cssi/SciSciGPT-SciSciNet huggingface dataset:
Non-asymptotic Theory of Random Matrices: Extreme Singular Values

The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to information theory operate with random matrices in fixed dimensions. This survey addresses the non-asymptotic theory of extreme singular values of random matrices with independent entries. We focus on recently developed geometric methods for estimating the hard edge of random matrices (the smallest singular value).
Transitive PSL(2,11)-invariant k-arcs in PG(4,q)

A k-arc in the projective space $$\mathrm{PG}(n,q)$$ is a set of k projective points such that no subcollection of $$n+1$$ points is contained in a hyperplane. In this paper, we construct new 60-arcs and 110-arcs in $$\mathrm{PG}(4,q)$$ that do not arise from rational or elliptic curves. We introduce computational methods that, when given a set $$\mathcal {P}$$ of projective points in the projective space of dimension n over an algebraic number field $${\mathbb {Q}}(\xi )$$ , determines a complete list of primes p for which the reduction modulo p of $$\mathcal {P}$$ to the projective space $$\mathrm{PG}(n,p^h)$$ may fail to be a k-arc. Using these methods, we prove that there are infinitely many primes p such that $$\mathrm{PG}(4,p)$$ contains a $$\mathrm{PSL}(2,11)$$ -invariant 110-arc, where $$\mathrm{PSL}(2,11)$$ is given in one of its natural irreducible representations as a subgroup of $$\mathrm{PGL}(5,p)$$ . Similarly, we show that there exist $$\mathrm{PSL}(2,11)$$ -invariant 110-arcs in $$\mathrm{PG}(4,p^2)$$ and $$\mathrm{PSL}(2,11)$$ -invariant 60-arcs in $$\mathrm{PG}(4,p)$$ for infinitely many primes p.
Boundary estimates in elliptic homogenization

For a family of systems of linear elasticity with rapidly oscillating periodic coefficients, we establish sharp boundary estimates with either Dirichlet or Neumann conditions, uniform down to the microscopic scale, without smoothness assumptions on the coefficients. Under additional smoothness conditions, these estimates, combined with the corresponding local estimates, lead to the full Rellich-type estimates in Lipschitz domains and Lipschitz estimates in C1,α domains. The Cα , W1,p , and Lp estimates in C1 domains for systems with VMO coefficients are also studied. The approach is based on certain estimates on convergence rates. As a biproduct, we obtain sharp O(e) error estimates in Lq(Ω) for q = 2d∕(d − 1) and a Lipschitz domain Ω, with no smoothness assumption on the coefficients.
Bott-Taubes-Vassiliev cohomology classes by cut-and-paste topology

Bott and Taubes used integrals over configuration spaces to produce finite-type a.k.a. Vassiliev knot invariants. Cattaneo, Cotta-Ramusino and Longoni then used these methods together with graph co...
Signature functions of knots

The signature function of a knot is an integer-valued step function on the unit circle in the complex plane. Necessary and sufficient conditions for a function to be the signature function of a knot are presented.
Non-Uniform Wavelet Sampling for RF Analog-to-Information Conversion

Feature extraction, such as spectral occupancy, interferer energy and type, or direction-of-arrival, from wideband radio-frequency (RF) signals finds use in a growing number of applications as it enhances RF transceivers with cognitive abilities and enables parameter tuning of traditional RF chains. In power and cost limited applications, e.g., for sensor nodes in the Internet of Things, wideband RF feature extraction with conventional, Nyquist-rate analog-to-digital converters is infeasible. However, the structure of many RF features (such as signal sparsity) enables the use of compressive sensing (CS) techniques that acquire such signals at sub-Nyquist rates; while such CS-based analog-to-information (A2I) converters have the potential to enable low-cost and energy-efficient wideband RF sensing, they suffer from a variety of real-world limitations, such as noise folding, low sensitivity, aliasing, and limited flexibility. This paper proposes a novel CS-based A2I architecture called non-uniform wavelet sampling. Our solution extracts a carefully-selected subset of wavelet coefficients directly in the RF domain, which mitigates the main issues of existing A2I converter architectures. For multi-band RF signals, we propose a specialized variant called non-uniform wavelet bandpass sampling (NUWBS), which further improves sensitivity and reduces hardware complexity by leveraging the multi-band signal structure. We use simulations to demonstrate that NUWBS approaches the theoretical performance limits of $\ell_{1}$ -norm-based sparse signal recovery. We investigate hardware-design aspects and show ASIC measurement results for the wavelet generation stage, which highlight the efficacy of NUWBS for a broad range of RF feature extraction tasks in cost- and power-limited applications.
Johnson’s bijections and their application to counting simultaneous core partitions

