cssi/SciSciGPT-SciSciNet huggingface dataset:
A refinement of the Shuffle Conjecture with cars of two sizes and $t=1/q$

The original Shuffle Conjecture of Haglund et al. has a symmetric function side and a combinatorial side. The symmetric function side may be simply expressed as $ $ where \nabla is the Macdonald polynomial eigen-operator of Bergeron and Garsia and $h_\mu$ is the homogeneous basis indexed by $\mu=(\mu_1,\mu_2,...,\mu_k)$ partitions of n. The combinatorial side q,t-enumerates a family of Parking Functions whose reading word is a shuffle of k successive segments of 1,2,3,...,n of respective lengths $\mu_1,\mu_2,...,\mu_k$. It can be shown that for t=1/q the symmetric function side reduces to a product of q-binomial coefficients and powers of q. This reduction suggests a surprising combinatorial refinement of the general Shuffle Conjecture. Here we prove this refinement for k=2 and t=1/q. The resulting formula gives a q-analogue of the well studied Narayana numbers.
The improper infinite derivatives of Takagi's nowhere-differentiable function

Abstract Let T be Takagi's continuous but nowhere-differentiable function. Using a representation in terms of Rademacher series due to N. Kono [Acta Math. Hungar. 49 (1987) 315–324], we give a complete characterization of those points where T has a left-sided, right-sided, or two-sided infinite derivative. This characterization is illustrated by several examples. A consequence of the main result is that the sets of points where T ′ ( x ) = ± ∞ have Hausdorff dimension one. As a byproduct of the method of proof, some exact results concerning the modulus of continuity of T are also obtained.
A Generalized Schur–Horn Theorem and Optimal Frame Completions

Abstract The Schur–Horn theorem is a classical result in matrix analysis which characterizes the existence of positive semidefinite matrices with a given diagonal and spectrum. In recent years, this theorem has been used to characterize the existence of finite frames whose elements have given lengths and whose frame operator has a given spectrum. We provide a new generalization of the Schur–Horn theorem which characterizes the spectra of all possible finite frame completions. That is, we characterize the spectra of the frame operators of the finite frames obtained by adding new vectors of given lengths to an existing frame. We then exploit this characterization to give a new and simple algorithm for computing the optimal such completion.
Initial growth of tin on niobium for vapor diffusion coating of Nb3Sn

Nb3Sn has the potential to achieve superior performance in terms of quality factor, accelerating gradient and operating temperature (4.2 K vs 2 K) resulting in significant reduction in both capital and operating costs compared to traditional niobium SRF accelerator cavities. Tin vapor diffusion coating of Nb3Sn on niobium appears to be a simple, yet most efficient technique so far to fabricate such cavities. Here, cavity interior surface coatings are obtained by a two step process: nucleation followed by deposition. The first step is normally accomplished with Sn/SnCl2 at a constant low temperature (500 °C) for several hours. To elucidate the role of this step, we systematically studied the niobium surface nucleated under varying process conditions. The surfaces obtained in typical tin/tin chloride processes were characterized using SEM/EDS, AFM, XPS, SAM and TEM. Examination of the surfaces nucleated under the standard conditions revealed not only tin particles, but also tin film on the surfaces resembling the surface obtained by Stranski-Krastanov growth mode. All the nucleation attempted with SnCl2 yielded better uniformity of Nb3Sn coating compared to coating obtained without nucleation, which often included random patchy regions with irregular grain structure. Even though the variation of nucleation parameters was able to produce different surfaces following nucleation, no evidence was found for any significant impact on the final coating.
Fixed points of the equivariant algebraic $K$-theory of spaces

In a recent work Malkiewich and Merling proposed a definition of the equivariant $K$-theory of spaces for spaces equipped with an action of a finite group. We show that the fixed points of this spectrum admit a tom Dieck-type splitting. We also show that this splitting is compatible with the splitting of the equivariant suspension spectrum. The first of these results has been obtained independently by John Rognes.
Reconciling Selfish Routing with Social Good

Selfish routing is a central problem in algorithmic game theory, with one of the principal applications being that of routing in road networks. Inspired by the emergence of routing technologies and autonomous driving, we revisit selfish routing and consider three possible outcomes of it: (i) \(\theta \)-Positive Nash Equilibrium flow, where every path that has non-zero flow on all of its edges has cost no greater than \(\theta \) times the cost of any other path, (ii) \(\theta \)-Used Nash Equilibrium flow, where every used path that appears in the path flow decomposition has cost no greater than \(\theta \) times the cost of any other path, and (iii) \(\theta \)-Envy Free flow, where every path that appears in the path flow decomposition has cost no greater than \(\theta \) times the cost of any other path in the path flow decomposition. We first examine the relations of these outcomes among each other and then measure their possible impact on the network’s performance. Right after, we examine the computational complexity of finding such flows of minimum social cost and give a range for \(\theta \) for which this task is easy and a range of \(\theta \) for which this task is NP-hard for the concepts of \(\theta \)-Used Nash Equilibrium flow and \(\theta \)-Envy Free flow. Finally, we propose strategies which, in a worst-case approach, can be used by a central planner in order to provide good \(\theta \)-flows.
On projectivized vector bundles and positive holomorphic sectional curvature

