cssi/SciSciGPT-SciSciNet huggingface dataset:
A causal framework for explaining the predictions of black-box sequence-to-sequence models

We interpret the predictions of any black-box structured input-structured output model around a specific input-output pair. Our method returns an “explanation” consisting of groups of input-output tokens that are causally related. These dependencies are inferred by querying the model with perturbed inputs, generating a graph over tokens from the responses, and solving a partitioning problem to select the most relevant components. We focus the general approach on sequence-to-sequence problems, adopting a variational autoencoder to yield meaningful input perturbations. We test our method across several NLP sequence generation tasks.
Stochastic Geometry-Based Uplink Analysis of Massive MIMO Systems With Fractional Pilot Reuse

In this paper, we analyze the performance of the uplink (UL) of a massive MIMO network considering an asymptotically large number of antennas at base stations (BSs). We model the locations of BSs as a homogeneous Poisson point process and assume that their service regions are limited to their respective Poisson-Voronoi cells (PVCs). Furthermore, for each PVC, based on a threshold radius, we model the cell center (CC) region as the Johnson-Mehl (JM) cell of its BS while the rest of the PVC is deemed as the cell edge (CE) region. The CC and CE users are located uniformly at random independently of each other in the JM cell and CE region, respectively. In addition, we consider fractional pilot reuse (FPR) scheme where two different sets of pilot sequences are used for CC and CE users with the objective of reducing the interference due to the pilot contamination for the CE users. Based on the above system model, we derive analytical expressions for the UL signal-to-interference-and-noise ratio ( $\mathtt {SINR}$ ) coverage probability and average spectral efficiency (SE) for randomly selected CC and CE users. In addition, we present an approximate expression for the average cell SE. One of the key intermediate results in our analysis is the approximate but accurate characterization of the distributions of the CC and CE areas of a typical cell. Another key intermediate step is the accurate characterization of the pair correlation functions of the point processes formed by the interfering CC and CE users that subsequently enables the coverage probability analysis. From our system analysis, we present a partitioning rule for the number of pilot sequences to be used for CC and CE users as a function of threshold radius that improves the average CE user SE, while achieving similar CC user SE with respect to the unity pilot reuse.
Constrained Least Squares, SDP, and QCQP Perspectives on Joint Biconvex Radar Receiver and Waveform design

Joint radar receive filter and waveform design is non-convex, but is individually convex for a fixed receiver filter while optimizing the waveform, and vice versa. Such classes of problems are fre- quently encountered in optimization, and are referred to biconvex programs. Alternating minimization (AM) is perhaps the most popu- lar, effective, and simplest algorithm that can deal with bi-convexity. In this paper we consider new perspectives on this problem via older, well established problems in the optimization literature. It is shown here specifically that the radar waveform optimization may be cast as constrained least squares, semi-definite programs (SDP), and quadratically constrained quadratic programs (QCQP). The bi-convex constraint introduces sets which vary for each iteration in the alternat- ing minimization. We prove convergence of alternating minimization for biconvex problems with biconvex constraints by showing the equivalence of this to a biconvex problem with constrained Cartesian product convex sets but for convex hulls of small diameter.
Sharp Models on Dull Hardware: Fast and Accurate Neural Machine Translation Decoding on the CPU

Attentional sequence-to-sequence models have become the new standard for machine translation, but one challenge of such models is a significant increase in training and decoding cost compared to phrase-based systems. In this work we focus on efficient decoding, with a goal of achieving accuracy close the state-of-the-art in neural machine translation (NMT), while achieving CPU decoding speed/throughput close to that of a phrasal decoder. We approach this problem from two angles: First, we describe several techniques for speeding up an NMT beam search decoder, which obtain a 4.4x speedup over a very efficient baseline decoder without changing the decoder output. Second, we propose a simple but powerful network architecture which uses an RNN (GRU/LSTM) layer at bottom, followed by a series of stacked fully-connected layers applied at every timestep. This architecture achieves similar accuracy to a deep recurrent model, at a small fraction of the training and decoding cost. By combining these techniques, our best system achieves a very competitive accuracy of 38.3 BLEU on WMT English-French NewsTest2014, while decoding at 100 words/sec on single-threaded CPU. We believe this is the best published accuracy/speed trade-off of an NMT system.
Challenges and Characteristics of Intelligent Autonomy for Internet of Battle Things in Highly Adversarial Environments.