Abstract Johnson recently proved Armstrong’s conjecture which states that the average size of an ( a , b ) -core partition is ( a + b + 1 ) ( a − 1 ) ( b − 1 ) ∕ 24 . He used various coordinate changes and one-to-one correspondences that are useful for counting problems about simultaneous core partitions. We give an expression for the number of ( b 1 , b 2 , … , b n ) -core partitions where { b 1 , b 2 , … , b n } contains at least one pair of relatively prime numbers. We also evaluate the largest size of a self-conjugate ( s , s + 1 , s + 2 ) -core partition.
Numerical approximation of fractional powers of elliptic operators

We present and study a novel numerical algorithm to approximate the action of $T^\beta:=L^{-\beta}$ where $L$ is a symmetric and positive definite unbounded operator on a Hilbert space $H_0$. The numerical method is based on a representation formula for $T^{-\beta}$ in terms of Bochner integrals involving $(I+t^2L)^{-1}$ for $t\in(0,\infty)$. To develop an approximation to $T^\beta$, we introduce a finite element approximation $L_h$ to $L$ and base our approximation to $T^\beta$ on $T_h^\beta:= L_h^{-\beta}$. The direct evaluation of $T_h^{\beta}$ is extremely expensive as it involves expansion in the basis of eigenfunctions for $L_h$. The above mentioned representation formula holds for $T_h^{-\beta}$ and we propose three quadrature approximations denoted generically by $Q_h^\beta$. The two results of this paper bound the errors in the $H_0$ inner product of $T^\beta-T_h^\beta\pi_h$ and $T_h^\beta-Q_h^\beta$ where $\pi_h$ is the $H_0$ orthogonal projection into the finite element space. We note that the evaluation of $Q_h^\beta$ involves application of $(I+(t_i)^2L_h)^{-1}$ with $t_i$ being either a quadrature point or its inverse. Efficient solution algorithms for these problems are available and the problems at different quadrature points can be straightforwardly solved in parallel. Numerical experiments illustrating the theoretical estimates are provided for both the quadrature error $T_h^\beta-Q_h^\beta$ and the finite element error $T^\beta-T_h^\beta\pi_h$.
Asymptotic analysis of objectives based on fisher information in active learning

Obtaining labels can be costly and time-consuming. Active learning allows a learning algorithm to intelligently query samples to be labeled for a more efficient learning. Fisher information ratio (FIR) has been used as an objective for selecting queries. However, little is known about the theory behind the use of FIR for active learning. There is a gap between the underlying theory and the motivation of its usage in practice. In this paper, we attempt to fill this gap and provide a rigorous framework for analyzing existing FIR-based active learning methods. In particular, we show that FIR can be asymptotically viewed as an upper bound of the expected variance of the log-likelihood ratio. Additionally, our analysis suggests a unifying framework that not only enables us to make theoretical comparisons among the existing querying methods based on FIR, but also allows us to give insight into the development of new active learning approaches based on this objective.
Some Applications of Weight Structures of Bondarko

We construct a functor from the triangulated category of Voevodsky motives to a certain derived category of mixed Hodge structures enriched with integral weight filtration. We use this construction to prove a strong integral version of the Deligne conjecture on 1-motives which was known previously only up to isogeny.
Regret of Queueing Bandits

We consider a variant of the multiarmed bandit problem where jobs queue for service, and service rates of different servers may be unknown. We study algorithms that minimize queue-regret: the (expected) difference between the queue-lengths obtained by the algorithm, and those obtained by a genie-aided matching algorithm that knows exact service rates. A naive view of this problem would suggest that queue-regret should grow logarithmically: since queue-regret cannot be larger than classical regret, results for the standard MAB problem give algorithms that ensure queue-regret increases no more than logarithmically in time. Our paper shows surprisingly more complex behavior. In particular, the naive intuition is correct as long as the bandit algorithm's queues have relatively long regenerative cycles: in this case queue-regret is similar to cumulative regret, and scales (essentially) logarithmically. However, we show that this "early stage" of the queueing bandit eventually gives way to a "late stage", where the optimal queue-regret scaling is O(1/t). We demonstrate an algorithm that (order-wise) achieves this asymptotic queue-regret, and also exhibits close to optimal switching time from the early stage to the late stage.
Enabling bio-plausible multi-level STDP using CMOS neurons with dendrites and bistable RRAMs

Large-scale integration of emerging nanoscale non-volatile memory devices, e.g. resistive random-access memory (RRAM), can enable a new generation of neuromorphic computers that can solve a wide range of machine learning problems. Such hybrid CMOS-RRAM neuromorphic architectures will result in several orders of magnitude reduction in energy consumption at a very small form factor, and herald autonomous learning machines capable of self-adapting to their environment. However, the progress in this area has been impeded from the realization that the actual memory devices fall well short of their expected behavior. In this work, we discuss the challenges associated with these memory devices and their use in neuromorphic computing circuits, and propose pathways to overcome these limitations by introducing ‘dendritic learning’.
Towards a Hands-Free Query Optimizer through Deep Learning.

