cssi/SciSciGPT-SciSciNet huggingface dataset:
Differential Performance Debugging with Discriminant Regression Trees

Differential performance debugging is a technique to find performance problems. It applies in situations where the performance of a program is (unexpectedly) different for different classes of inputs. The task is to explain the differences in asymptotic performance among various input classes in terms of program internals. We propose a data-driven technique based on discriminant regression tree (DRT) learning problem where the goal is to discriminate among different classes of inputs. We propose a new algorithm for DRT learning that first clusters the data into functional clusters, capturing different asymptotic performance classes, and then invokes off-the-shelf decision tree learning algorithms to explain these clusters. We focus on linear functional clusters and adapt classical clustering algorithms (K-means and spectral) to produce them. For the K-means algorithm, we generalize the notion of the cluster centroid from a point to a linear function. We adapt spectral clustering by defining a novel kernel function to capture the notion of linear similarity between two data points. We evaluate our approach on benchmarks consisting of Java programs where we are interested in debugging performance. We show that our algorithm significantly outperforms other well-known regression tree learning algorithms in terms of running time and accuracy of classification.
Exponential deficiency of convolutions of densities

If a probability density p(x) (x 2 R k ) is bounded and R(t) := R e h x,tui p(x) dx < 1 for some linear functional u and all t 2 (0, 1), then, for each t 2 (0, 1) and all large enough n, the n-fold convolution of the t- tilted density ˜ pt(x) := e h x,tui p(x)/R(t) is bounded. This is a corollary of a general, "non-i.i.d." result, which is also shown to enjoy a certain optimality property. Such results are useful for saddle-point approximations. AMS 2000 subject classifications: Primary 60E05, 60E10; secondary 60F10, 62E20, 60E15. Keywords and phrases: probability density, saddle-point approximation, sums of independent random variables/vectors, convolution, exponential integrability, boundedness, tilting, exponential families.
Robust Recovery of Positive Stream of Pulses

The problem of estimating the delays and amplitudes of a positive stream of pulses appears in many applications, such as single-molecule microscopy. This paper suggests estimating the delays and amplitudes using a convex program, which is robust in the presence of noise (or model mismatch). Particularly, the recovery error is proportional to the noise level. We further show that the error grows exponentially with the density of the delays and also depends on the localization properties of the pulse.
mRSC: Multi-dimensional Robust Synthetic Control

When evaluating the impact of a policy (e.g., gun control) on a metric of interest (e.g., crime-rate), it may not be possible or feasible to conduct a randomized control trial. In such settings where only observational data is available, synthetic control (SC) methods \citeabadie1, abadie2, abadie3 provide a popular data-driven approach to estimate a "synthetic'' or "virtual'' control by combining measurements of "similar'' alternatives or units (called "donors'').Recently, robust synthetic control (RSC) \citersc1 was proposed as a generalization of SC to overcome the challenges of missing data and high levels of noise, while removing the reliance on expert domain knowledge for selecting donors. However, both SC and RSC (and its variants) suffer from poor estimation when the pre-intervention period is too short. As the main contribution of this work, we propose a generalization of unidimensional RSC to multi-dimensional Robust Synthetic Control, mRSC. Our proposed mechanism, mRSC, incorporates multiple types of measurements (or metrics) in addition to the measurement of interest for estimating a synthetic control, thus overcoming the challenge of poor inference due to limited amounts of pre-intervention data. We show that the mRSC algorithm, when using K relevant metrics, leads to a consistent estimator of the synthetic control for the target unit of interest under any metric. Our finite-sample analysis suggests that the mean-squared error (MSE) of our predictions decays to zero at a rate faster than the RSC algorithm by a factor of K and $\sqrtK $ for the training (pre-intervention) and testing (post-intervention) periods, respectively. Additionally, we propose a principled scheme to combine multiple metrics of interest via a diagnostic test that evaluates if adding a metric can be expected to result in improved inference.Our mechanism for validating mRSC performance is also an important and related contribution of this work: time series prediction. We propose a method to predict the future evolution of a time series based on limited data when the notion of time is relative and not absolute, i.e., where we have access to a donor pool that has already undergone the desired future evolution.We conduct extensive experimentation to establish the efficacy of mRSC in three different scenarios: predicting the evolution of a metric of interest using synthetically generated data from a known factor model, and forecasting weekly sales and score trajectories of a Walmart store and Cricket game, respectively.
Some p‐ranks related to a conic in PG(2, q)

Let A be the incidence matrix of lines and points of the classical projective plane PG(2, q) with q odd. With respect to a conic in PG(2, q), the matrix A is partitioned into 9 submatrices. The rank of each of these submatrices over Fq, the defining field of PG(2, q), is determined. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 224–236, 2010
Censors’ Delay in Blocking Circumvention Proxies