Numerous, artificially intelligent, networked things will populate the battlefield of the future, operating in close collaboration with human warfighters, and fighting as teams in highly adversarial environments. This paper explores the characteristics, capabilities and intelligence required of such a network of intelligent things and humans - Internet of Battle Things (IOBT). It will experience unique challenges that are not yet well addressed by the current generation of AI and machine learning.
Zeros of a random analytic function approach perfect spacing under repeated differentiation

We consider an analytic function $f$ whose zero set forms a unit intensity Poisson process on the real line. We show that repeated differentiation causes the zero set to converge in distribution to a random translate of the integers.
Lattice points in a circle for generic unimodular shears

Given a unimodular lattice Λ ⊆ ℝ2 consider the counting function &#x1d4a9;Λ(T) counting the number of lattice points of norm less than T, and the remainder ℛΛ(T) = &#x1d4a9;(T) − πT2. We give an elementary proof that the mean square of the remainder over the set of all shears of a unimodular lattice is bounded by O(Tlog2(T)).
Brouwer and Euclid

Abstract We explore the relationship between Brouwer’s intuitionistic mathematics and Euclidean geometry. Brouwer wrote a paper in 1949 called The contradictority of elementary geometry . In that paper, he showed that a certain classical consequence of the parallel postulate implies Markov’s principle, which he found intuitionistically unacceptable. But Euclid’s geometry, having served as a beacon of clear and correct reasoning for two millennia, is not so easily discarded. Brouwer started from a “theorem” that is not in Euclid, and requires Markov’s principle for its proof. That means that Brouwer’s paper did not address the question whether Euclid’s Elements really requires Markov’s principle. In this paper we show that there is a coherent theory of “non-Markovian Euclidean geometry”. We show in some detail that our theory is an adequate formal rendering of (at least) Euclid’s Book I, and suffices to define geometric arithmetic, thus refining the author’s previous investigations (which include Markov’s principle as an axiom). Philosophically, Brouwer’s proof that his version of the parallel postulate implies Markov’s principle could be read just as well as geometric evidence for the truth of Markov’s principle, if one thinks the geometrical “intersection theorem” with which Brouwer started is geometrically evident.
Classification of smooth horizontal Schubert varieties

We show that the smooth horizontal Schubert subvarieties of a rational homogeneous variety G / P are homogeneously embedded cominuscule , and are classified by subdiagrams of a Dynkin diagram. This generalizes the classification of smooth Schubert varieties in cominuscule G / P.
Sums of products of fractional parts

We prove upper and lower bounds for certain sums of products of fractional parts by using majoring and minorizing functions from Fourier analysis. In special cases the lower bounds are sharp if there exist counterex- amples to the Littlewood conjecture in Diophantine approximation. We show that our more general lower bounds are sharp if there exist multiplicatively badly approximable matrices as considered in recent papers of Y. Bugeaud and O. N. German. We prove upper bounds for sums of products of fractional parts that hold on the complement of a set of small measure. We also give an alternative proof of German's transference principle for multiplicatively badly approximable matrices. G1 = (R=Z) MN ; and G2 = (R=Z) M : We write 1 and 2, respectively, for Haar measures on the Borel subsets of these groups normalized so that 1(G1) = 2(G2) = 1. We write the elements of the group G1 as M N matrices with entries in R=Z. That is, we write A = ( mn); where mn2 R=Z; for a generic element of G1. Obviously addition in the group G1 coincides with addition of matrices. We write the elements of the group G2 as M 1 column matrices. If is an N 1 column vector in Z N then
Diffusion of self-propelled particles in complex media

An investigation of the behavior of self-propelled particles in complex media finds a transition from thermal diffusion to collision-driven diffusion as the particle area fraction is increased. Collisions with passive particles increases the rotational diffusion of the self-propelled particles, leading to their ``self-trapping.''
Learning from the hindsight plan — Episodic MPC improvement

Model predictive control (MPC) is a popular control method that has proved effective for robotics, among other fields. MPC performs re-planning at every time step. Re-planning is done with a limited horizon per computational and real-time constraints and often also for robustness to potential model errors. However, the limited horizon leads to suboptimal performance. In this work, we consider the iterative learning setting, where the same task can be repeated several times, and propose a policy improvement scheme for MPC. The main idea is that between executions we can, offline, run MPC with a longer horizon, resulting in a hindsight plan. To bring the next real-world execution closer to the hindsight plan, our approach learns to re-shape the original cost function with the goal of satisfying the following property: short horizon planning (as realistic during real executions) with respect to the shaped cost should result in mimicking the hindsight plan. This effectively consolidates long-term reasoning into the short-horizon planning. We empirically evaluate our approach in contact-rich manipulation tasks both in simulated and real environments, such as peg insertion by a real PR2 robot.
Gendered Conversation in a Social Game-Streaming Platform

Online social media and games are increasingly replacing offline social activities. Social media is now an indispensable mode of communication; online gaming is not only a genuine social activity but also a popular spectator sport. Although online interaction shrinks social and geographical barriers, it is argued that social disparities, such as gender inequality, persists. For instance, online gaming communities have been criticized for objectifying women, which is a pressing question as gaming evolves into a social platform. However, few large-scale, systematic studies of gender inequality and objectification in social gaming platforms exist. Here we analyze more than one billion chat messages from Twitch, a social game-streaming platform, to study how the gender of streamers is associated with the nature of conversation. We find that female streamers receive significantly more objectifying comments while male streamers receive more game- related comments. This difference is more pronounced for popular streamers. We also show that the viewers’ choice of channels is also strongly gendered. Our findings suggest that gendered conversation and objectification is prevalent, and most users produce strongly gendered messages.
Comparing powers of edge ideals