We generalize a construction of Hitchin to prove that, given any compact Kahler manifold $M$ with positive holomorphic sectional curvature and any holomorphic vector bundle $E$ over $M$, the projectivized vector bundle ${\mathbb P}(E)$ admits a Kahler metric with positive holomorphic sectional curvature.
On the existence of stationary patches

Abstract In this paper, we show the existence of the first nontrivial family of analytic stationary patch solutions of the SQG and gSQG equations. This answers an open problem in F. de la Hoz et al. (2016) [13] .
The NES Music Database: A multi-instrumental dataset with expressive performance attributes

Existing research on music generation focuses on composition, but often ignores the expressive performance characteristics required for plausible renditions of resultant pieces. In this paper, we introduce the Nintendo Entertainment System Music Database (NES-MDB), a large corpus allowing for separate examination of the tasks of composition and performance. NES-MDB contains thousands of multi-instrumental songs composed for playback by the compositionally-constrained NES audio synthesizer. For each song, the dataset contains a musical score for four instrument voices as well as expressive attributes for the dynamics and timbre of each voice. Unlike datasets comprised of General MIDI files, NES-MDB includes all of the information needed to render exact acoustic performances of the original compositions. Alongside the dataset, we provide a tool that renders generated compositions as NES-style audio by emulating the device's audio processor. Additionally, we establish baselines for the tasks of composition, which consists of learning the semantics of composing for the NES synthesizer, and performance, which involves finding a mapping between a composition and realistic expressive attributes.
Angular and Temporal Correlation of V2X Channels across Sub-6 GHz and mmWave Bands

5G millimeter wave (mmWave) technology is envisioned to be an integral part of next- generation vehicle-to-everything (V2X) networks and autonomous vehicles due to its broad bandwidth, wide field of view sensing, and precise localization capabilities. The reliability of mmWave links may be compromised due to difficulties in beam alignment for mobile channels and due to blocking effects between a mmWave transmitter and a receiver. To address such challenges, out-of-band information from sub-6 GHz channels can be utilized for predicting the temporal and angular channel characteristics in mmWave bands, which necessitates a good understanding of how propagation characteristics are coupled across different bands. In this paper, we use ray tracing simulations to characterize the angular and temporal correlation across a wide range of propagation frequencies for V2X channels ranging from 900 MHz up to 73 GHz, for a vehicle maintaining line-of-sight (LOS) and non-LOS (NLOS) beams with a transmitter in an urban environment. Our results shed light on increasing sparsity behavior of propagation channels with increasing frequency and highlight the strong temporal/angular correlation among 5.9 GHz and 28 GHz bands especially for LOS channels.
Infinite partitions and Rokhlin towers

We find a countable partition $P$ on\textbf{} a Lebesgue space, labeled $\{1,2,3...$\}, for any non-periodic measure preserving transformation $T$ such that $P$ generates $T$ and for the $T,P$ process, if you see an $n$ on time -1 then you only have to look at times $-n,1-n,...-1$ to know the positive integer $i$ to put at time 0. We alter that proof to extend every non-periodic $T$ to a uniform martingale (i.e. continuous $g$ function) on an infinite alphabet. If $T$ has positive entropy and the weak Pinsker property, this extension can be made to be an isomorphism. We pose remaining questions on uniform martingales. In the process of proving the uniform martingale result we make a complete analysis of Rokhlin towers which is of interest in and of itself. We also give an example that looks something like an i.i.d. process on $\mathbb{Z}^2$ when you read from right to left but where each column determines the next if you read left to right.
Optimal change point detection in Gaussian processes

Abstract We study the problem of detecting a change in the mean of one-dimensional Gaussian process data in the fixed domain regime. We propose a detection procedure based on the generalized likelihood ratio test (GLRT), and show that our method achieves asymptotically near-optimal rate in a minimax sense. The notable feature of the proposed method is that it exploits in an efficient way the data dependence captured by the Gaussian process covariance structure. When the covariance is not known, we propose the plug-in GLRT method and derive conditions under which the method remains asymptotically near-optimal. By contrast, the standard CUSUM method, which does not account for the covariance structure, is shown to be suboptimal. Our algorithms and asymptotic analysis are applicable to a number of covariance structures, including the Matern class, the powered exponential class, and others. The plug-in GLRT method is shown to perform well for maximum likelihood estimators with a dense covariance matrix.
An electrical probe of the phonon mean-free path spectrum