Censors of the Internet must continually discover and block new circumvention proxy servers. We seek to understand this process; specifically, the length of the delay between when a proxy first becomes discoverable and when it is actually blocked. We measure this delay in the case of obfuscated Tor bridges, by testing their reachability before and after their introduction into Tor Browser. We test from sites in the U.S., China, and Iran, over a period of five months. China's national firewall blocked new bridges after a varying delay of between 2 and 36 days. Blocking occurred only after end-user software releases, despite bridges being potentially discoverable earlier through other channels. While the firewall eventually discovered the bridges of Tor Browser, those that appeared only in Orbot, a version of Tor for mobile devices, remained unblocked. Our findings highlight the fact that censors can behave in ways that defy intuition, presenting difficulties for threat modeling but also opportunities for evasion.
The empirical likelihood prior applied to bias reduction of general estimating equations.

Abstract The practice of employing empirical likelihood (EL) components in place of parametric likelihood functions in the construction of Bayesian-type procedures has been well-addressed in the modern statistical literature. The EL prior, a Jeffreys-type prior, which asymptotically maximizes the Shannon mutual information between data and the parameters of interest, is rigorously derived. The focus of the proposed approach is on an integrated Kullback–Leibler distance between the EL-based posterior and prior density functions. The EL prior density is the density function for which the corresponding posterior form is asymptotically negligibly different from the EL. The proposed result can be used to develop a methodology for reducing the asymptotic bias of solutions of general estimating equations and M-estimation schemes by removing the first-order term. This technique is developed in a similar manner to methods employed to reduce the asymptotic bias of maximum likelihood estimates via penalizing the underlying parametric likelihoods by their Jeffreys invariant priors. A real data example related to a study of myocardial infarction illustrates the attractiveness of the proposed technique in practical aspects.
Approximate Message Passing for Amplitude Based Optimization

We consider an $\ell_2$-regularized non-convex optimization problem for recovering signals from their noisy phaseless observations. We design and study the performance of a message passing algorithm that aims to solve this optimization problem. We consider the asymptotic setting $m,n \rightarrow \infty$, $m/n \rightarrow \delta$ and obtain sharp performance bounds, where $m$ is the number of measurements and $n$ is the signal dimension. We show that for complex signals the algorithm can perform accurate recovery with only $m=\left ( \frac{64}{\pi^2}-4\right)n\approx 2.5n$ measurements. Also, we provide sharp analysis on the sensitivity of the algorithm to noise. We highlight the following facts about our message passing algorithm: (i) Adding $\ell_2$ regularization to the non-convex loss function can be beneficial even in the noiseless setting; (ii) spectral initialization has marginal impact on the performance of the algorithm.
Lower bounds in real Schubert calculus

We describe a large-scale computational experiment study- ing structure in the numbers of real solutions to osculating instances of Schubert problems. This investigation uncovered Schubert problems whose computed numbers of real solutions variously exhibit nontriv- ial upper bounds, lower bounds, gaps, and a congruence modulo four. We present a family of Schubert problems, one in each Grassmannian, and prove that their real osculating instances have the observed lower bounds and gaps.
The 2-Class Tower of $$\mathbb {Q}(\sqrt{-5460})$$

The seminal papers in the field of root-discriminant bounds are those of Odlyzko and Martinet. Both papers include the question of whether the field \(\mathbb {Q}(\sqrt{-5460})\) has finite or infinite 2-class tower. This is a critical case that will either substantially lower the best known upper bound for lim inf of root discriminants (if infinite) or else give a counter-example to what is often termed Martinet’s conjecture or question (if finite). Using extensive computation and introducing some new techniques, we give strong evidence that the tower is in fact finite, establishing other properties of its Galois group en route.
ProjE: embedding projection for knowledge graph completion

With the large volume of new information created every day, determining the validity of information in a knowledge graph and filling in its missing parts are crucial tasks for many researchers and practitioners. To address this challenge, a number of knowledge graph completion methods have been developed using low-dimensional graph embeddings. Although researchers continue to improve these models using an increasingly complex feature space, we show that simple changes in the architecture of the underlying model can outperform state-of-the-art models without the need for complex feature engineering. In this work, we present a shared variable neural network model called ProjE that fills-in missing information in a knowledge graph by learning joint embeddings of the knowledge graph's entities and edges, and through subtle, but important, changes to the standard loss function. In doing so, ProjE has a parameter size that is smaller than 11 out of 15 existing methods while performing 37% better than the current-best method on standard datasets. We also show, via a new fact checking task, that ProjE is capable of accurately determining the veracity of many declarative statements.
Birack Dynamical Cocycles and Homomorphism Invariants