Given a nontrivial homogeneous ideal I ⊆ k[x1,x2,…,xd], a problem of great recent interest has been the comparison of the rth ordinary power of I and the mth symbolic power I(m). This comparison ha...
A two-stage online monitoring procedure for high-dimensional data streams

Advanced computing and data acquisition technologies have made possible the collection of high-dimensional data streams in many fields. Efficient online monitoring tools that can correctly identify any abnormal data stream for such data are highly sough..
Stable Big Bang formation in near-FLRW solutions to the Einstein-scalar field and Einstein-stiff fluid systems

We prove a stable blowup result for solutions to the Einstein-scalar field and Einstein-stiff fluid systems. Our result applies to small perturbations of the spatially flat Friedmann–Lemaitre–Robertson–Walker (FLRW) solution with topology $$(0,\infty ) \times \mathbb {T}^3$$ . The FLRW solution models a spatially uniform scalar-field/stiff fluid evolving in a spacetime that expands towards the future and that has a “Big Bang” singularity at $$\lbrace 0 \rbrace \times \mathbb {T}^3$$ , where various curvature invariants blow up. We place “initial” data on a Cauchy hypersurface $$\Sigma _1'$$ that are close, as measured by a Sobolev norm, to the FLRW data induced on $$\lbrace 1 \rbrace \times \mathbb {T}^3$$ . We then study the asymptotic behavior of the perturbed solution in the collapsing direction and prove that its basic qualitative and quantitative features closely resemble those of the FLRW solution. In particular, for the perturbed solution, we construct constant mean curvature-transported spatial coordinates covering $$(t,x) \in (0,1] \times \mathbb {T}^3$$ and show that it also has a Big Bang at $$\lbrace 0 \rbrace \times \mathbb {T}^3$$ , where its curvature blows up. The blowup confirms Penrose’s Strong Cosmic Censorship hypothesis for the “past-half” of near-FLRW solutions. Furthermore, we show that the equations are dominated by kinetic (that is, time-derivative-involving) terms that induce approximately monotonic behavior near the Big Bang. As a consequence of the monotonicity, we also show that various time-rescaled components of the solution converge to regular functions of x as $$t \downarrow 0$$ . The most difficult aspect of the proof is showing that the solution exists for $$(t,x) \in (0,1] \times \mathbb {T}^3$$ , and to this end, we derive a hierarchy of energy estimates that allow for the possibility of mild energy blowup as $$t \downarrow 0$$ . To close these estimates, it is essential that we are able to rule out more singular energy blowup, a step that is in turn tied to the most important ingredient in our analysis: a collection of integral identities that, when combined in the right proportions, yield an $$L^2$$ -type approximate monotonicity inequality, a key point being that the error terms are controllable up to the singularity for near-FLRW solutions. In a companion article, we derived similar approximate monotonicity inequalities for linearized versions of the Einstein-scalar field equations and used them to prove linear stability results for a family of spatially homogeneous background solutions. The present article shows that the linear stability of the FLRW background solution can be upgraded to a full proof of the nonlinear stability of its singularity.
Projection Theorems Using Effective Dimension.

In this paper we use the theory of computing to study fractal dimensions of projections in Euclidean spaces. A fundamental result in fractal geometry is Marstrand's projection theorem, which shows that for every analytic set E, for almost every line L, the Hausdorff dimension of the orthogonal projection of E onto L is maximal. We use Kolmogorov complexity to give two new results on the Hausdorff and packing dimensions of orthogonal projections onto lines. The first shows that the conclusion of Marstrand's theorem holds whenever the Hausdorff and packing dimensions agree on the set E, even if E is not analytic. Our second result gives a lower bound on the packing dimension of projections of arbitrary sets. Finally, we give a new proof of Marstrand's theorem using the theory of computing.
A condition for distinguishing sceneries on non-abelian groups

Abstract A scenery f on a finite group G is a function from G to { 0 , 1 } . A random walk v ( t ) on G is said to be able to distinguish two sceneries if the distributions of the sceneries evaluated on the random walk with uniform initial distribution are identical only if one scenery is a shift of the other scenery. This paper generalizes a sufficient condition of Finucane, Tamuz, and Yaari for distinguishing two sceneries on finite abelian groups to one for finite non-abelian groups but shows that no random walks on finite non-abelian groups satisfy this sufficient condition.
Approximate Convex Hull of Data Streams