Most studies of the mean-free path accumulation function (MFPAF) rely on optical techniques to probe heat transfer at length scales on the order of the phonon mean-free path. In this paper, we propose and implement a purely electrical probe of the MFPAF that relies on photo-lithographically defined heater-thermometer separation to set the length scale. An important advantage of the proposed technique is its insensitivity to the thermal interfacial impedance and its compatibility with a large array of temperature-controlled chambers that lack optical ports. Detailed analysis of the experimental data based on the enhanced Fourier law (EFL) demonstrates that heat-carrying phonons in gallium arsenide have a much wider mean-free path spectrum than originally thought.
Counterfactual Language Model Adaptation for Suggesting Phrases

Mobile devices use language models to suggest words and phrases for use in text entry. Traditional language models are based on contextual word frequency in a static corpus of text. However, certain types of phrases, when offered to writers as suggestions, may be systematically chosen more often than their frequency would predict. In this paper, we propose the task of generating suggestions that writers accept, a related but distinct task to making accurate predictions. Although this task is fundamentally interactive, we propose a counterfactual setting that permits offline training and evaluation. We find that even a simple language model can capture text characteristics that improve acceptability.
Wonderful Symmetric Varieties and Schubert Polynomials

Extending results of Wyser, we determine formulas for the equivariant cohomology classes of closed orbits of certain families of spherical subgroups of the general linear group on the flag variety. Combining this with a slight extension of results of Can, Joyce and Wyser, we arrive at a family of polynomial identities which show that certain explicit sums of Schubert polynomials factor as products of linear forms.
A discrete Schrödinger equation via optimal transport on graphs

Abstract In 1966, Edward Nelson presented an interesting derivation of the Schrodinger equation using Brownian motion. Recently, this derivation is linked to the theory of optimal transport, which shows that the Schrodinger equation is a Hamiltonian system on the probability density manifold equipped with the Wasserstein metric. In this paper, we consider similar matters on a finite graph. By using discrete optimal transport and its corresponding Nelson's approach, we derive a discrete Schrodinger equation on a finite graph. The proposed system is quite different from the commonly referred discretized Schrodinger equations. It is a system of nonlinear ordinary differential equations (ODEs) with many desirable properties. Several numerical examples are presented to illustrate the properties.
Rationalization: A Neural Machine Translation Approach to Generating Natural Language Explanations

We introduce \em AI rationalization, an approach for generating explanations of autonomous system behavior as if a human had performed the behavior. We describe a rationalization technique that uses neural machine translation to translate internal state-action representations of an autonomous agent into natural language. We evaluate our technique in the Frogger game environment, training an autonomous game playing agent to rationalize its action choices using natural language. A natural language training corpus is collected from human players thinking out loud as they play the game. We motivate the use of rationalization as an approach to explanation generation and show the results of two experiments evaluating the effectiveness of rationalization. Results of these evaluations show that neural machine translation is able to accurately generate rationalizations that describe agent behavior, and that rationalizations are more satisfying to humans than other alternative methods of explanation.
Stochastic Wasserstein Barycenters

We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and allows the support of the barycenter to be adjusted in each iteration. We tackle the problem without regularization, allowing us to recover a sharp output whose support is contained within the support of the true barycenter. We give examples where our algorithm recovers a more meaningful barycenter than previous work. Our method is versatile and can be extended to applications such as generating super samples from a given distribution and recovering blue noise approximations.
Image-to-GPS Verification Through A Bottom-Up Pattern Matching Network

The image-to-GPS verification problem asks whether a given image is taken at a claimed GPS location. In this paper, we treat it as an image verification problem – whether a query image is taken at the same place as a reference image retrieved at the claimed GPS location. We make three major contributions: (1) we propose a novel custom bottom-up pattern matching (BUPM) deep neural network solution; (2) we demonstrate that the verification can be directly done by cross-checking a perspective-looking query image and a panorama reference image, and (3) we collect and clean a dataset of 30K pairs query and reference. Our experimental results show that the proposed BUPM solution outperforms the state-of-the-art solutions in terms of both verification and localization.
Multivariate CLT follows from strong Rayleigh property.