Query optimization remains one of the most important and well-studied problems in database systems. However, traditional query optimizers are complex heuristically-driven systems, requiring large amounts of time to tune for a particular database and requiring even more time to develop and maintain in the first place. In this vision paper, we argue that a new type of query optimizer, based on deep reinforcement learning, can drastically improve on the state-of-the-art. We identify potential complications for future research that integrates deep learning with query optimization, and we describe three novel deep learning based approaches that can lead the way to end-to-end learning-based query optimizers.
Gov2Vec: Learning Distributed Representations of Institutions and Their Legal Text

We compare policy differences across institutions by embedding representations of the entire legal corpus of each institution and the vocabulary shared across all corpora into a continuous vector space. We apply our method, Gov2Vec, to Supreme Court opinions, Presidential actions, and official summaries of Congressional bills. The model discerns meaningful differences between government branches. We also learn representations for more fine-grained word sources: individual Presidents and (2-year) Congresses. The similarities between learned representations of Congresses over time and sitting Presidents are negatively correlated with the bill veto rate, and the temporal ordering of Presidents and Congresses was implicitly learned from only text. With the resulting vectors we answer questions such as: how does Obama and the 113th House differ in addressing climate change and how does this vary from environmental or economic perspectives? Our work illustrates vector-arithmetic-based investigations of complex relationships between word sources based on their texts. We are extending this to create a more comprehensive legal semantic map.
Visible Light Communication for Next Generation Untethered Virtual Reality Systems

Virtual and augmented reality (VR&#x002F;AR) systems are emerging technologies requiring data rates of multiple Gbps. Existing high quality VR headsets require connections through HDMI cables to a computer rendering rich graphic contents to meet the extremely high data transfer rate requirement. Such a cable connection limits the VR user&#x0027;s mobility and interferes with the VR experience. Current wireless technologies such as WiFi cannot support the multi-Gbps graphics data transfer. Instead, we propose to use visible light communication (VLC) for establishing high speed wireless links between a rendering computer and a VR headset. But, VLC transceivers are highly directional with narrow beams and require constant maintenance of line-of-sight (LOS) alignment between the transmitter and the receiver. Thus, we present a novel multi-detector hemispherical VR headset design to tackle the beam misalignment problem caused by the VR user&#x0027;s random head orientation. We provide detailed analysis on how the number of detectors on the headset can be minimized while maintaining the required beam alignment and providing high quality VR experience.
Stochastic generative hashing

Learning-based binary hashing has become a powerful paradigm for fast search and retrieval in massive databases. However, due to the requirement of discrete outputs for the hash functions, learning such functions is known to be very challenging. In addition, the objective functions adopted by existing hashing techniques are mostly chosen heuristically. In this paper, we propose a novel generative approach to learn hash functions through Minimum Description Length principle such that the learned hash codes maximally compress the dataset and can also be used to regenerate the inputs. We also develop an efficient learning algorithm based on the stochastic distributional gradient, which avoids the notorious difficulty caused by binary output constraints, to jointly optimize the parameters of the hash function and the associated generative model. Extensive experiments on a variety of large-scale datasets show that the proposed method achieves better retrieval results than the existing state-of-the-art methods.
Population empirical Bayes

Bayesian predictive inference analyzes a dataset to make predictions about new observations. When a model does not match the data, predictive accuracy suffers. We develop population empirical Bayes (POP-EB), a hierarchical framework that explicitly models the empirical population distribution as part of Bayesian analysis. We introduce a new concept, the latent dataset, as a hierarchical variable and set the empirical population as its prior. This leads to a new predictive density that mitigates model mismatch. We efficiently apply this method to complex models by proposing a stochastic variational inference algorithm, called bumping variational inference (BUMP-VI). We demonstrate improved predictive accuracy over classical Bayesian inference in three models: a linear regression model of health data, a Bayesian mixture model of natural images, and a latent Dirichlet allocation topic model of scientific documents.
On the maximal graded shifts of ideals and modules

Abstract We generalize a result of Eisenbud, Huneke and Ulrich on the maximal graded shifts of a module with prescribed annihilator and prove a linear regularity bound for ideals in a polynomial ring depending only on the first p − c steps in the resolution, where p = pd ( S / I ) and c = codim ( I ) .
Coherent sheaves on formal complete intersections via DG Lie algebras

We establish a criterion for sheaves on an adically complete DG scheme to be coherent. We deduce a description of coherent sheaves on an adically complete lci singularity in terms of modules for a DG Lie algebra.
Modeling of radiation-induced defect recovery in 3C-SiC under high field bias conditions

Abstract In this work, the implications of high field bias conditions in radiation-induced defect recovery in 3C-SiC crystals is studied. It is well known that transient heating effects (or thermal spikes) occur when energetic swift heavy ions (SHIs) deposit energy to the surrounding medium via ionization. Here, we explore the dynamics of this transient event under high background electric fields in 3C-SiC, which is what occurs when an ion strike coincides with field-sensitive volumes. In this study, we use the Ensemble Monte Carlo method to quantify how the energy deposition of the ionized regions change in response to high background electric fields. Subsequently, we study the relationship between the radiation-induced thermal spike and defect recovery using molecular dynamics simulations. We find that field strengths below the critical breakdown of wide bandgap devices are sufficient to exacerbate the localized heating, which subsequently enhances the defect recovery effect. This work is beneficial for 3C-SiC electronics and materials used in high radiation environments.
On the Direction of Discrimination: An Information-Theoretic Analysis of Disparate Impact in Machine Learning