Given a finite set of points P subseteq R^d, we would like to find a small subset S subseteq P such that the convex hull of S approximately contains P. More formally, every point in P is within distance epsilon from the convex hull of S. Such a subset S is called an epsilon-hull. Computing an epsilon-hull is an important problem in computational geometry, machine learning, and approximation algorithms. In many applications, the set P is too large to fit in memory. We consider the streaming model where the algorithm receives the points of P sequentially and strives to use a minimal amount of memory. Existing streaming algorithms for computing an epsilon-hull require O(epsilon^{(1-d)/2}) space, which is optimal for a worst-case input. However, this ignores the structure of the data. The minimal size of an epsilon-hull of P, which we denote by OPT, can be much smaller. A natural question is whether a streaming algorithm can compute an epsilon-hull using only O(OPT) space. We begin with lower bounds that show, under a reasonable streaming model, that it is not possible to have a single-pass streaming algorithm that computes an epsilon-hull with O(OPT) space. We instead propose three relaxations of the problem for which we can compute epsilon-hulls using space near-linear to the optimal size. Our first algorithm for points in R^2 that arrive in random-order uses O(log n * OPT) space. Our second algorithm for points in R^2 makes O(log(epsilon^{-1})) passes before outputting the epsilon-hull and requires O(OPT) space. Our third algorithm, for points in R^d for any fixed dimension d, outputs, with high probability, an epsilon-hull for all but delta-fraction of directions and requires O(OPT * log OPT) space.
Extended Kalman filter on SE(3) for geometric control of a quadrotor UAV

An extended Kalman filter (EKF) is developed on the special Euclidean group, SE(3) for geometric control of a quadrotor UAV. It is obtained by performing an extensive linearization on SE(3) to estimate the state of the quadrotor from noisy measurements. Proposed estimator considers all the coupling effects between rotational and translational dynamics, and it is developed in a coordinate-free fashion. The desirable features of the proposed EKF are illustrated by numerical examples and experimental results for several scenarios. The proposed estimation scheme on SE(3) has been unprecedented and these results can be particularly useful for aggressive maneuvers in GPS denied environments or in situations where parts of onboard sensors fail.
Signed Support Recovery for Single Index Models in High-Dimensions

In this paper we study the support recovery problem for single index models $Y=f(\boldsymbol{X}^{\intercal} \boldsymbol{\beta},\varepsilon)$, where $f$ is an unknown link function, $\boldsymbol{X}\sim N_p(0,\mathbb{I}_{p})$ and $\boldsymbol{\beta}$ is an $s$-sparse unit vector such that $\boldsymbol{\beta}_{i}\in \{\pm\frac{1}{\sqrt{s}},0\}$. In particular, we look into the performance of two computationally inexpensive algorithms: (a) the diagonal thresholding sliced inverse regression (DT-SIR) introduced by Lin et al. (2015); and (b) a semi-definite programming (SDP) approach inspired by Amini & Wainwright (2008). When $s=O(p^{1-\delta})$ for some $\delta>0$, we demonstrate that both procedures can succeed in recovering the support of $\boldsymbol{\beta}$ as long as the rescaled sample size $\kappa=\frac{n}{s\log(p-s)}$ is larger than a certain critical threshold. On the other hand, when $\kappa$ is smaller than a critical value, any algorithm fails to recover the support with probability at least $\frac{1}{2}$ asymptotically. In other words, we demonstrate that both DT-SIR and the SDP approach are optimal (up to a scalar) for recovering the support of $\boldsymbol{\beta}$ in terms of sample size. We provide extensive simulations, as well as a real dataset application to help verify our theoretical observations.
When is scalar multiplication decidable

Abstract Let K be a subfield of R . The theory of R viewed as an ordered K-vector space and expanded by a predicate for Z is decidable if and only if K is a real quadratic field.
Preserving Link Privacy in Social Network Based Systems.

A growing body of research leverages social network based trust relationships to improve the functionality of the system. However, these systems expose users’ trust relationships, which is considered sensitive information in today’s society, to an adversary. In this work, we make the following contributions. First, we propose an algorithm that perturbs the structure of a social graph in order to provide link privacy, at the cost of slight reduction in the utility of the social graph. Second we define general metrics for characterizing the utility and privacy of perturbed graphs. Third, we evaluate the utility and privacy of our proposed algorithm using real world social graphs. Finally, we demonstrate the applicability of our perturbation algorithm on a broad range of secure systems, including Sybil defenses and secure routing.
Movie moves for knotted surfaces with markings

We present a marked analog of Carter and Saito’s movie theorem. Our definition of marking was chosen to coincide with the markings that arise in link Floer homology. In order to deal with complications arising from certain isotopes, we define three equivalences for marked surfaces and work over an equivalence class of marked surfaces when proving our generalization of Carter and Saito’s movie theorem.
Moment-based quantile sketches for efficient high cardinality aggregation queries