Let $(X_1 , \ldots , X_d)$ be random variables taking nonnegative integer values and let $f(z_1, \ldots , z_d)$ be the probability generating function. Suppose that $f$ is real stable; equivalently, suppose that the polarization of this probability distribution is strong Rayleigh. In specific examples, such as occupation counts of disjoint sets by a determinantal point process, it is known~\cite{soshnikov02} that the joint distribution must approach a multivariate Gaussian distribution. We show that this conclusion follows already from stability of $f$.
Distributed-memory large deformation diffeomorphic 3D image registration

We present a parallel distributed-memory algorithm for large deformation diffeomorphic registration of volumetric images that produces large isochoric deformations (locally volume preserving). Image registration is a key technology in medical image analysis. Our algorithm uses a partial differential equation constrained optimal control formulation. Finding the optimal deformation map requires the solution of a highly nonlinear problem that involves pseudo-differential operators, biharmonic operators, and pure advection operators both forward and backward in time. A key issue is the time to solution, which poses the demand for efficient optimization methods as well as an effective utilization of high performance computing resources. To address this problem we use a preconditioned, inexact, Gauss-Newton-Krylov solver. Our algorithm integrates several components: a spectral discretization in space, a semi-Lagrangian formulation in time, analytic adjoints, different regularization functionals (including volume-preserving ones), a spectral preconditioner, a highly optimized distributed Fast Fourier Transform, and a cubic interpolation scheme for the semi-Lagrangian time-stepping. We demonstrate the scalability of our algorithm on images with resolution of up to 10243 on the "Maverick" and "Stampede" systems at the Texas Advanced Computing Center (TACC). The critical problem in the medical imaging application domain is strong scaling, that is, solving registration problems of a moderate size of 2563---a typical resolution for medical images. We are able to solve the registration problem for images of this size in less than five seconds on 64 ×86 nodes of TACC's "Maverick" system.
Adaptive Monte Carlo Multiple Testing via Multi-Armed Bandits

Monte Carlo (MC) permutation test is considered the gold standard for statistical hypothesis testing, especially when standard parametric assumptions are not clear or likely to fail. However, in modern data science settings where a large number of hypothesis tests need to be performed simultaneously, it is rarely used due to its prohibitive computational cost. In genome-wide association studies, for example, the number of hypothesis tests $m$ is around $10^6$ while the number of MC samples $n$ for each test could be greater than $10^8$, totaling more than $nm$=$10^{14}$ samples. In this paper, we propose Adaptive MC multiple Testing (AMT) to estimate MC p-values and control false discovery rate in multiple testing. The algorithm outputs the same result as the standard full MC approach with high probability while requiring only $\tilde{O}(\sqrt{n}m)$ samples. This sample complexity is shown to be optimal. On a Parkinson GWAS dataset, the algorithm reduces the running time from 2 months for full MC to an hour. The AMT algorithm is derived based on the theory of multi-armed bandits.
Contact of a thin free boundary with a fixed one in the Signorini problem

We study the Signorini problem near a fixed boundary, where the solution is “clamped down” or “glued.” We show that in general the solutions are at least C1/2 regular and that this regularity is sharp. We prove that near the actual points of contact of the free boundary with the fixed one the blowup solutions must have homogeneity κ ≥ 3/2, while at the non-contact points the homogeneity must take one of the values: 1/2, 3/2, . . . , m− 1/2, . . . .
A change-point problem and inference for segment signals

We address the problem of detection and estimation of one or two change-points in the mean of a series of random variables. We use the formalism of set estimation in regression: to each point of a design is attached a binary label that indicates whether that point belongs to an unknown segment and this label is contaminated with noise. The endpoints of the unknown segment are the change-points. We study the minimal size of the segment which allows statistical detection in different scenarios, including when the endpoints are separated from the boundary of the domain of the design, or when they are separated from one another. We compare this minimal size with the minimax rates of convergence for estimation of the segment under the same scenarios. The aim of this extensive study of a simple yet fundamental version of the change-point problem is two-fold: understanding the impact of the location and the separation of the change points on detection and estimation and bringing insights about the estimation and detection of convex bodies in higher dimensions.
A fully nonlinear version of the Yamabe problem on locally conformally flat manifolds with umbilic boundary

Abstract We prove existence and compactness of solutions to a fully nonlinear Yamabe problem on locally conformally flat Riemannian manifolds with umbilic boundary.
Passive Array Imaging in Random Media

We present a novel algorithm for a high-resolution coherent imaging of sound sources in random scattering media using time-resolved measurements of the acoustic pressure at an array of receivers. The sound waves travel a long distance between the sources and receivers so that they are significantly affected by scattering in the random medium. We model the scattering effects by large random wavefront distortions, but the results extend to stronger effects, as long as the waves retain some coherence, i.e., before the onset of wave diffusion. It is known that scattering in random media can be mitigated in imaging using coherent interferometry (CINT). This method introduces a statistical stabilization in the image formation, at the cost of image blur. We show how to modify the CINT method in order to image wave sources that are too close to each other to be distinguished by CINT alone. We introduce the algorithm from first principles and demonstrate its performance with numerical simulations.
Efficient Calculation of Meta Distributions and the Performance of User Percentiles