In the context of machine learning, disparate impact refers to a form of systematic discrimination whereby the output distribution of a model depends on the value of a sensitive attribute (e.g., race or gender). In this paper, we propose an information-theoretic framework to analyze the disparate impact of a binary classification model. We view the model as a fixed channel, and quantify disparate impact as the divergence in output distributions over two groups. Our aim is to find a correction function that can perturb the input distributions of each group to align their output distributions. We present an optimization problem that can be solved to obtain a correction function that will make the output distributions statistically indistinguishable. We derive closed-form expressions to efficiently compute the correction function, and demonstrate the benefits of our framework on a recidivism prediction problem based on the ProPublica COMPAS dataset.
Epidemic thresholds with external agents

We study the effect of external infection sources on phase transitions in epidemic processes. In particular, we consider an epidemic spreading on a network via the SIS/SIR dynamics, which in addition is aided by external agents sources unconstrained by the graph, but possessing a limited infection rate or virulence. Such a model captures many existing models of externally aided epidemics, and finds use in many settings epidemiology, marketing and advertising, network robustness, etc. We provide a detailed characterization of the impact of external agents on epidemic thresholds. In particular, for the SIS model, we show that any external infection strategy with constant virulence either fails to significantly affect the lifetime of an epidemic, or at best, sustains the epidemic for a lifetime which is polynomial in the number of nodes. On the other hand, a random external-infection strategy, with rate increasing linearly in the number of infected nodes, succeeds under some conditions to sustain an exponential epidemic lifetime. We obtain similar sharp thresholds for the SIR model, and discuss the relevance of our results in a variety of settings.
Eigenforms and Quantum Physics

Our essay begins with explication of the notion of eigenform as pioneered by Heinz von Foerster in his papers (Foerster, 1981, pp. 258–271, pp. 274–285, pp. 288–309) and explored in papers of the author (Kauffman, 2003, pp. 73–90, 2005, pp. 129–150; 2009, pp. 121–137, 2010, pp. 48–89). In Foerster (1981, pp. 274–285) the familiar objects of our existence can be seen as tokens for the behaviors of the organism, creating apparently stable forms. Such an attitude toward objects makes it impossible to discriminate between the object as an element of a world and the object as a token or symbol that is simultaneously a process. The notion of an eigenform is inextricably linked with second-order cybernetics. One starts on the road to such a concept as soon as one begins to consider a pattern of patterns, the form of form or the cybernetics of cybernetics. Such concepts appear to loop around upon themselves, and at the same time they lead outward to new points of view. Such circularities suggest a possibility of transcending the boundaries of a system from within. When a circular concept is called into being, the boundaries turn inside out. An object, in itself, is a symbolic entity, participating in a network of interactions, taking on its apparent solidity and stability from these interactions. We ourselves are such objects, we as human beings are signs for ourselves, a concept originally due to the American philosopher C. S. Peirce (Kauffman, 2001, pp. 79–110). Eigenforms are mathematical companions to Peirce’s work. In an observing system, what is observed is not distinct from the system itself, nor can one make a separation between the observer and the observed. The observer and
Identifiability of Phylogenetic Parameters from k-mer Data Under the Coalescent.

Distances between sequences based on their k-mer frequency counts can be used to reconstruct phylogenies without first computing a sequence alignment. Past work has shown that effective use of k-mer methods depends on (1) model-based corrections to distances based on k-mers and (2) breaking long sequences into blocks to obtain repeated trials from the sequence-generating process. Good performance of such methods is based on having many high-quality blocks with many homologous sites, which can be problematic to guarantee a priori. Nature provides natural blocks of sequences into homologous regions—namely, the genes. However, directly using past work in this setting is problematic because of possible discordance between different gene trees and the underlying species tree. Using the multispecies coalescent model as a basis, we derive model-based moment formulas that involve the species divergence times and the coalescent parameters. From this setting, we prove identifiability results for the tree and branch length parameters under the Jukes–Cantor model of sequence mutations.
On 2d Incompressible Euler Equations with Partial Damping

We consider various questions about the 2d incompressible Navier–Stokes and Euler equations on a torus when dissipation is removed from or added to some of the Fourier modes.
Structured Variational Learning of Bayesian Neural Networks with Horseshoe Priors

Bayesian Neural Networks (BNNs) have recently received increasing attention for their ability to provide well-calibrated posterior uncertainties. However, model selection---even choosing the number of nodes---remains an open question. Recent work has proposed the use of a horseshoe prior over node pre-activations of a Bayesian neural network, which effectively turns off nodes that do not help explain the data. In this work, we propose several modeling and inference advances that consistently improve the compactness of the model learned while maintaining predictive performance, especially in smaller-sample settings including reinforcement learning.
Sparse estimation of multivariate Poisson log‐normal models from count data