Biracks are algebraic structures related to knots and links. We define a new enhancement of the birack counting invariant for oriented knots and links via algebraic structures called birack dynamical cocycles. The new invariants can also be understood in terms of partitions of the set of birack labelings of a link diagram determined by a homomorphism p : X → Y between finite labeling biracks. We provide examples to show that the new invariant is stronger than the unenhanced birack counting invariant and examine connections with other knot and link invariants.
Entropy and generic mean curvature flow in curved ambient spaces

In the article, we generalize some recent results of Colding and Minicozzi on generic singularities of mean curvature flow to curved ambient spaces. To do so, we make use of a weighted monotonicity formula to derive an "almost monotonicity" for the entropy upon embedding into $\R^\ell$. We are also lead to study the continuity of the entropy functional in certain cases.
Multispectral palmprint recognition using textural features

In order to utilize identification to the best extent, we need robust and fast algorithms and systems to process the data. Having palmprint as a reliable and unique characteristic of every person, we extract and use its features based on its geometry, lines and angles. There are countless ways to define measures for the recognition task. To analyze a new point of view, we extracted textural features and used them for palmprint recognition. Co-occurrence matrix can be used for textural feature extraction. As classifiers, we have used the minimum distance classifier (MDC) and the weighted majority voting system (WMV). The proposed method is tested on a well-known multispectral palmprint dataset of 6000 samples and an accuracy rate of 99.96–100% is obtained for most scenarios which outperforms all previous works in multispectral palmprint recognition.
Stable Determination of a Simple Metric, a Covector Field and a Potential from the Hyperbolic Dirichlet-to-Neumann Map

Let (ℳ, g) be a compact Riemmanian manifold with non-empty boundary. Consider the second order hyperbolic initial-boundary value problem where is a first-order perturbation of the Laplace operator ...
Complex Monge–Ampère equations and totally real submanifolds

Abstract We study the Dirichlet problem for complex Monge–Ampere equations in Hermitian manifolds with general (non-pseudoconvex) boundary. Our main result (Theorem 1.1) extends the classical theorem of Caffarelli, Kohn, Nirenberg and Spruck in C n . We also consider the equation on compact manifolds without boundary, attempting to generalize Yau's theorems in the Kahler case. As applications of the main result we study some connections between the homogeneous complex Monge–Ampere (HCMA) equation and totally real submanifolds, and a special Dirichlet problem for the HCMA equation related to Donaldson's conjecture on geodesics in the space of Kahler metrics.
Interleaved text/image deep mining on a large-scale radiology database for automated image interpretation

Despite tremendous progress in computer vision, there has not been an attempt to apply machine learning on very large-scale medical image databases. We present an interleaved text/image deep learning system to extract and mine the semantic interactions of radiology images and reports from a national research hospital's Picture Archiving and Communication System. With natural language processing, we mine a collection of ∼216K representative two-dimensional images selected by clinicians for diagnostic reference and match the images with their descriptions in an automated manner. We then employ a weakly supervised approach using all of our available data to build models for generating approximate interpretations of patient images. Finally, we demonstrate a more strictly supervised approach to detect the presence and absence of a number of frequent disease types, providing more specific interpretations of patient scans. A relatively small amount of data is used for this part, due to the challenge in gathering quality labels from large raw text data. Our work shows the feasibility of large-scale learning and prediction in electronic patient records available in most modern clinical institutions. It also demonstrates the trade-offs to consider in designing machine learning systems for analyzing large medical data.
Classification of solutions to Toda systems of types C and B with singular sources

In this paper, the classification in Lin et al. (Invent. Math. 190(1):169–207, 2012) of solutions to Toda systems of type A with singular sources is generalized to Toda systems of types C and B. Like in the A case, the solution space is shown to be parametrized by the abelian subgroup and a subgroup of the nilpotent subgroup in the Iwasawa decomposition of the corresponding complex simple Lie group. The method is by studying the Toda systems of types C and B as reductions of Toda systems of type A with symmetries. The theories of Toda systems as integrable systems as developed in Leznov (Teoret. Mat. Fiz. 42(3):343–349, 1980), Leznov and Saveliev (Group-theoretical methods for integration of nonlinear dynamical systems, Progress in Physics, vol. 15. Birkhauser, Verlag, 1992), Nie (J. Geom. Phys. 62(12):2424–2442, 2012), Nie (J. Nonlinear Math. Phys. 21(1):120–131, 2014), in particular the W-symmetries and the iterated integral solutions, play essential roles in this work, together with certain characterizing properties of minors of symplectic and orthogonal matrices.
Online Learning Schemes for Power Allocation in Energy Harvesting Communications