Interactive analytics increasingly involves querying for quantiles over sub-populations of high cardinality datasets. Data processing engines such as Druid and Spark use mergeable summaries to estimate quantiles, but summary merge times can be a bottleneck during aggregation. We show how a compact and efficiently mergeable quantile sketch can support aggregation workloads. This data structure, which we refer to as the moments sketch, operates with a small memory footprint (200 bytes) and computationally efficient (50ns) merges by tracking only a set of summary statistics, notably the sample moments. We demonstrate how we can efficiently estimate quantiles using the method of moments and the maximum entropy principle, and show how the use of a cascade further improves query time for threshold predicates. Empirical evaluation shows that the moments sketch can achieve less than 1 percent quantile error with 15× less overhead than comparable summaries, improving end query time in the MacroBase engine by up to 7× and the Druid engine by up to 60×.
Estimators for Multivariate Information Measures in General Probability Spaces

Information theoretic quantities play an important role in various settings in machine learning, including causality testing, structure inference in graphical models, time-series problems, feature selection as well as in providing privacy guarantees. A key quantity of interest is the mutual information and generalizations thereof, including conditional mutual information, multivariate mutual information, total correlation and directed information. While the aforementioned information quantities are well defined in arbitrary probability spaces, existing estimators employ a $\Sigma H$ method, which can only work in purely discrete space or purely continuous case since entropy (or differential entropy) is well defined only in that regime. In this paper, we define a general graph divergence measure ($\mathbb{GDM}$), generalizing the aforementioned information measures and we construct a novel estimator via a coupling trick that directly estimates these multivariate information measures using the Radon-Nikodym derivative. These estimators are proven to be consistent in a general setting which includes several cases where the existing estimators fail, thus providing the only known estimators for the following settings: (1) the data has some discrete and some continuous valued components (2) some (or all) of the components themselves are discrete-continuous \textit{mixtures} (3) the data is real-valued but does not have a joint density on the entire space, rather is supported on a low-dimensional manifold. We show that our proposed estimators significantly outperform known estimators on synthetic and real datasets.
Interdefinability of defeasible logic and logic programming under the well-founded semantics

We provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the ambiguity propagating defeasible logic ADL correspond to those of the well-founded semantics for normal logic programs, and so it turns out that the two formalisms are closely related. Using the same translation of logic programs into defeasible theories, the semantics for the ambiguity blocking defeasible logic NDL can be seen as indirectly providing an ambiguity blocking semantics for logic programs. We also provide antimonotone operators for both ADL and NDL, each based on the Gelfond-Lifschitz GL operator for logic programs. For defeasible theories without defeaters or priorities on rules, the operator for ADL corresponds to the GL operator and so can be seen as partially capturing the consequences according to ADL. Similarly, the operator for NDL captures the consequences according to NDL, though in this case no restrictions on theories apply. Both operators can be used to define stable model semantics for defeasible theories.
K-contact Lie groups of dimension five or greater

We prove that a K-contact Lie group of dimension five or greater is the central extension of a symplectic Lie group by complexifying the Lie algebra and applying a result from complex contact geometry, namely, that, if the adjoint action of the complex Reeb vector field on a complex contact Lie algebra is diagonalizable, then it is trivial.
Posterior contraction in Gaussian process regression using Wasserstein approximations

We study posterior rates of contraction in Gaussian process regression with unbounded covariate domain. Our argument relies on developing a Gaussian approximation to the posterior of the leading coefficients of a Karhunen--Lo\'{e}ve expansion of the Gaussian process. The salient feature of our result is deriving such an approximation in the $L^2$ Wasserstein distance and relating the speed of the approximation to the posterior contraction rate using a coupling argument. Specific illustrations are provided for the Gaussian or squared-exponential covariance kernel.
Electron emission by long and short wavelength lasers: Essentials for the design of plasmonic photocathodes

The theory of electron emission by metallic photocathodes under the exposure of long wavelength lasers will be studied. Photon energy in long wavelength lasers is less than the work function of the photocathode's material and can only emit electrons via tunneling through the potential barrier. The optical resonance effects (e.g., plasmonic resonances) will be studied as an improvement to the performance of photocathodes. This paper is intended to provide self-sufficient materials to design optical resonant surfaces (e.g., metasurfaces) for electron emission applications.
Enhanced Quantum Procedures that Resolve Difficult Problems

A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The new tools are applied to several examples including: (1) A quantum formulation that is invariant under arbitrary classical canonical transformations of coordinates; (2) A toy model that for all positive energy solutions has singularities which are removed at the classical level when the correct quantum corrections are applied; (3) A fairly simple model field theory with non-trivial classical behavior that, when conventionally quantized, becomes trivial, but nevertheless finds a proper solution using the enhanced procedures; (4) A model of scalar field theories with non-trivial classical behavior that, when conventionally quantized, becomes trivial, but nevertheless finds a proper solution using the enhanced procedures; (5) A viable formulation of the kinematics of quantum gravity that respects the strict positivity of the spatial metric in both its classical and quantum versions; and (6) A proposal for a non-trivial quantization of that is ripe for study by Monte Carlo computational methods. All of these examples use fairly general arguments that can be understood by a broad audience.
Approximate Kalman filter Q-Learning for continuous state-space MDPs