Meta distributions (MDs) are refined performance metrics in wireless networks modeled using point processes. While there is no known method to directly calculate MDs, the moments of the underlying conditional distributions (given the point process) can often be expressed in exact analytical form. The problem of finding the MD given the moments has several solutions, but the standard approaches are inefficient and sensitive to the choices of a number of parameters. Here we propose and explore the use of a method based on binomial mixtures, which has several key advantages over other methods, since it is based on a simple linear transform of the moments.
Polar Transformer Networks

Convolutional neural networks (CNNs) are inherently equivariant to translation. Efforts to embed other forms of equivariance have concentrated solely on rotation. We expand the notion of equivariance in CNNs through the Polar Transformer Network (PTN). PTN combines ideas from the Spatial Transformer Network (STN) and canonical coordinate representations. The result is a network invariant to translation and equivariant to both rotation and scale. PTN is trained end-to-end and composed of three distinct stages: a polar origin predictor, the newly introduced polar transformer module and a classifier. PTN achieves state-of-the-art on rotated MNIST and the newly introduced SIM2MNIST dataset, an MNIST variation obtained by adding clutter and perturbing digits with translation, rotation and scaling. The ideas of PTN are extensible to 3D which we demonstrate through the Cylindrical Transformer Network.
Time-varying metasurfaces and Lorentz non-reciprocity

A cornerstone equation of optics – Snell's law – relates the angles of incidence and refraction for light passing through an interface between two media. It is built on two fundamental constraints: the conservation of tangential momentum and the conservation of energy. By relaxing the classical Snell’s law photon momentum conservation constrain when using space-gradient phase discontinuity, optical metasurfaces enabled an entirely new class of ultrathin optical devices. Here, we show that by eradicating the photon energy conservation constrain when introducing time-gradient phase discontinuity, we can further empower the area of flat photonics and obtain a new genus of optical devices. With this approach, classical Snell’s relations are developed into a more universal form not limited by Lorentz reciprocity, hence, meeting all the requirements for building magnetic-free optical isolators. Furthermore, photons experience inelastic interaction with time-gradient metasurfaces, which modifies photonic energy eigenstates and results in a Doppler-like wavelength shift. Consequently, metasurfaces with both space- and time-gradients can have a strong impact on a plethora of photonic applications and provide versatile control over the physical properties of light.
A Gaia DR2 Confirmation that 2MASS J12074836-3900043 is a Member of the TW HYA Association

We use new data from Gaia DR2 to confirm that the young L1 $\gamma$ candidate member of the TW Hya association (TWA) is now a bona fide member with a model-dependent mass estimate of ~15 $M_{Jup}$. The ambiguous M9 $\gamma$ candidate member 2MASS J12474428---3816464 also gets a higher Bayesian membership probability for TWA membership as a result of Gaia DR2 data and a new radial velocity measurement, but it remains unclear whether it is a true member of TWA or if it is an unrelated young interloper, because it is separated by 4.6 km/s from the locus of TWA members in UVW space.
Correcting the bias in least squares regression with volume-rescaled sampling

Consider linear regression where the examples are generated by an unknown distribution on R^d x R. Without any assumptions on the noise, the linear least squares solution for any i.i.d. sample will typically be biased w.r.t. the least squares optimum over the entire distribution. However, we show that if an i.i.d. sample of any size k is augmented by a certain small additional sample, then the solution of the combined sample becomes unbiased. We show this when the additional sample consists of d points drawn jointly according to the input distribution rescaled by the squared volume spanned by the points. Furthermore, we propose algorithms to sample from this volume-rescaled distribution when the data distribution is only known through an i.i.d sample.
C *-crossed products by partial actions and actions of inverse semigroups

The recently developed theory of partial actions of discrete groups on C *-algebras is extended. A related concept of actions of inverse semigroups on C *-algebras is defined, including covariant representations and crossed products. The main result is that every partial crossed product is a crossed product by a semigroup action.
In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning

• Being representable by NN is not enough as an inductive bias: In fact, any O T time computable function can be represented by O T size network (Sipser, 2006). Without any regularization, even with zero training error (and zero approximation error), increasing the number of hidden units reduces estimation error. a) Reducing #samples: Reducing the size of training set to 2000. b) Censoring Labels: Switching the labels to the predictions of a network with a small number H0 of hidden units that is trained on the entire dataset (training+validation+test). c) Label Noise: Adding 5 percent noise to the labels.
Correcting bursty and localized deletions using guess & check codes

We consider the problem of constructing binary codes for correcting deletions that are localized within a certain part of the codeword that is unknown a priori. The model that we study is when δ ≤ w deletions occur in a window of size at most w bits. These δ deletions are not necessarily consecutive, but are restricted to a window of size w. The localized deletions model is a generalization of the bursty model, where all the deleted bits are consecutive. In this work we propose new explicit codes, based on the family of Guess & Check codes [1,2], that can correct, with high probability, δ ≤ w deletions that are localized within a window of size at most w = O (log k), where k is the length of the information message. These codes have deterministic polynomial time encoding and decoding schemes. The redundancy of these codes is c log k + w + 1, where c is a constant representing a code parameter.
(Delta+1) Coloring in the Congested Clique Model