We consider the problem of power allocation over one or more time-varying channels with unknown distributions in energy harvesting communications. In the single-channel case, the transmitter chooses the transmit power based on the amount of stored energy in its battery with the goal of maximizing the average rate over time. We model this problem as a Markov decision process (MDP) with transmitter as the agent, battery status as the state, transmits power as the action and rate as the reward. The average reward maximization problem can be modeled by a linear program (LP) that uses the transition probabilities for the state-action pairs and their reward values to select a power allocation policy. This problem is challenging because the uncertainty in channels implies that the mean rewards associated with the state-action pairs are unknown. We therefore propose two online learning algorithms: linear program of sample means (LPSM) and Epoch-LPSM that learn these rewards and adapt their policies over time. For both algorithms, we prove that their regret is upper-bounded by a constant. To our knowledge this is the first result showing constant regret learning algorithms for MDPs with unknown mean rewards. We also prove an even stronger result about LPSM: that its policy matches the optimal policy exactly in finite expected time. Epoch-LPSM incurs a higher regret compared with the LPSM, while reducing the computational requirements substantially. We further consider a multi-channel scenario, where the agent also chooses a channel in each slot, and present our multi-channel LPSM (MC-LPSM) algorithm that explores different channels and uses that information to solve the LP during exploitation. MC-LPSM incurs a regret that scales logarithmically in time and linearly in the number of channels. Through a matching lower bound on the regret of any algorithm, we also prove the asymptotic order optimality of MC-LPSM.
Iterative Deep Learning Based Unbiased Stereology with Human-in-the-Loop

Lack of enough labeled data is a major problem in building machine learning based models when the manual annotation (labeling) is error-prone, expensive, tedious, and time-consuming. In this paper, we introduce an iterative deep learning based method to improve segmentation and counting of cells based on unbiased stereology applied to regions of interest of extended depth of field (EDF) images. This method uses an existing machine learning algorithm called the adaptive segmentation algorithm (ASA) to generate masks (verified by a user) for EDF images to train deep learning models. Then an iterative deep learning approach is used to feed newly predicted and accepted deep learning masks/images (verified by a user) to the training set of the deep learning model. The error rate in unbiased stereology count of cells on an unseen test set reduced from about 3 % to less than 1 % after 5 iterations of the iterative deep learning based unbiased stereology process.
On the inductive bias of dropout

Dropout is a simple but effective technique for learning in neural networks and other settings. A sound theoretical understanding of dropout is needed to determine when dropout should be applied and how to use it most effectively. In this paper we continue the exploration of dropout as a regularizer pioneered by Wager et al. We focus on linear classification where a convex proxy to the misclassification loss (i.e. the logistic loss used in logistic regression) is minimized. We show: • when the dropout-regularized criterion has a unique minimizer, • when the dropout-regularization penalty goes to infinity with the weights, and when it remains bounded, • that the dropout regularization can be non-monotonic as individual weights increase from 0, and • that the dropout regularization penalty may not be convex. This last point is particularly surprising because the combination of dropout regularization with any convex loss proxy is always a convex function. In order to contrast dropout regularization with L2 regularization, we formalize the notion of when different random sources of data are more compatible with different regularizers. We then exhibit distributions that are provably more compatible with dropout regularization than L2 regularization, and vice versa. These sources provide additional insight into how the inductive biases of dropout and L2 regularization differ. We provide some similar results for L1 regularization.
Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation

We give a goal-oriented a posteriori error estimator for the atomistic-continuum modeling error in the quasicontinuum method, and we use this estimator to design an adaptive algorithm to compute a quantity of interest to a given tolerance by using a nearly minimal number of atomistic degrees of freedom. We present computational results that demonstrate the effectiveness of our algorithm for a periodic array of dislocations described by a Frenkel-Kontorova type model.
Linking number and writhe in random linear embeddings of graphs

In order to model entanglements of polymers in a confined region, we consider the linking numbers and writhes of cycles in random linear embeddings of complete graphs in a cube. Our main results are that for a random linear embedding of $$K_n$$ in a cube, the mean sum of squared linking numbers and the mean sum of squared writhes are of the order of $$\theta (n(n!))$$ . We obtain a similar result for the mean sum of squared linking numbers in linear embeddings of graphs on n vertices, such that for any pair of vertices, the probability that they are connected by an edge is p. We also obtain experimental results about the distribution of linking numbers for random linear embeddings of these graphs. Finally, we estimate the probability of specific linking configurations occurring in random linear embeddings of the graphs $$K_6$$ and $$K_{3,3,1}$$ .
A generalization of Arc-Kayles