We seek to learn an effective policy for a Markov Decision Process (MDP) with continuous states via Q-Learning. Given a set of basis functions over state action pairs we search for a corresponding set of linear weights that minimizes the mean Bellman residual. Our algorithm uses a Kalman filter model to estimate those weights and we have developed a simpler approximate Kalman filter model that outperforms the current state of the art projected TD-Learning methods on several standard benchmark problems.
The solution of the Kadison-Singer Problem

These lecture notes are meant to accompany two lectures given at the CDM 2016 conference, about the Kadison-Singer Problem. They are meant to complement the survey by the same authors (along with Spielman) which appeared at the 2014 ICM. In the first part of this survey we will introduce the Kadison-Singer problem from two perspectives ($C^*$ algebras and spectral graph theory) and present some examples showing where the difficulties in solving it lie. In the second part we will develop the framework of interlacing families of polynomials, and show how it is used to solve the problem. None of the results are new, but we have added annotations and examples which we hope are of pedagogical value.
Strategic Bidding for Producers in Nodal Electricity Markets: A Convex Relaxation Approach

Strategic bidding problems in electricity markets are widely studied in power systems, often by formulating complex bi-level optimization problems that are hard to solve. The state-of-the-art approach to solve such problems is to reformulate them as mixed-integer linear programs (MILPs). However, the computational time of such MILP reformulations grows dramatically, once the network size increases, scheduling horizon increases, or randomness is taken into consideration. In this paper, we take a fundamentally different approach and propose effective and customized convex programming tools to solve the strategic bidding problem for producers in nodal electricity markets. Our approach is inspired by the Schmudgen's Positivstellensatz Theorem in semialgebraic geometry; but then we go through several steps based upon both convex optimization and mixed-integer programming that results in obtaining close to optimal bidding solutions, as evidenced by several numerical case studies, besides having a huge advantage on reducing computation time. While the computation time of the state-of-the-art MILP approach grows exponentially when we increase the scheduling horizon or the number of random scenarios, the computation time of our approach increases rather linearly.
Efficient computation of the Kauffman bracket

This paper bounds the computational cost of computing the Kauffman bracket of a link in terms of the crossing number of that link. Specifically, it is shown that the image of a tangle with g boundary points and n crossings in the Kauffman bracket skein module is a linear combination of O(2g) basis elements, with each coefficient a polynomial with at most n non-zero terms, each with integer coefficients, and that the link can be built one crossing at a time as a sequence of tangles with maximum number of boundary points bounded by for some C. From this it follows that the computation of the Kauffman bracket of the link takes time and memory a polynomial in n times .
Patterns in Khovanov link and chromatic graph homology

Khovanov homology of a link and chromatic graph homology are known to be isomorphic in a range of homological gradings that depend on the girth of a graph. We discuss patterns shared by these two h...
On Yau’s uniformization conjecture

Let $M^n$ be a complete noncompact Kahler manifold with nonnegative bisectional curvature and maximal volume growth, we prove that $M$ is biholomorphic to $\mathbb{C}^n$. This confirms Yau's uniformization conjecture when M has maximal volume growth.
Distributed Bargaining in Dyadic-Exchange Networks

This paper considers dyadic-exchange networks in which individual agents autonomously form coalitions of size two and agree on how to split a transferable utility. Valid results for this game include stable (if agents have no unilateral incentive to deviate), balanced (if matched agents obtain similar benefits from collaborating), or Nash (both stable and balanced) outcomes. We design provably correct continuous-time algorithms to find each of these classes of outcomes in a distributed way. Our algorithmic design to find Nash bargaining solutions builds on the other two algorithms by having the dynamics for finding stable outcomes feeding into the one for finding balanced ones. Our technical approach to establish convergence and robustness combines notions and tools from optimization, graph theory, nonsmooth analysis, and Lyapunov stability theory and provides a useful framework for further extensions. We illustrate our results in a wireless communication scenario where single-antenna devices have the possibility of working as 2-antenna virtual devices to improve channel capacity.
Proximity in the age of distraction: robust approximate nearest neighbor search

We introduce a new variant of the nearest neighbor search problem, which allows for some coordinates of the dataset to be arbitrarily corrupted or unknown. Formally, given a dataset of n points P = {x1, . . . , xn} in high-dimensions, and a parameter k, the goal is to preprocess the dataset, such that given a query point q, one can compute quickly a point x ∈ P, such that the distance of the query to the point x is minimized, when ignoring the "optimal" k coordinates. Note, that the coordinates being ignored are a function of both the query point and the point returned.We present a general reduction from this problem to answering ANN queries, which is similar in spirit to LSH (locality sensitive hashing) [19]. Specifically, we give a sampling technique which achieves a bi-criterion approximation for this problem. If the distance to the nearest neighbor after ignoring k coordinates is r, the data-structure returns a point that is within a distance of O(r) after ignoring O(k) coordinates. We also present other applications and further extensions and refinements of the above result.The new data-structures are simple and (arguably) elegant, and should be practical - specifically, all bounds are polynomial in all relevant parameters (including the dimension of the space, and the robustness parameter k).
Average Energy Approximation of the Ideal Bose-Einstein Gas and Condensate

