reached. This enables learning effective and control-centric representations that lead to more autonomous reinforcement learning algorithms. Our experiments on three simulated environments and two real-world manipulation problems show that our method can learn effective goal metrics from unlabeled interaction, and use the learned goal metrics for autonomous reinforcement learning.
A delay-optimal packet scheduler for M2M uplink

In this paper, we present a delay-optimal packet scheduler for processing the M2M uplink traffic at the M2M application server (AS). Due to the delay-heterogeneity in uplink traffic, we classify it broadly into delay-tolerant and delay-sensitive traffic. We then map the diverse delay requirements of each class to sigmoidal functions of packet delay and formulate a utility-maximization problem that results in a proportionally fair delay-optimal scheduler. We note that solving this optimization problem is equivalent to solving for the optimal fraction of time each class is served with (preemptive) priority such that it maximizes the system utility. Using Monte-Carlo simulations for the queuing process at AS, we verify the correctness of the analytical result for optimal scheduler and show that it outperforms other state-of-the-art packet schedulers such as weighted round robin, max-weight scheduler, fair scheduler and priority scheduling. We also note that at higher traffic arrival rate, the proposed scheduler results in a near-minimal delay variance for the delay-sensitive traffic which is highly desirable. This comes at the expense of somewhat higher delay variance for delay-tolerant traffic which is usually acceptable due to its delay-tolerant nature.
What can topology tell us about the neural code

Neuroscience is undergoing a period of rapid experimental progress and expansion. New mathematical tools, previously unknown in the neuroscience community, are now being used to tackle fundamental questions and analyze emerging data sets. Consistent with this trend, the last decade has seen an uptick in the use of topological ideas and methods in neuroscience. In this talk I will survey recent applications of topology in neuroscience, and explain why topology is an especially natural tool for understanding neural codes. Note: This is a write-up of my talk for the Current Events Bulletin, held at the 2016 Joint Math Meetings in Seattle, WA.
An Integer Linear Programming Solution to the Telescope Network Scheduling Problem

Telescope networks are gaining traction due to their promise of higher resource utilization than single telescopes and as enablers of novel astronomical observation modes. However, as telescope network sizes increase, the possibility of scheduling them completely or even semi-manually disappears. In an earlier paper, a step towards software telescope scheduling was made with the specification of the Reservation formalism, through the use of which astronomers can express their complex observation needs and preferences. In this paper we build on that work. We present a solution to the discretized version of the problem of scheduling a telescope network. We derive a solvable integer linear programming (ILP) model based on the Reservation formalism. We show computational results verifying its correctness, and confirm that our Gurobi-based implementation can address problems of realistic size. Finally, we extend the ILP model to also handle the novel observation requests that can be specified using the more advanced Compound Reservation formalism.
Comparing curves in homogeneous spaces

Abstract Of concern is the study of the space of curves in homogeneous spaces. Motivated by applications in shape analysis we identify two curves if they only differ by their parametrization and/or a rigid motion. For curves in Euclidean space the Square-Root-Velocity-Function (SRVF) allows to define and efficiently compute a distance on this infinite dimensional quotient space. In this article we present a generalization of the SRVF to curves in homogeneous spaces. We prove that, under mild conditions on the curves, there always exist optimal reparametrizations realizing the quotient distance and demonstrate the efficiency of our framework in selected numerical examples.
Equivariant Littlewood-Richardson skew tableaux

We give a positive equivariant Littlewood-Richardson rule also discovered independently by Molev. Our proof generalizes a proof by Stembridge of the classical Littlewood-Richardson rule. We describe a weight-preserving bijection between our indexing tableaux and trapezoid puzzles which restricts to a bijection between positive indexing tableaux and Knutson-Tao puzzles.
Construction of simultaneous confidence bands for multiple logistic regression models over restricted regions

ABSTRACTThis article presents methods for constructing an asymptotic hyperbolic band under the multiple logistic regression model when the predictor variables are restricted to a specific region X. Scheffe's method yields unnecessarily wide, and hence conservative, bands if the predictor variables can be restricted to a certain region. Piegorsch and Casella [Confidence bands for logistic regression with restricted predictor variables. Biometrics. 1988;44:739–750] developed a procedure to build an asymptotic confidence band for the multiple logistic regression model over particular regions. Those regions are shown to be special cases of the region X, which was first investigated by Seppanen and Uusipaikka [Confidence bands for linear regression over restricted regions. Scand J Stat. 1992;19:73–81] in the multiple linear regression context. This article also provides methods for constructing conservative confidence bands when the restricted region is not of the specified form. Particularly, rectangular rest...
Dressing with Control: Using Integrability to Generate Desired Solutions to Einstein’s Equations