In this paper, we present improved algorithms for the (Delta+1) (vertex) coloring problem in the Congested Clique model of distributed computing. In this model, the input is a graph on n nodes, initially each node knows only its incident edges, and per round each two nodes can exchange O(log n) bits of information. Our key result is a randomized (Delta+1) vertex coloring algorithm that works in O(log log Delta * log^* Delta)-rounds. This is achieved by combining the recent breakthrough result of [Chang-Li-Pettie, STOC'18] in the {LOCAL} model and a degree reduction technique. We also get the following results with high probability: (1) (Delta+1)-coloring for Delta=O((n/log n)^{1-epsilon}) for any epsilon in (0,1), within O(log(1/epsilon)log^* Delta) rounds, and (2) (Delta+Delta^{1/2+o(1)})-coloring within O(log^* Delta) rounds. Turning to deterministic algorithms, we show a (Delta+1)-coloring algorithm that works in O(log Delta) rounds. Our new bounds provide exponential improvements over the state of the art.
Asymptotic Theory of Rerandomization in Treatment-Control Experiments

Although complete randomization ensures covariate balance on average, the chance of observing significant differences between treatment and control covariate distributions increases with many covariates. Rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion, generally resulting in better covariate balance and more precise estimates of causal effects. Previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes, Gaussian covariate and outcome distributions, or additive causal effects, but not for the general sampling distribution of the difference-in-means estimator for the average causal effect. We develop asymptotic theory for rerandomization without these assumptions, which reveals a non-Gaussian asymptotic distribution for this estimator, specifically a linear combination of a Gaussian random variable and truncated Gaussian random variables. This distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals. We demonstrate that, compared with complete randomization, rerandomization reduces the asymptotic quantile ranges of the difference-in-means estimator. Moreover, our work constructs accurate large-sample confidence intervals for the average causal effect.
Electron scattering on halo nuclei

The inelastic scattering of electrons on weakly-bound nuclei is studied with a simple model based on the long range behavior of the bound state wavefunction and on the effective-range expansion for the continuum wavefunctions. Three mechanisms have been considered: (a) dissociation of halo nuclei by high energy electrons, (b) dissociation by electrons present in a fixed target, and (c) Coulomb dissociation. It is shown that the properties of halo nuclei can be studied in electron-radioactive beam colliders using the electro-disintegration process. A comparison with fixed-target experiments is also performed.
Regular rings and perfect(oid) algebras

AbstractWe prove a p-adic analog of Kunz’s theorem: a p-adically complete noetherian ring is regular exactly when it admits a faithfully flat map to a perfectoid ring. This result is deduced from a...
Two extremal problems on intersecting families

Abstract In this short note, we address two problems in extremal set theory regarding intersecting families. The first problem is a question posed by Kupavskii: is it true that given two disjoint cross-intersecting families A , B ⊂ [ n ] k , they must satisfy min { | A | , | B | } ≤ 1 2 n − 1 k − 1 ? We give an affirmative answer for n ≥ 2 k 2 , and construct families showing that this range is essentially the best one could hope for, up to a constant factor. The second problem is a conjecture of Frankl. It states that for n ≥ 3 k , the maximum diversity of an intersecting family F ⊂ [ n ] k is equal to n − 3 k − 2 . We are able to find a construction beating the conjectured bound for n slightly larger than 3 k , which also disproves a conjecture of Kupavskii.
On the complexity of simple and optimal deterministic mechanisms for an additive buyer

We show that the Revenue-Optimal Deterministic Mechanism Design problem for a single additive buyer is #P-hard, even when the distributions have support size 2 for each item and, more importantly, even when the optimal solution is guaranteed to be of a very simple kind: the seller picks a price for each individual item and a price for the grand bundle of all the items; the buyer can purchase either the grand bundle at its given price or any subset of items at their total individual prices. The following problems are also #P-hard, as immediate corollaries of the proof: 1. determining if individual item pricing is optimal for a given instance, 2. determining if grand bundle pricing is optimal, and 3. computing the optimal (deterministic) revenue. On the positive side, we show that when the distributions are i.i.d. with support size 2, the optimal revenue obtainable by any mechanism, even a randomized one, can be achieved by a simple solution of the above kind (individual item pricing with a discounted price for the grand bundle) and furthermore, it can be computed in polynomial time. The problem can be solved in polynomial time too when the number of items is constant.
Graph-Based Ascent Algorithms for Function Maximization