If the N bosons that compose an ideal Bose-Einstein gas with energy E and volume V are each assumed to have the average energy of the system E/N, the entropy is easily expressed in terms of the number of bosons N and the number of single-particle microstates n they can occupy. Because the entropy derived is a function of only N and n, and the latter is a function of the extensive variables, E, V, and N, this entropy describes all that can be known of the thermodynamics of this system. In particular, the entropy very simply recovers the SakurTetrode entropy in the classical limit and at sufficiently low temperature describes an unstable system. A thermodynamic stability analysis recovers the Bose-Einstein condensate and a twophase region. Apart from numerical factors of order one, results are identical with those derived via standard, probabilistic methods. PACS: 67.10.-j 67.85.Bc 67.10.Ba Submitted To: European Journal of Physics
When is the self-intersection of a subvariety a fibration?

Abstract We provide a necessary and sufficient condition for the derived self-intersection of a smooth subscheme inside a smooth scheme to be a fibration over the subscheme. As a consequence we deduce a generalized HKR isomorphism. We also investigate the relationship of our result to path spaces in homotopy theory, Buchweitz–Flenner formality in algebraic geometry, and draw parallels with similar results in Lie theory and symplectic geometry.
Robobarista: Object Part Based Transfer of Manipulation Trajectories from Crowd-Sourcing in 3D Pointclouds

There is a large variety of objects and appliances in human environments, such as stoves, coffee dispensers, juice extractors, and so on. It is challenging for a roboticist to program a robot for each of these object types and for each of their instantiations. In this work, we present a novel approach to manipulation planning based on the idea that many household objects share similarly-operated object parts. We formulate the manipulation planning as a structured prediction problem and design a deep learning model that can handle large noise in the manipulation demonstrations and learns features from three different modalities: point-clouds, language and trajectory. In order to collect a large number of manipulation demonstrations for different objects, we developed a new crowd-sourcing platform called Robobarista. We test our model on our dataset consisting of 116 objects with 249 parts along with 250 language instructions, for which there are 1225 crowd-sourced manipulation demonstrations. We further show that our robot can even manipulate objects it has never seen before.
On gaps in the closures of images of divisor functions

Given a complex number c, define the divisor function σc : ℕ → ℂ by σc(n) =∑d|ndc. In this paper, we look at σ−r(ℕ)¯, the topological closure of the image of σ−r, when r > 1. We exhibit new lower b...
Colorful combinatorics and Macdonald polynomials

Abstract The non-negative integer cocharge statistic on words was introduced in the 1970s by Lascoux and Schutzenberger to combinatorially characterize the Hall–Littlewood polynomials. Cocharge has since been used to explain phenomena ranging from the graded decomposition of Garsia–Procesimodules to the cohomology structure of the Grassmann variety. Although its application to contemporary variations of these problems had been deemed intractable, we prove that the two-parameter, symmetric Macdonald polynomials are generating functions of a distinguished family of colored words. Cocharge adorns one parameter and the second measure its deviation from cocharge on words without color. We use the same framework to expand the plactic monoid, apply Kashiwara’s crystal theory to various Garsia–Haiman modules, and to address problems in K -theoretic Schubert calculus.
NORMAL SUBGROUPS GENERATED BY A SINGLE POLYNOMIAL AUTOMORPHISM

We study criteria for deciding when the normal subgroup generated by a single special polynomial automorphism of 𝔸n is as large as possible, namely, equal to the normal closure of the special linear group in the special automorphism group. In particular, we investigate m-triangular automorphisms, i.e., those that can be expressed as a product of affine automorphisms and m triangular automorphisms. Over a field of characteristic zero, we show that every nontrivial 4-triangular special automorphism generates the entire normal closure of the special linear group in the special tame subgroup, for any dimension n ≥ 2. This generalizes a result of Furter and Lamy in dimension 2.
Measuring conflict in a multi-source environment as a normal measure

In a multi-source environment, each source has its own credibility. If there is no external knowledge about credibility then we can use the information provided by the sources to assess their credibility. In this paper, we propose a way to measure conflict in a multi-source environment as a normal measure. We examine our algorithm using three simulated examples of increasing conflict and one experimental example. The results demonstrate that the proposed measure can represent conflict in a meaningful way similar to what a human might expect and from it we can identify conflict within our sources.
Degrees of Freedom in Wireless Interference Networks With Cooperative Transmission and Backhaul Load Constraints