Modeling data with multivariate count responses is a challenging problem due to the discrete nature of the responses. Existing methods for univariate count responses cannot be easily extended to the multivariate case since the dependency among multiple responses needs to be properly accommodated. In this paper, we propose a multivariate Poisson log-normal regression model for multivariate data with count responses. By simultaneously estimating the regression coefficients and inverse covariance matrix over the latent variables with an efficient Monte Carlo EM algorithm, the proposed regression model takes advantages of association among multiple count responses to improve the model prediction performance. Simulation studies and applications to real world data are conducted to systematically evaluate the performance of the proposed method in comparison with conventional methods.
“FabSearch”: A 3D CAD Model-Based Search Engine for Sourcing Manufacturing Services

In this paper, we present "FabSearch", a prototype search engine for sourcing manufacturer service providers, by making use of the product manufacturing information contained within a 3D digital file of a product. FabSearch is designed to take in a query 3D model, such as the .STEP file of a part model which then produces a ranked list of job shop service providers who are best suited to fabricate the part. Service providers may have potentially built hundreds to thousands of parts with associated part 3D models over time. FabSearch assumes that these service providers have shared shape signatures of the part models built previously to enable the algorithm to most effectively rank the service providers who have the most experience to build the query part model. FabSearch has two important features that helps it produce relevant results. First, it makes use of the shape characteristics of the 3D part by calculating the Spherical Harmonics signature of the part to calculate the most similar shapes built previously be job shop service providers. Second, FabSearch utilizes meta-data about each part, such as material specification, tolerance requirements to help improve the search results based on the specific query model requirements. The algorithm is tested against a repository containing more than 2000 models distributed across various job shop service providers. For the first time, we show the potential for utilizing the rich information contained within a 3D part model to automate the sourcing and eventual selection of manufacturing service providers.
Fourier transforms and $p$-adic ‘Weil II’

We give a purity theorem in the manner of Deligne's ‘Weil II’ theorem for rigid cohomology with coefficients in an overconvergent $F$ -isocrystal; the proof mostly follows Laumon's Fourier-theoretic approach, transposed into the setting of arithmetic $\mathcal{D}$ -modules. This yields in particular a complete, purely $p$ -adic proof of the Weil conjectures when combined with recent results on $p$ -adic differential equations by Andre, Christol, Crew, Kedlaya, Matsuda, Mebkhout and Tsuzuki.
Concatenated Coding for the AWGN Channel With Noisy Feedback

The use of open-loop coding can be easily extended to a closed-loop concatenated code if the transmitter has access to feedback. This can be done by introducing a feedback transmission scheme as an inner code. In this paper, this process is investigated for the case when a linear feedback scheme is implemented as an inner code and, in particular, over an additive white Gaussian noise (AWGN) channel with noisy feedback. To begin, we look to derive an optimal linear feedback scheme by optimizing over the received signal-to-noise ratio (SNR). From this optimization, a linear feedback scheme is produced that is asymptotically optimal in the sense of blocklength-normalized SNR; it is then compared to other well-known schemes. Then, the linear feedback scheme is implemented as an inner code to a concatenated code over the AWGN channel with noisy feedback. This code shows improvements not only in error exponent bounds, but also in bit error rate (BER) and frame error rate (FER). It is also shown that if the concatenated code has total blocklength L and the inner code has blocklength, N, the inner code blocklength should scale as N = O(C/R), where C is the capacity of the channel and R is the rate of the concatenated code. Simulations with low-density parity-check (LDPC) and turbo codes are provided to display practical applications and their error rate benefits.
Convolutional Pose Machines

Pose Machines provide a sequential prediction framework for learning rich implicit spatial models. In this work we show a systematic design for how convolutional networks can be incorporated into the pose machine framework for learning image features and image-dependent spatial models for the task of pose estimation. The contribution of this paper is to implicitly model long-range dependencies between variables in structured prediction tasks such as articulated pose estimation. We achieve this by designing a sequential architecture composed of convolutional networks that directly operate on belief maps from previous stages, producing increasingly refined estimates for part locations, without the need for explicit graphical model-style inference. Our approach addresses the characteristic difficulty of vanishing gradients during training by providing a natural learning objective function that enforces intermediate supervision, thereby replenishing back-propagated gradients and conditioning the learning procedure. We demonstrate state-of-the-art performance and outperform competing methods on standard benchmarks including the MPII, LSP, and FLIC datasets.
Selective and Rapid Cell-Permeable Inhibitor of Human Caspase-3