Motivated by integrability of the sine-Gordon equation, we investigate a technique for constructing desired solutions to Einstein’s equations by combining a dressing technique with a control-theory approach. After reviewing classical integrability, we recall two well-known Killing field reductions of Einstein’s equations, unify them using a harmonic map formulation, and state two results on the integrability of the equations and solvability of the dressing system. The resulting algorithm is then combined with an asymptotic analysis to produce constraints on the degrees of freedom arising in the solution-generation mechanism. The approach is carried out explicitly for the Einstein vacuum equations. Applications of the technique to other geometric field theories are also discussed.
A phase model approach for thermostatically controlled load demand response

Abstract A significant portion of electricity consumed worldwide is used to power thermostatically controlled loads (TCLs) such as air conditioners, refrigerators, and water heaters. Because the short-term timing of operation of such systems is inconsequential as long as their long-run average power consumption is maintained, they are increasingly used in demand response (DR) programs to balance supply and demand on the power grid. Here, we present an ab initio phase model for general TCLs, and use the concept to develop a continuous oscillator model of a TCL and compute its phase response to changes in temperature and applied power. This yields a simple control system model that can be used to evaluate control policies for modulating the power consumption of aggregated loads with parameter heterogeneity and stochastic drift. We demonstrate this concept by comparing simulations of ensembles of heterogeneous loads using the continuous state model and an established hybrid state model. The developed phase model approach is a novel means of evaluating DR provision using TCLs, and is instrumental in estimating the capacity of ancillary services or DR on different time scales. We further propose a novel phase response based open-loop control policy that effectively modulates the aggregate power of a heterogeneous TCL population while maintaining load diversity and minimizing power overshoots. This is demonstrated by low-error tracking of a regulation signal by filtering it into frequency bands and using TCL sub-ensembles with duty cycles in corresponding ranges. Control policies that can maintain a uniform distribution of power consumption by aggregated heterogeneous loads will enable distribution system management (DSM) approaches that maintain stability as well as power quality, and further allow more integration of renewable energy sources.
A Generic Framework for Interesting Subspace Cluster Detection in Multi-attributed Networks

Detection of interesting (e.g., coherent or anomalous) clusters has been studied extensively on plain or univariate networks, with various applications. Recently, algorithms have been extended to networks with multiple attributes for each node in the real-world. In a multi-attributed network, often, a cluster of nodes is only interesting for a subset (subspace) of attributes, andthis type of clusters is called subspace clusters. However, in the current literature, few methods are capable of detecting subspace clusters, which involves concurrent feature selection and network cluster detection. These relevant methods are mostly heuristic-driven and customized for specific application scenarios. In this work, we present a generic and theoretical framework for detection of interesting subspace clusters in large multi-attributed networks. Specifically, we propose a subspace graph-structured matching pursuit algorithm, namely, SG-Pursuit, to address a broad class of such problems for different scorefunctions (e.g., coherence or anomalous functions) and topology constraints (e.g., connected subgraphs and dense subgraphs). We prove that our algorithm 1) runs in nearly-linear time on the network size and the total number of attributes and 2) enjoys rigorous guarantees (geometrical convergence rate and tight error bound) analogous to those of the state-of-the-art algorithms for sparse feature selection problems and subgraph detection problems. As a case study, we specialize SG-Pursuit to optimizea number of well-known score functions for two typical tasks, including detection of coherent dense and anomalous connected subspace clusters in real-world networks. Empirical evidence demonstrates that our proposed generic algorithm SG-Pursuit is superior over state-of-the-art methods that are designed specifically for these two tasks.
Some special cases of Bobadilla's conjecture

Abstract We prove two special cases of a conjecture of J. Fernandez de Bobadilla for hypersurfaces with 1-dimensional critical loci. We do this via a new numerical invariant for such hypersurfaces, called the beta invariant, first defined and explored by the second author in 2014. The beta invariant is an algebraically calculable invariant of the local ambient topological-type of the hypersurface, and the vanishing of the beta invariant is equivalent to the hypotheses of Bobadilla's conjecture.
A relative higher index theorem, diffeomorphisms and positive scalar curvature