Degrees of freedom (DoFs) gains are studied in wireless networks with cooperative transmission under a backhaul load constraint that limits the average number of messages that can be delivered from a centralized controller to base station transmitters. The backhaul load is defined as the sum of all the messages available at all the transmitters per channel use, normalized by the number of users. For Wyner’s linear interference network, where each transmitter is connected to the receiver having the same index as well as one succeeding receiver, the per user DoF is characterized and the optimal scheme is presented. Furthermore, it is shown that the optimal assignment of messages to transmitters is asymmetric and satisfies a local cooperation constraint and the optimal coding scheme relies only on one-shot cooperative zero-forcing transmit beamforming. Using insights from the analysis of Wyner’s linear interference network, the results are extended to the more practical hexagonal sectored cellular network, and coding schemes based on cooperative zero-forcing are shown to deliver significant DoF gains. It is established that by allowing for cooperative transmission and a flexible message assignment that is constrained only by an average backhaul load, one can deliver the rate gains promised by information-theoretic upper bounds with practical one-shot schemes that incur little or no additional load on the backhaul. Finally, useful upper bounds on the per user DoF for schemes based on cooperative zero-forcing are presented for lower values of the average backhaul load constraint, and an optimization framework is formulated for the general converse problem.
Hyperspaces of smooth convex bodies up to congruence

Abstract We determine the homeomorphism type of the hyperspace of positively curved C ∞ convex bodies in R n , and derive various properties of its quotient by the group of Euclidean isometries. We make a systematic study of hyperspaces of convex bodies that are at least C 1 . We show how to destroy the symmetry of a family of convex bodies, and prove that this cannot be done modulo congruence.
FractalNet: Ultra-Deep Neural Networks without Residuals.

We introduce a design strategy for neural network macro-architecture based on self-similarity. Repeated application of a simple expansion rule generates deep networks whose structural layouts are precisely truncated fractals. These networks contain interacting subpaths of different lengths, but do not include any pass-through or residual connections; every internal signal is transformed by a filter and nonlinearity before being seen by subsequent layers. In experiments, fractal networks match the excellent performance of standard residual networks on both CIFAR and ImageNet classification tasks, thereby demonstrating that residual representations may not be fundamental to the success of extremely deep convolutional neural networks. Rather, the key may be the ability to transition, during training, from effectively shallow to deep. We note similarities with student-teacher behavior and develop drop-path, a natural extension of dropout, to regularize co-adaptation of subpaths in fractal architectures. Such regularization allows extraction of high-performance fixed-depth subnetworks. Additionally, fractal networks exhibit an anytime property: shallow subnetworks provide a quick answer, while deeper subnetworks, with higher latency, provide a more accurate answer.@@@We introduce a design strategy for neural network macro-architecture based on self-similarity. Repeated application of a simple expansion rule generates deep networks whose structural layouts are precisely truncated fractals. These networks contain interacting subpaths of different lengths, but do not include any pass-through or residual connections; every internal signal is transformed by a filter and nonlinearity before being seen by subsequent layers. In experiments, fractal networks match the excellent performance of standard residual networks on both CIFAR and ImageNet classification tasks, thereby demonstrating that residual representations may not be fundamental to the success of extremely deep convolutional neural networks. Rather, the key may be the ability to transition, during training, from effectively shallow to deep. We note similarities with student-teacher behavior and develop drop-path, a natural extension of dropout, to regularize co-adaptation of subpaths in fractal architectures. Such regularization allows extraction of high-performance fixed-depth subnetworks. Additionally, fractal networks exhibit an anytime property: shallow subnetworks provide a quick answer, while deeper subnetworks, with higher latency, provide a more accurate answer.
An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs

In this work, we develop an adaptive, multivariate partitioning algorithm for solving nonconvex, Mixed-Integer Nonlinear Programs (MINLPs) with polynomial functions to global optimality. In particular, we present an iterative algorithm that exploits piecewise, convex relaxation approaches via disjunctive formulations to solve MINLPs that is different than conventional spatial branch-and-bound approaches. The algorithm partitions the domains of variables in an adaptive and non-uniform manner at every iteration to focus on productive areas of the search space. Furthermore, domain reduction techniques based on sequential, optimization-based bound-tightening and piecewise relaxation techniques, as a part of a presolve step, are integrated into the main algorithm. Finally, we demonstrate the effectiveness of the algorithm on well-known benchmark problems (including Pooling and Blending instances) from MINLPLib and compare our algorithm with state-of-the-art global optimization solvers. With our novel approach, we solve several large-scale instances, some of which are not solvable by state-of-the-art solvers. We also succeed in reducing the best known optimality gap for a hard, generalized pooling problem instance.
Identification of conditional interventional distributions

The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting distributions on post-action outcomes given a set of measurements. We provide a necessary and sufficient graphical condition for the cases where such distributions can be uniquely computed from the available information, as well as an algorithm which performs this computation whenever the condition holds. Furthermore, we use our results to prove completeness of do-calculus [Pearl, 1995] for the same identification problem, and show applications to sequential decision making.