The game Arc-Kayles is played on an undirected graph with two players taking turns deleting an edge and its endpoints from the graph. We study a generalization of this game, Weighted Arc Kayles (WAK for short), played on graphs with counters on the vertices. The two players alternate choosing an edge and removing one counter on both endpoints. An edge can no longer be selected if any of its endpoints has no counter left. The last player to play a move wins. We give a winning strategy for WAK on trees of depth 2. Moreover, we show that the Grundy values of WAK and Arc-Kayles are unbounded. We also prove a periodicity result on the outcome of WAK when the number of counters is fixed for all the vertices but one. Finally, we show links between this game and a variation of the non-attacking queens game on a chessboard.
Scheduling Resource-Bounded Monitoring Devices for Event Detection and Isolation in Networks

In networked systems, monitoring devices such as sensors are typically deployed to monitor various target locations. Targets are the points in the physical space at which events of some interest, such as random faults or attacks, can occur. Most often, monitoring devices have limited energy supplies, and they can operate for a limited duration. As a result, energy-efficient monitoring of target locations through a set of monitoring devices with limited energy supplies is a crucial problem in networked systems. In this paper, we study optimal scheduling of monitoring devices to maximize network coverage for detecting and isolating events on targets for a given network lifetime. The monitoring devices considered could remain active only for a fraction of the overall network lifetime. We formulate the problem of scheduling of monitoring devices as a graph labeling problem, which unlike other existing solutions, allows us to directly utilize the underlying network structure to explore the trade-off between coverage and network lifetime. In this direction, first we present a greedy heuristic, and then a game-theoretic solution to the graph labeling problem. The proposed setup can be used to simultaneously solve the scheduling and placement of monitoring devices, which, as our simulations illustrate, gives improved performance as compared to separately solving the placement and scheduling problems. Finally, we illustrate our results on various networks, including real-world water distribution networks and random geometric networks.
Nonstandard Local Discontinuous Galerkin Methods for Fully Nonlinear Second Order Elliptic and Parabolic Equations in High Dimensions

This paper is concerned with developing accurate and efficient numerical methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in multiple spatial dimensions. It presents a general framework for constructing high order local discontinuous Galerkin (LDG) methods for approximating viscosity solutions of these fully nonlinear PDEs. The proposed LDG methods are natural extensions of a narrow-stencil finite difference framework recently proposed by the authors for approximating viscosity solutions. The idea of the methodology is to use multiple approximations of first and second order derivatives as a way to resolve the potential low regularity of the underlying viscosity solution. Consistency and generalized monotonicity properties are proposed that ensure the numerical operator approximates the differential operator. The resulting algebraic system has several linear equations coupled with only one nonlinear equation that is monotone in many of its arguments. The structure can be explored to design nonlinear solvers. This paper also presents and analyzes numerical results for several numerical test problems in two dimensions which are used to gauge the accuracy and efficiency of the proposed LDG methods.
On (conditional) positive semidefiniteness in a matrix-valued context

In a nutshell, we intend to extend Schoenberg's classical theorem connecting conditionally positive semidefinite functions $F\colon \mathbb{R}^n \to \mathbb{C}$, $n \in \mathbb{N}$, and their positive semidefinite exponentials $\exp(tF)$, $t > 0$, to the case of matrix-valued functions $F \colon \mathbb{R}^n \to \mathbb{C}^{m \times m}$, $m \in \mathbb{N}$. Moreover, we study the closely associated property that $\exp(t F(- i \nabla))$, $t>0$, is positivity preserving and its failure to extend directly in the matrix-valued context.
Correlating cell shape and cellular stress in motile confluent tissues

Collective cell migration is a highly regulated process involved in wound healing, cancer metastasis, and morphogenesis. Mechanical interactions among cells provide an important regulatory mechanism to coordinate such collective motion. Using a self-propelled Voronoi (SPV) model that links cell mechanics to cell shape and cell motility, we formulate a generalized mechanical inference method to obtain the spatiotemporal distribution of cellular stresses from measured traction forces in motile tissues and show that such traction-based stresses match those calculated from instantaneous cell shapes. We additionally use stress information to characterize the rheological properties of the tissue. We identify a motility-induced swim stress that adds to the interaction stress to determine the global contractility or extensibility of epithelia. We further show that the temporal correlation of the interaction shear stress determines an effective viscosity of the tissue that diverges at the liquid-solid transition, suggesting the possibility of extracting rheological information directly from traction data.
The Picard–Vessiot theory, constrained cohomology, and linear differential algebraic groups

Abstract We prove that a differential field K is algebraically closed and Picard–Vessiot closed if and only if the differential Galois cohomology group, H ∂ 1 ( K , G ) , is trivial for any linear differential algebraic group G over K. We give applications to the parameterized Picard–Vessiot theory and pose several problems.
A multimodular algorithm for computing Bernoulli numbers