Individual roles and overlapping functionalities of 12 human caspases during apoptosis and other cellular processes remain poorly resolved primarily due to a lack of chemical tools. Here we present a new selective caspase-3 inhibitor, termed Ac-ATS010-KE, with rapid and irreversible binding kinetics. Relative to previously designed caspase-3-selective molecules that have tremendously abated inhibitory rates and thus limited use in biological settings, the improved kinetics of Ac-ATS010-KE permits its use in a cell-based capacity. We demonstrate that Ac-ATS010-KE prevents apoptosis with comparable efficacy to the general caspase inhibitor Ac-DEVD-KE and surprisingly does so without side-chain methylation. This observation is in contrast to the well-established peptide modification strategy typically employed for improving cellular permeability. Ac-ATS010-KE protects against extrinsic apoptosis, which demonstrates the utility of a thiophene carboxylate leaving group in biological settings, challenges the requisite neutralization of free carboxylic acids to improve cell permeability, and provides a tool-like compound to interrogate the role of caspase-3 in a variety of cellular processes.
Zeta functions and asymptotic additive bases with some unusual sets of primes

Fix \(\delta \in (0,1]\), \(\sigma _0\in [0,1)\) and a real-valued function \(\varepsilon (x)\) for which \(\varlimsup _{x\rightarrow \infty }\varepsilon (x)\leqslant 0\). For every set of primes \(\mathcal {P}\) whose counting function \(\pi _\mathcal {P}(x)\) satisfies an estimate of the form $$\begin{aligned} \pi _\mathcal {P}(x)=\delta \,\pi (x)+O\bigl (x^{\sigma _0+\varepsilon (x)}\bigr ), \end{aligned}$$ we define a zeta function \(\zeta _\mathcal {P}(s)\) that is closely related to the Riemann zeta function \(\zeta (s)\). For \(\sigma _0\leqslant \frac{1}{2}\), we show that the Riemann hypothesis is equivalent to the non-vanishing of \(\zeta _\mathcal {P}(s)\) in the region \(\{\sigma >\frac{1}{2}\}\).
III-V gate-all-around nanowire MOSFET process technology: From 3D to 4D

In this paper, we have experimentally demonstrated, for the first time, III-V 4D transistors with vertically stacked InGaAs nanowire (NW) channels and gate-all-around (GAA) architecture. Novel process technology enabling the transition from 3D to 4D structure has been developed and summarized. The successful fabrication of InGaAs lateral and vertical NW arrays has led to 4× increase in MOSFET drive current. The top-down technology developed in this paper has opened a viable pathway towards future low-power logic and RF transistors with high-density III-V NWs.
FDR-Corrected Sparse Canonical Correlation Analysis With Applications to Imaging Genomics

Reducing the number of false discoveries is presently one of the most pressing issues in the life sciences. It is of especially great importance for many applications in neuroimaging and genomics, where data sets are typically high-dimensional, which means that the number of explanatory variables exceeds the sample size. The false discovery rate (FDR) is a criterion that can be employed to address that issue. Thus it has gained great popularity as a tool for testing multiple hypotheses. Canonical correlation analysis (CCA) is a statistical technique that is used to make sense of the cross-correlation of two sets of measurements collected on the same set of samples (e.g., brain imaging and genomic data for the same mental illness patients), and sparse CCA extends the classical method to high-dimensional settings. Here, we propose a way of applying the FDR concept to sparse CCA, and a method to control the FDR. The proposed FDR correction directly influences the sparsity of the solution, adapting it to the unknown true sparsity level. Theoretical derivation as well as simulation studies show that our procedure indeed keeps the FDR of the canonical vectors below a user-specified target level. We apply the proposed method to an imaging genomics data set from the Philadelphia Neurodevelopmental Cohort. Our results link the brain connectivity profiles derived from brain activity during an emotion identification task, as measured by functional magnetic resonance imaging, to the corresponding subjects’ genomic data.
Machine Learning Applied to the Reionization History of the Universe in the 21 cm Signal

The Epoch of Reionization (EoR) features a rich interplay between the first luminous sources and the low-density gas of the intergalactic medium (IGM), where photons from these sources ionize the IGM. There are currently few observational constraints on key observables related to the EoR, such as the midpoint and duration of reionization. Although upcoming observations of the 21 cm power spectrum with next-generation radio interferometers such as the Hydrogen Epoch of Reionization Array (HERA) and the Square Kilometre Array (SKA) are expected to provide information about the midpoint of reionization readily, extracting the duration from the power spectrum alone is a more difficult proposition. As an alternative method for extracting information about reionization, we present an application of convolutional neural networks (CNNs) to images of reionization. These images are two-dimensional in the plane of the sky, and extracted at a series of redshift values to generate "image cubes" that are qualitatively similar to those of the HERA and the SKA will generate in the near future. Additionally, we include the impact that the bright foreground signal from the the Milky Way imparts on such image cubes from interferometers, but do not include the noise induced from observations. We show that we are able to recover the duration of reionization $\Delta$z to within 5% using CNNs, assuming that the midpoint of reionization is already relatively well constrained. These results have exciting impacts for estimating $\tau$, the optical depth to the cosmic microwave background, which can help constrain other cosmological parameters.
Oriented Point Sampling for Plane Detection in Unorganized Point Clouds