Abstract We prove a general relative higher index theorem for complete manifolds with positive scalar curvature towards infinity. We apply this theorem to study Riemannian metrics of positive scalar curvature on manifolds. For every two metrics of positive scalar curvature on a closed manifold and a Galois cover of the manifold, we define a secondary higher index class. Non-vanishing of this higher index class is an obstruction for the two metrics to be in the same connected component of the space of metrics of positive scalar curvature. In the special case where one metric is induced from the other by a diffeomorphism of the manifold, we obtain a formula for computing this higher index class. In particular, it follows that the higher index class lies in the image of the Baum–Connes assembly map.
On GROUSE and incremental SVD

GROUSE (Grassmannian Rank-One Update Subspace Estimation) [1] is an incremental algorithm for identifying a subspace of ℝn from a sequence of vectors in this subspace, where only a subset of components of each vector is revealed at each iteration. Recent analysis [2] has shown that GROUSE converges locally at an expected linear rate, under certain assumptions. GROUSE has a similar flavor to the incremental singular value decomposition algorithm [4], which updates the SVD of a matrix following addition of a single column. In this paper, we modify the incremental SVD approach to handle missing data, and demonstrate that this modified approach is equivalent to GROUSE, for a certain choice of an algorithmic parameter.
TrolleyMod v1.0: An Open-Source Simulation and Data-Collection Platform for Ethical Decision Making in Autonomous Vehicles

This paper presents TrolleyMod v1.0, an open-source platform based on the CARLA simulator for the collection of ethical decision-making data for autonomous vehicles. This platform is designed to facilitate experiments aiming to observe and record human decisions and actions in high-fidelity simulations of ethical dilemmas that occur in the context of driving. Targeting experiments in the class of trolley problems, TrolleyMod provides a seamless approach to creating new experimental settings and environments with the realistic physics-engine and the high-quality graphical capabilities of CARLA and the Unreal Engine. Also, TrolleyMod provides a straightforward interface between the CARLA environment and Python to enable the implementation of custom controllers, such as deep reinforcement learning agents. The results of such experiments can be used for sociological analyses, as well as the training and tuning of value-aligned autonomous vehicles based on social values that are inferred from observations.
Accelerated atomistic simulation study on the stability and mobility of carbon tri-interstitial cluster in cubic SiC

Abstract Using a combination of kinetic Activation Relaxation Technique with empirical potential and ab initio based climbing image nudged elastic band method, we perform an extensive search of the migration and rotation paths of the most stable carbon tri-interstitial cluster in cubic SiC. Our research reveals paths with the lowest energy barriers to migration, rotation, and dissociation of the most stable cluster. The kinetic properties of the most stable cluster, including its mobility, rotation behavior at different temperatures and stability against high temperature annealing, are discussed based on the calculated transition barriers. In addition to fundamental insights, our study provides a methodology for investigation of other extended defects in a technologically important material.
Inverse limits of uniform covering maps

Abstract In [N. Brodskiy, J. Dydak, B. LaBuz, A. Mitra, Rips complexes and covers in the uniform category, preprint] the authors define, following James, covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. Conditions for the existence of universal uniform covering maps and generalized uniform covering maps are given. This paper notes that the universal generalized uniform covering map is uniformly equivalent to the inverse limit of uniform covering maps and provides a characterization of generalized uniform covering maps that are uniformly equivalent to the inverse limit of uniform covering maps.
Decomposition of Schramm–Loewner evolution along its curve

Abstract We show that, for κ ∈ ( 0 , 8 ) , the integral of the laws of two-sided radial SLE κ curves through different interior points against a measure with SLE κ Green’s function density is the law of a chordal SLE κ curve, biased by the path’s natural length. We also show that, for κ > 0 , the integral of the laws of extended SLE κ ( − 8 ) curves through different interior points against a measure with a closed formula density restricted in a bounded set is the law of a chordal SLE κ curve, biased by the path’s capacity length restricted in that set. Another result is that, for κ ∈ ( 4 , 8 ) , if one integrates the laws of two-sided chordal SLE κ curves through different force points on R against a measure with density on R , then one also gets a law that is absolutely continuous w.r.t. that of a chordal SLE κ curve. To obtain these results, we develop a framework to study stochastic processes with random lifetime, and improve the traditional Girsanov’s Theorem.