We study the problem of finding the maximum of a function defined on the nodes of a connected graph. The goal is to identify a node where the function obtains its maximum. We focus on local iterative algorithms, which traverse the nodes of the graph along a path, and the next iterate is chosen from the neighbors of the current iterate with probability distribution determined by the function values at the current iterate and its neighbors. We study two algorithms corresponding to a Metropolis-Hastings random walk with different transition kernels: (i) The first algorithm is an exponentially weighted random walk governed by a parameter gamma. (ii) The second algorithm is defined with respect to the graph Laplacian and a smoothness parameter k. We derive convergence rates for the two algorithms in terms of total variation distance and hitting times. We also provide simulations showing the relative convergence rates of our algorithms in comparison to an unbiased random walk, as a function of the smoothness of the graph function. Our algorithms may be categorized as a new class of “descent-based” methods for function maximization on the nodes of a graph.
From Type Spaces to Probability Frames and Back, via Language.

We investigate the connection between the two major mathematical frameworks for modeling interactive beliefs: Harsanyi type spaces and possible-worlds style probability frames. While translating the former into the latter is straightforward, we demonstrate that the reverse translation relies implicitly on a background logical language. Once this "language parameter" is made explicit, it reveals a close relationship between universal type spaces and canonical models: namely, that they are essentially the same construct. As the nature of a canonical model depends heavily on the background logic used to generate it, this work suggests a new view into a corresponding landscape of universal type spaces.
Posted Pricing sans Discrimination.

In the quest for market mechanisms that are easy to implement, yet close to optimal, few seem as viable as posted pricing. Despite the growing body of impressive results, the performance of most posted price mechanisms however, rely crucially on price discrimination when multiple copies of a good are available. For the more general case with non-linear production costs on each good, hardly anything is known for general multi-good markets. With this in mind, we study a Bayesian setting where the seller can produce any number of copies of a good but faces convex production costs for the same, and buyers arrive sequentially. Our main contribution is a framework for non-discriminatory pricing in the presence of production costs: the framework yields posted price mechanisms with O(1)-approximation factors for fractionally subadditive (XoS) buyers, logarithmic approximations for subadditive buyers, and also extends to settings where the seller is oblivious to buyer valuations. Our work presents the first known results for Bayesian settings with production costs and is among the few posted price mechanisms that do not charge buyers differently for the same good.
TopicEq: A Joint Topic and Mathematical Equation Model for Scientific Texts

Scientific documents rely on both mathematics and text to communicate ideas. Inspired by the topical correspondence between mathematical equations and word contexts observed in scientific texts, we propose a novel topic model that jointly generates mathematical equations and their surrounding text (TopicEq). Using an extension of the correlated topic model, the context is generated from a mixture of latent topics, and the equation is generated by an RNN that depends on the latent topic activations. To experiment with this model, we create a corpus of 400K equation-context pairs extracted from a range of scientific articles from arXiv, and fit the model using a variational autoencoder approach. Experimental results show that this joint model significantly outperforms existing topic models and equation models for scientific texts. Moreover, we qualitatively show that the model effectively captures the relationship between topics and mathematics, enabling novel applications such as topic-aware equation generation, equation topic inference, and topic-aware alignment of mathematical symbols and words.
Duluth at SemEval--2016 Task 14 : Extending Gloss Overlaps to Enrich Semantic Taxonomies

This paper describes the Duluth systems that participated in Task 14 of SemEval 2016, Semantic Taxonomy Enrichment. There were three related systems in the formal evaluation which are discussed here, along with numerous post--evaluation runs. All of these systems identified synonyms between WordNet and other dictionaries by measuring the gloss overlaps between them. These systems perform better than the random baseline and one post--evaluation variation was within a respectable margin of the median result attained by all participating systems.
Logic Bug Detection and Localization Using Symbolic Quick Error Detection

We present Symbolic Quick Error Detection (Symbolic QED), a structured approach for logic bug detection and localization which can be used both during pre-silicon design verification as well as post-silicon validation and debug. This new methodology leverages prior work on Quick Error Detection (QED) which has been demonstrated to drastically reduce the latency, in terms of the number of clock cycles, of error detection following the activation of a logic (or electrical) bug. QED works through software transformations, including redundant execution and control flow checking, of the applied tests. Symbolic QED combines these error-detecting QED transformations with bounded model checking-based formal analysis to generate minimal-length bug activation traces that detect and localize any logic bugs in the design. We demonstrate the practicality and effectiveness of Symbolic QED using the OpenSPARC T2, a 500-million-transistor open-source multicore System-on-Chip (SoC) design, and using “difficult” logic bug scenarios observed in various state-of-the-art commercial multicore SoCs. Our results show that Symbolic QED: (i) is fully automatic, unlike manual techniques in use today that can be extremely time-consuming and expensive; (ii) requires only a few hours in contrast to manual approaches that might take days (or even months) or formal techniques that often take days or fail completely for large designs; and (iii) generates counter-examples (for activating and detecting logic bugs) that are up to 6 orders of magnitude shorter than those produced by traditional techniques. Significantly, this new approach does not require any additional hardware.
Global Analysis of Expectation Maximization for Mixtures of Two Gaussians

Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find stationary points of the likelihood objective, and these points may be far from any maximizer. This article addresses this disconnect between the statistical principles behind EM and its algorithmic properties. Specifically, it provides a global analysis of EM for specific models in which the observations comprise an i.i.d. sample from a mixture of two Gaussians. This is achieved by (i) studying the sequence of parameters from idealized execution of EM in the infinite sample limit, and fully characterizing the limit points of the sequence in terms of the initial parameters; and then (ii) based on this convergence analysis, establishing statistical consistency (or lack thereof) for the actual sequence of parameters produced by EM.
Approximation methods for analyzing multiscale stochastic vector-borne epidemic models.

Abstract Stochastic epidemic models, generally more realistic than deterministic counterparts, have often been seen too complex for rigorous mathematical analysis because of level of details it requires to comprehensively capture the dynamics of diseases. This problem further becomes intense when complexity of diseases increases as in the case of vector-borne diseases (VBD). The VBDs are human illnesses caused by pathogens transmitted among humans by intermediate species, which are primarily arthropods. In this study, a stochastic VBD model is developed and novel mathematical methods are described and evaluated to systematically analyze the model and understand its complex dynamics. The VBD model incorporates some relevant features of the VBD transmission process including demographical, ecological and social mechanisms, and different host and vector dynamic scales. The analysis is based on dimensional reductions and model simplifications via scaling limit theorems. The results suggest that the dynamics of the stochastic VBD depends on a threshold quantity R 0 , the initial size of infectives, and the type of scaling in terms of host population size. The quantity R 0 for deterministic counterpart of the model is interpreted as a threshold condition for infection persistence as is mentioned in the literature for many infectious disease models. Different scalings yield different approximations of the model, and in particular, if vectors have much faster dynamics, the effect of the vector dynamics on the host population averages out, which largely reduces the dimension of the model. Specific scenarios are also studied using simulations for some fixed sets of parameters to draw conclusions on dynamics.
Uniqueness of discrete solutions of nonmonotone PDEs without a globally fine mesh condition

Uniqueness of the finite element solution for nonmonotone quasilinear problems of elliptic type is established in one and two dimensions. In each case, we prove a comparison theorem based on locally bounding the variation of the discrete solution over each element. The uniqueness follows from this result, and does not require a globally small meshsize.
Hydrophobic Interactions and Dewetting between Plates with Hydrophobic and Hydrophilic Domains

We study by molecular dynamics simulations the wetting/dewetting transition and the dependence of the free energy on the distance between plates that contain both hydrophobic and hydrophilic particles. We show that dewetting is very sensitive to the distribution of hydrophobic and hydrophilic domains. In particular, we find that plates characterized by a large domain of hydrophobic sites induce a dewetting transition and an attractive solvent-induced interaction. On the other hand, a homogeneous distribution of the hydrophobic and hydrophilic particles on the plates prevents the dewetting transition and produces a repulsive solvent-induced interaction. We also present results for a system resembling a “Janus interface” in which one plate consists of hydrophobic particles and the other consists of hydrophilic particles showing that the interplate gap remains wet until steric constraints at small separations eject the water molecules. Our results indicate that the Cassie equation, for the contact angle of a heterogeneous plate, can not be used to predict the critical distance of dewetting. These results indicate that hydrophobic interactions between nanoscale surfaces with strong large lengthscale hydrophobicity can be highly cooperative and thus they argue against additivity of the hydrophobic interactions between different surface domains in these cases. These findings are pertinent to certain protein-protein interactions where additivity is commonly assumed.
Infrared Surveys for AGN

From the earliest extragalactic infrared studies AGN have shown themselves to be strong infrared sources, and IR surveys have revealed new populations of AGN. I briefly review current motivations for AGN surveys in the infrared and results from previous IR surveys. The Luminous Infrared Galaxies, which in some cases house dust-enshrouded AGN, submillimeter surveys, and recent studies of the cosmic x-ray and infrared backgrounds suggest that there is a population of highly-obscured AGN at high redshift. ISO Surveys have begun to resolve the infrared background and may have detected this obscured AGN population. New infrared surveys, particularly the SIRTF Wide-area Infrared Extragalactic Legacy Survey ( SWIRE ) will detect this population and provide a platform for understanding the evolution of AGN, Starbursts and passively evolving galaxies in the context of large-scale structure and environment.