Plane detection in 3D point clouds is a crucial pre-processing step for applications such as point cloud segmentation, semantic mapping and SLAM. In contrast to many recent plane detection methods that are only applicable on organized point clouds, our work is targeted to unorganized point clouds that do not permit a 2D parametrization. We compare three methods for detecting planes in point clouds efficiently. One is a novel method proposed in this paper that generates plane hypotheses by sampling from a set of points with estimated normals. We named this method Oriented Point Sampling (OPS) to contrast with more conventional techniques that require the sampling of three unoriented points to generate plane hypotheses. We also implemented an efficient plane detection method based on local sampling of three unoriented points and compared it with OPS and the 3D-KHT algorithm, which is based on octrees, on the detection of planes on 10,000 point clouds from the SUN RGB-D dataset.
Heterogeneous impacts of China's economic and development zone program

This paper examines the impact of economic and development zones (EDZs) on the productivity of incumbent firms in China. To deal with the selection issue, I first take into account potentially different selection mechanisms across two popular types of EDZs—economic and technological development zones (ETDZs) and high‐tech development zones (HTDZs)—by relying on multiple treatment propensity scores matching techniques. Next, I apply the difference‐in‐differences estimator to the matched sample and conduct an event study analysis. The results show that the respective effects of ETDZs and HTDZs on firm productivity are positive, but subject to a nonlinear trend over time. The size of the productivity gains depends critically on the type of EDZ, however. A new HTDZ (ETDZ) leads to an average productivity gain of up to 30.2% (18.4%) for incumbent firms in the 5 years after the zone was created. These findings suggest that the size of productivity spillovers for spatially targeted firms differ quite significantly depending on the strategic development and policy goals of the EDZ: HTDZs that focus on promoting indigenous‐based factors of learning lead to higher productivity spillovers compared with ETDZs that focus on promoting extra‐local linkages.
Seismic imaging and optimal transport

Seismology has been an active science for a long time. It changed character about 50 years ago when the earth's vibrations could be measured on the surface more accurately and more frequently in space and time. The full wave field could be determined, and partial differential equations (PDE) started to be used in the inverse process of finding properties of the interior of the earth. We will briefly review earlier techniques but mainly focus on Full Waveform Inversion (FWI) for the acoustic formulation. FWI is a PDE constrained optimization in which the variable velocity in a forward wave equation is adjusted such that the solution matches measured data on the surface. The minimization of the mismatch is usually coupled with the adjoint state method, which also includes the solution to an adjoint wave equation. The least-squares norm is the conventional objective function measuring the difference between simulated and measured data, but it often results in the minimization trapped in local minima. One way to mitigate this is by selecting another misfit function with better convexity properties. Here we propose using the quadratic Wasserstein metric as a new misfit function in FWI. The optimal map defining the quadratic Wasserstein metric can be computed by solving a Monge-Ampere equation. Theorems pointing to the advantages of using optimal transport over the least-squares norm will be discussed, and a number of large-scale computational examples will be presented.
Parallel genomic architecture underlies repeated sexual signal divergence in Hawaiian Laupala crickets

When the same phenotype evolves repeatedly, we can explore the predictability of genetic changes underlying phenotypic evolution. Theory suggests that genetic parallelism is less likely when phenot...
Conditional Stable Soliton Resolution for a Semi-linear Skyrme Equation

We study a semi-linear version of the Skyrme system due to Adkins and Nappi. The objects in this system are maps from $$(1+3)$$-dimensional Minkowski space into the 3-sphere and 1-forms on $$\mathbb {R}^{1+3}$$, coupled via a Lagrangian action. Under a co-rotational symmetry reduction we establish the existence, uniqueness, and unconditional asymptotic stability of a family of stationary solutions $$Q_n$$, indexed by the topological degree $$n \in \mathbb {N}\cup \{0\}$$ of the underlying map. We also prove that an arbitrarily large equivariant perturbation of $$Q_n$$ leads to a globally defined solution that scatters to $$Q_n$$ in infinite time as long as the critical norm for the solution remains bounded on the maximal interval of existence given by the local Cauchy theory. We remark that the evolution equations are super-critical with respect to the conserved energy.
Tornado Damage Ratings Estimated with Cumulative Logistic Regression

AbstractEmpirical studies have led to improvements in evaluating and quantifying the tornado threat. However, more work is needed to put the research onto a solid statistical foundation. Here the a...
EntropyDB: a probabilistic approach to approximate query processing