We describe an algorithm for computing Bernoulli numbers. Using a parallel implementation, we have computed B k for k = 10 8 , a new record. Our method is to compute B k modulo p for many small primes p and then reconstruct B k via the Chinese Remainder Theorem. The asymptotic time complexity is O(k 2 log 2+e k), matching that of existing algorithms that exploit the relationship between B k and the Riemann zeta function. Our implementation is significantly faster than several existing implementations of the zeta-function method.
On the paradox of pesticides

Abstract The paradox of pesticides was observed experimentally, which says that pesticides may dramatically increase the population of a pest when the pest has a natural predator. Here we use a mathematical model to study the paradox. We find that the timing for the application of pesticides is crucial for the resurgence or non-resurgence of the pests. In particular, regularly applying pesticides is not a good idea as also observed in experiments [3,7]. In fact, the best time to apply pesticides is when the pest population is reasonably high.
Classes of Weierstrass points on genus 2 curves

We study the codimension n locus of curves of genus 2 with n distinct marked Weierstrass points inside the moduli space of genus 2, n-pointed curves, for n <= 6. We give a recursive description of the classes of the closure of these loci inside the moduli space of stable curves. For n<= 4, we express these classes using a generating function over stable graphs indexing the boundary strata of moduli spaces of pointed stable curves. Similarly, we express the closure of these classes inside the moduli space of curves of compact type for all n. This is a first step in the study of the structure of hyperelliptic classes in all genera.
A Weak Reverse Hölder Inequality for Caloric Measure

Following a result of Bennewitz–Lewis for non-doubling harmonic measure, we prove a criterion for non-doubling caloric measure to satisfy a weak reverse Holder inequality on an open set $$\Omega \subset \mathbb {R}^{n+1}$$, assuming as a background hypothesis only that the essential boundary of $$\Omega $$ satisfies an appropriate parabolic version of Ahlfors–David regularity (which entails some backwards in time thickness). We also show that the weak reverse Holder estimate is equivalent to solvability of the initial Dirichlet problem with “lateral” data in $$L^p$$, for some $$p<\infty $$, in this setting.
A Deterministic Projector Configuration Interaction Approach for the Ground State of Quantum Many-Body Systems

In this work we propose a novel approach to solve the Schrodinger equation which combines projection onto the ground state with a path-filtering truncation scheme. The resulting projector configuration interaction (PCI) approach realizes a deterministic version of the full configuration interaction quantum Monte Carlo (FCIQMC) method [Booth, G. H.; Thom, A. J. W.; Alavi, A. J. Chem. Phys. 2009, 131, 054106]. To improve upon the linearized imaginary-time propagator, we develop an optimal projector scheme based on an exponential Chebyshev expansion in the limit of an infinite imaginary time step. After writing the exact projector as a path integral in determinant space, we introduce a path filtering procedure that truncates the size of the determinantal basis and approximates the Hamiltonian. The path filtering procedure is controlled by one real threshold that determines the accuracy of the PCI energy and is not biased toward any determinant. Therefore, the PCI approach can equally well describe static and...
Effects of Beam Size and Pulse Duration on the Laser Drilling Process

A two-dimensional axisymmetric transient laser drilling model is used to analyze the effects of laser beam diameter and laser pulse duration on the laser drilling process. The model includes conduction and convection heat transfer, melting, solidification and vaporization, as well as material removal resulting from the vaporization and melt ejection. The validated model is applied to study the effects of laser beam size and pulse duration on the geometry of the drilled hole. It is found that the ablation effect decrease with the increasing beam diameter due to the effect of increased vaporization rate, and deeper hole is observed for the larger pulse width due to the higher thermal ablation efficiency.
Twisted logarithmic modules of lattice vertex algebras

Twisted modules over vertex algebras formalize the relations among twisted vertex operators and have applications to conformal field theory and representation theory. A recent generalization, called twisted logarithmic module, involves the logarithm of the formal variable and is related to logarithmic conformal field theory. We investigate twisted logarithmic modules of lattice vertex algebras, reducing their classification to the classification of modules over a certain group. This group is a semidirect product of a discrete Heisenberg group and a central extension of the additive group of the lattice.
Optimized household demand management with local solar PV generation

Demand Side Management (DSM) strategies are often associated with the objectives of smoothing the load curve and reducing peak load. Although the future of demand side management is technically dependent on remote and automatic control of residential loads, the end-users play a significant role by shifting the use of appliances to the off-peak hours when they are exposed to Day-ahead market price. This paper proposes an optimum solution to the problem of scheduling of household demand side management in the presence of PV generation under a set of technical constraints such as dynamic electricity pricing and voltage deviation. The proposed solution is implemented based on the Clonal Selection Algorithm (CSA). This solution is evaluated through a set of scenarios and simulation results show that the proposed approach results in the reduction of electricity bills and the import of energy from the grid.
Orthogonal Machine Learning: Power and Limitations

Double machine learning provides √n-consistent estimates of parameters of interest even when high-dimensional or nonparametric nuisance parameters are estimated at an n −1/4 rate. The key is to employ Neyman-orthogonal moment equations which are first-order insensitive to perturbations in the nuisance parameters. We show that the n −1/4 requirement can be improved to n −1/(2k+2) by employing a k -th order notion of orthogonality that grants robustness to more complex or higher-dimensional nuisance parameters. In the partially linear regression setting popular in causal inference, we show that we can construct second-order orthogonal moments if and only if the treatment residual is not normally distributed. Our proof relies on Stein’s lemma and may be of independent interest. We conclude by demonstrating the robustness benefits of an explicit doubly-orthogonal estimation procedure for treatment effect.
Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces

We present the first to date weighted and mixed-norm Sobolev estimates for fully nonlinear elliptic and parabolic equations in the whole space under a relaxed convexity condition with almost VMO dependence on space-time variables. The corresponding interior and boundary estimates are also obtained.
A new result on the complexity of heuristic estimates for the A★ algorithm☆

Abstract Relaxed models are abstract problem descriptions generated by ignoring constraints that are present in base-level problems. They play an important role in planning and search algorithms, as it has been shown that the length of an optimal solution to a relaxed model yields a monotone heuristic for an A★ search of a base-level problem. Optimal solutions to a relaxed model may be computed algorithmically or by search in a further relaxed model, leading to a search that explores a hierarchy of relaxed models. In this paper, we review the traditional definition of problem relaxation and show that searching in the abstraction hierarchy created by problem relaxation will not reduce the computational effort required to find optimal solutions to the base-level problem, unless the relaxed problem found in the hierarchy can be transformed by some optimization (e.g., subproblem factoring). Specifically, we prove that any A★ search of the base-level using a heuristic h2 will largely dominate an A★ search of the base-level using a heuristic h1, if h1 must be computed by an A★ search of the relaxed model usingh2.
Rational Cayley inner Herglotz–Agler functions: Positive-kernel decompositions and transfer-function realizations

Abstract The Bessmertnyĭ class consists of rational matrix-valued functions of d complex variables representable as the Schur complement of a block of a linear pencil A ( z ) = z 1 A 1 + ⋯ + z d A d whose coefficients A k are positive semidefinite matrices. We show that it coincides with the subclass of rational functions in the Herglotz–Agler class over the right poly-halfplane which are homogeneous of degree one and which are Cayley inner. The latter means that such a function is holomorphic on the right poly-halfplane and takes skew-Hermitian matrix values on ( i R ) d , or equivalently, is the double Cayley transform (over the variables and over the matrix values) of an inner function on the unit polydisk. Using Agler–Knese's characterization of rational inner Schur–Agler functions on the polydisk, extended now to the matrix-valued case, and applying appropriate Cayley transformations, we obtain characterizations of matrix-valued rational Cayley inner Herglotz–Agler functions both in the setting of the polydisk and of the right poly-halfplane, in terms of transfer-function realizations and in terms of positive-kernel decompositions. In particular, we extend Bessmertnyĭ's representation to rational Cayley inner Herglotz–Agler functions on the right poly-halfplane, where a linear pencil A ( z ) is now in the form A ( z ) = A 0 + z 1 A 1 + ⋯ + z d A d with A 0 skew-Hermitian and the other coefficients A k positive semidefinite matrices.
The Minimum Number of Edges in Uniform Hypergraphs with Property O

An oriented k-uniform hypergraph (a family of ordered k-sets) has the ordering property (or Property O) if, for every linear order of the vertex set, there is some edge oriented consistently with the linear order. We find bounds on the minimum number of edges in a hypergraph with Property O.
On line arrangements with applications to 3-nets

We show a one-to-one correspondence between arrangements of d lines in the projective plane, and lines in P^{d-2}. We apply this correspondence to classify (3,q)-nets over the complex numbers for all q<=6. When q=6, we have twelve possible combinatorial cases, but we prove that only nine of them are realizable. This new case shows several new properties for 3-nets: different dimensions for moduli, strict realization over certain fields, etc. We also construct a three dimensional family of (3,8)-nets corresponding to the Quaternion group.
Fusion of an Ensemble of Augmented Image Detectors for Robust Object Detection.