We present, an interactive data exploration system that uses a probabilistic approach to generate a small, query-able summary of a dataset. Departing from traditional summarization techniques, we use the Principle of Maximum Entropy to generate a probabilistic representation of the data that can be used to give approximate query answers. We develop the theoretical framework and formulation of our probabilistic representation and show how to use it to answer queries. We then present solving techniques, give two critical optimizations to improve preprocessing time and query execution time, and explore methods to reduce query error. Lastly, we experimentally evaluate our work using a 5 GB dataset of flights within the USA and a 210 GB dataset from an astronomy particle simulation. While our current work only supports linear queries, we show that our technique can successfully answer queries faster than sampling while introducing, on average, no more error than sampling and can better distinguish between rare and nonexistent values. We also discuss extensions that can allow for data updates and linear queries over joins.
The Impact of Probabilistic Classifiers on Appointment Scheduling with No-Shows

Appointment no-shows are common in outpatient clinics and increase clinic costs and patients’ dissatisfaction. We develop a framework to predict the no-show probabilities of a given set of patients, and to subsequently employ these predictions to find the optimal appointment schedule. Some existing work assumes that all patients have the same no-show probability (1-class approach); other work assumes that patients have either a low or a high no-show probability (2-class approach). In contrast, we utilize probabilistic classifiers to obtain the individual patients’ no-show probabilities (N-class approach). Our approach results in better-quality schedules, as measured by a weighted average of patient waiting time and provider overtime. We also find that a small increase in the prediction performance (measured by the Brier score) translates into a large decrease in the schedule cost. Our results are obtained through a large-scale computational study and validated on a real-world data set from an outpatient clinic.
Differences in high-definition transcranial direct current stimulation over the motor hotspot versus the premotor cortex on motor network excitability

The effectiveness of transcranial direct current stimulation (tDCS) placed over the motor hotspot (thought to represent the primary motor cortex (M1)) to modulate motor network excitability is highly variable. The premotor cortex-particularly the dorsal premotor cortex (PMd)-may be a promising alternative target to reliably modulate motor excitability, as it influences motor control across multiple pathways, one independent of M1 and one with direct connections to M1. This double-blind, placebo-controlled preliminary study aimed to differentially excite motor and premotor regions using high-definition tDCS (HD-tDCS) with concurrent functional magnetic resonance imaging (fMRI). HD-tDCS applied over either the motor hotspot or the premotor cortex demonstrated high inter-individual variability in changes on cortical motor excitability. However, HD-tDCS over the premotor cortex led to a higher number of responders and greater changes in local fMRI-based complexity than HD-tDCS over the motor hotspot. Furthermore, an analysis of individual motor hotspot anatomical locations revealed that, in more than half of the participants, the motor hotspot is not located over anatomical M1 boundaries, despite using a canonical definition of the motor hotspot. This heterogeneity in stimulation site may contribute to the variability of tDCS results. Altogether, these preliminary findings provide new considerations to enhance tDCS reliability.
Sensing Volume Coverage of Robot Workspace using On-Robot Time-of-Flight Sensor Arrays for Safe Human Robot Interaction

In this paper, an analysis of the sensing volume coverage of robot workspace as well as the shared humanrobot collaborative workspace for various configurations of onrobot Time-of-Flight (ToF) sensor array rings is presented. A methodology for volumetry using octrees to quantity the detection/sensing volume of the sensors is proposed. The change in sensing volume coverage by increasing the number of sensors per ToF sensor array ring and also increasing the number of rings mounted on robot link is also studied. Considerations of maximum ideal volume around the robot workspace that a given ToF sensor array ring placement and orientation setup should cover for safe human robot interaction are presented. The sensing volume coverage measurements in this maximum ideal volume are tabulated and observations on various ToF configurations and their coverage for close and far zones of the robot are determined.
Mass–spring–damper networks for distributed optimization in non-Euclidean spaces

Abstract We consider the problem of minimizing the sum of non-smooth convex functions in non-Euclidean spaces, e.g., probability simplex, via only local computation and communication on an undirected graph. We propose two algorithms motivated by mass–spring–damper dynamics. The first algorithm uses an explicit update that computes subgradients and Bregman projections only, and matches the convergence behavior of centralized mirror descent. The second algorithm uses an implicit update that solves a penalized subproblem at each iteration, and achieves the iteration complexity of O ( 1 ∕ K ) . The results are also demonstrated via numerical examples.
The Bousfield-Kuhn functor and topological André-Quillen cohomology

We construct a natural transformation from the Bousfield-Kuhn functor evaluated on a space to the Topological Andre-Quillen cohomology of the K(n)-local Spanier–Whitehead dual of the space, and show that the map is an equivalence in the case where the space is a sphere. This results in a method for computing unstable $$v_n$$-periodic homotopy groups of spheres from their Morava E-cohomology (as modules over the Dyer-Lashof algebra of Morava E-theory). We relate the resulting algebraic computations to the algebraic geometry of isogenies between Lubin–Tate formal groups.
On Universal Cycles of Labeled Graphs

A universal cycle is a compact listing of a class of combinatorial objects. In this paper, we prove the existence of universal cycles of classes of labeled graphs, including simple graphs, trees, graphs with m edges, graphs with loops, graphs with multiple edges (with up to m duplications of each edge), directed graphs, hypergraphs, and k-uniform hypergraphs.