A significant challenge in object detection is accurate identification of an object’s position in image space, whereas one algorithm with one set of parameters is usually not enough, and the fusion of multiple algorithms and/or parameters can lead to more robust results. Herein, a new computational intelligence fusion approach based on the dynamic analysis of agreement among object detection outputs is proposed. Furthermore, we propose an online versus just in training image augmentation strategy. Experiments comparing the results both with and without fusion are presented. We demonstrate that the augmented and fused combination results are the best, with respect to higher accuracy rates and reduction of outlier influences. The approach is demonstrated in the context of cone, pedestrian and box detection for Advanced Driver Assistance Systems (ADAS) applications.
Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0

We prove an asymptotic formula for the number of SL3(Z)-equivalence classes of integral ternary cubic forms having bounded invariants. We use this result to show that the average size of the 3-Selmer group of all elliptic curves, when ordered by height, is equal to 4. This implies that the average rank of all elliptic curves, when ordered by height, is less than 1.17. Combining our counting techniques with a recent result of Dokchitser and Dokchitser, we prove that a positive proportion of all elliptic curves have rank 0. Assuming the niteness of the Tate{Shafarevich group, we also show that a positive proportion of elliptic curves have rank 1. Finally, combining our counting results with the recent work of Skinner and Urban, we show that a positive proportion of elliptic curves have analytic rank 0; i.e., a positive proportion of elliptic curves have nonvanishing L-function at s = 1. It follows that a positive proportion of all elliptic curves satisfy BSD.
New constructions of SD and MR codes over small finite fields

Data storage applications require erasure-correcting codes with prescribed sets of dependencies between data symbols and redundant symbols. The most common arrangement is to have k data symbols and h redundant symbols (that each depends on all data symbols) be partitioned into a number of disjoint groups, where for each group one allocates an additional (local) redundant symbol storing the parity of all symbols in the group. A code as above is maximally recoverable, if it corrects all erasure patterns that are information theoretically correctable given the dependency constraints. A slightly weaker guarantee is provided by SD codes. One key consideration in the design of MR and SD codes is the size of the finite field underlying the code as using small finite fields facilitates encoding and decoding operations. In this paper we present new explicit constructions of SD and MR codes over small finite fields.
Reactive solute transport in physically and chemically heterogeneous porous media with multimodal reactive mineral facies: The Lagrangian approach

Physical and chemical heterogeneities have a large impact on reactive transport in porous media. Examples of heterogeneous attributes affecting reactive mass transport are the hydraulic conductivity (K), and the equilibrium sorption distribution coefficient (Kd). This paper uses the Deng et al. (2013) conceptual model for multimodal reactive mineral facies and a Lagrangian-based stochastic theory in order to analyze the reactive solute dispersion in three-dimensional anisotropic heterogeneous porous media with hierarchical organization of reactive minerals. An example based on real field data is used to illustrate the time evolution trends of reactive solute dispersion. The results show that the correlation between the hydraulic conductivity and the equilibrium sorption distribution coefficient does have a significant effect on reactive solute dispersion. The anisotropy ratio does not have a significant effect on reactive solute dispersion. Furthermore, through a sensitivity analysis we investigate the impact of changing the mean, variance, and integral scale of K and Kd on reactive solute dispersion.
Estimating the trade elasticity over time

Abstract This paper estimates the trade elasticity in a continuous way. Following a trade cost shock, trade elasticity estimates are about 1 after one quarter, about 5 after one year, and about 7 after five years.
Failure-Scenario Maker for Rule-Based Agent using Multi-agent Adversarial Reinforcement Learning and its Application to Autonomous Driving.

We examine the problem of adversarial reinforcement learning for multi-agent domains including a rule-based agent. Rule-based algorithms are required in safety-critical applications for them to work properly in a wide range of situations. Hence, every effort is made to find failure scenarios during the development phase. However, as the software becomes complicated, finding failure cases becomes difficult. Especially in multi-agent domains, such as autonomous driving environments, it is much harder to find useful failure scenarios that help us improve the algorithm. We propose a method for efficiently finding failure scenarios; this method trains the adversarial agents using multi-agent reinforcement learning such that the tested rule-based agent fails. We demonstrate the effectiveness of our proposed method using a simple environment and autonomous driving simulator.
A Benchmark Dataset for Learning to Intervene in Online Hate Speech.

Countering online hate speech is a critical yet challenging task, but one which can be aided by the use of Natural Language Processing (NLP) techniques. Previous research has primarily focused on the development of NLP methods to automatically and effectively detect online hate speech while disregarding further action needed to calm and discourage individuals from using hate speech in the future. In addition, most existing hate speech datasets treat each post as an isolated instance, ignoring the conversational context. In this paper, we propose a novel task of generative hate speech intervention, where the goal is to automatically generate responses to intervene during online conversations that contain hate speech. As a part of this work, we introduce two fully-labeled large-scale hate speech intervention datasets collected from Gab and Reddit. These datasets provide conversation segments, hate speech labels, as well as intervention responses written by Mechanical Turk Workers. In this paper, we also analyze the datasets to understand the common intervention strategies and explore the performance of common automatic response generation methods on these new datasets to provide a benchmark for future research.