cssi/SciSciGPT-SciSciNet huggingface dataset:
Generic cospark of a matrix can be computed in polynomial time

The cospark of a matrix is the cardinality of the sparsest vector in the column space of the matrix. Computing the cospark of a matrix is well known to be an NP hard problem. Given the sparsity pattern (i.e., the locations of the non-zero entries) of a matrix, if the non-zero entries are drawn from independently distributed continuous probability distributions, it is shown that the cospark equals, with probability one, to a particular number we term the generic cospark of the matrix. It is proven that, unlike the cospark, the generic cospark of a matrix can be computed in polynomial time. An efficient algorithm that achieves this is offered.
Pieri integral formula and asymptotics of Jack unitary characters

We introduce Jack (unitary) characters and prove two kinds of formulas that are suitable for their asymptotics, as the lengths of the signatures that parametrize them go to infinity. The first kind includes several integral representations for Jack characters of one variable. The second identity we prove is the Pieri integral formula for Jack characters which, in a sense, is dual to the well known Pieri rule for Jack polynomials. The Pieri integral formula can also be seen as a functional equation for irreducible spherical functions of virtual Gelfand pairs. As an application of our formulas, we study the asymptotics of Jack characters as the corresponding signatures grow to infinity in the sense of Vershik–Kerov. We prove the existence of a small $$\delta > 0$$ such that the Jack characters of m variables have a uniform limit on the $$\delta $$ -neighborhood of the m-dimensional torus. Our result specializes to a theorem of Okounkov and Olshanski.
Pointwise bounds and blow-up for nonlinear fractional parabolic inequalities

Abstract We investigate pointwise upper bounds for nonnegative solutions u ( x , t ) of the nonlinear initial value problem (0.1) 0 ≤ ( ∂ t − Δ ) α u ≤ u λ in R n × R , n ≥ 1 , (0.2) u = 0 in R n × ( − ∞ , 0 ) where λ and α are positive constants. To do this we first give a definition—tailored for our study of (0.1) , (0.2) —of fractional powers of the heat operator ( ∂ t − Δ ) α : Y → X where X and Y are linear spaces whose elements are real valued functions on R n × R and 0 α α 0 for some α 0 which depends on n, X and Y. We then obtain, when they exist, optimal pointwise upper bounds on R n × ( 0 , ∞ ) for nonnegative solutions u ∈ Y of the initial value problem (0.1) , (0.2) with particular emphasis on those bounds as t → 0 + and as t → ∞ .
Analysis of heterogeneous cardiac pacemaker tissue models and traveling wave dynamics.

Abstract The sinoatrial-node (SAN) is a complex heterogeneous tissue that generates a stable rhythm in healthy hearts, yet a general mechanistic explanation for when and how this tissue remains stable is lacking. Although computational and theoretical analyses could elucidate these phenomena, such methods have rarely been used in realistic (large-dimensional) gap-junction coupled heterogeneous pacemaker tissue models. In this study, we adapt a recent model of pacemaker cells (Severi et al., 2012), incorporating biophysical representations of ion channel and intracellular calcium dynamics, to capture physiological features of a heterogeneous population of pacemaker cells, in particular “center” and “peripheral” cells with distinct intrinsic frequencies and action potential morphology. Large-scale simulations of the SAN tissue, represented by a heterogeneous tissue structure of pacemaker cells, exhibit a rich repertoire of behaviors, including complete synchrony, traveling waves of activity originating from periphery to center, and transient traveling waves originating from the center. We use phase reduction methods that do not require fully simulating the large-scale model to capture these observations. Moreover, the phase reduced models accurately predict key properties of the tissue electrical dynamics, including wave frequencies when synchronization occurs, and wave propagation direction in a variety of tissue models. With the reduced phase models, we analyze the relationship between cell distributions and coupling strengths and the resulting transient dynamics. Further, the reduced phase model predicts parameter regimes of irregular electrical dynamics. Thus, we demonstrate that phase reduced oscillator models applied to realistic pacemaker tissue is a useful tool for investigating the spatial-temporal dynamics of cardiac pacemaker activity.
Weak convergence of stationary empirical processes

Abstract We offer an umbrella type result which extends weak convergence of classical empirical processes on the line to that of more general processes indexed by functions of bounded variation. This extension is not contingent on the type of dependence of the underlying sequence of random variables. As a consequence we establish weak convergence for stationary empirical processes indexed by general classes of functions under α -mixing conditions.
SketchyGAN: Towards Diverse and Realistic Sketch to Image Synthesis

Synthesizing realistic images from human drawn sketches is a challenging problem in computer graphics and vision. Existing approaches either need exact edge maps, or rely on retrieval of existing photographs. In this work, we propose a novel Generative Adversarial Network (GAN) approach that synthesizes plausible images from 50 categories including motorcycles, horses and couches. We demonstrate a data augmentation technique for sketches which is fully automatic, and we show that the augmented data is helpful to our task. We introduce a new network building block suitable for both the generator and discriminator which improves the information flow by injecting the input image at multiple scales. Compared to state-of-the-art image translation methods, our approach generates more realistic images and achieves significantly higher Inception Scores.
A simplified Kronecker rule for one hook shape

Recently Blasiak gave a combinatorial rule for the Kronecker coefficient $g_{\lambda \mu \nu}$ when $\mu$ is a hook shape by defining a set of colored Yamanouchi tableaux with cardinality $g_{\lambda\mu\nu}$ in terms of a process called conversion. We give a characterization of colored Yamanouchi tableaux that does not rely on conversion, which leads to a simpler formulation and proof of the Kronecker rule for one hook shape.
K -Theory and Perturbations of Absolutely Continuous Spectra

We study the K0-group of the commutant modulo a normed ideal of an n-tuple of commuting Hermitian operators in some of the simplest cases. In case n = 1, the results, under some technical conditions are rather complete and show the key role of the absolutely continuous part when the ideal is the trace-class. For a commuting n-tuple, $${n \ge 3}$$ and the Lorentz (n,1) ideal, we show under an absolute continuity assumption that the commutant determines a canonical direct summand in K0. Also, certain properties involving the compact ideal, established assuming quasicentral approximate units mod the normed ideal, have weaker versions which hold assuming only finiteness of the obstruction to quasicentral approximate units.
Investigating the X-ray emission from the Galactic TeV Gamma-ray Source MGRO J1908+06

MGRO J1908+06 is a bright, extended TeV gamma-ray source located near the Galactic plane. The TeV emission has previously been attributed to the pulsar wind nebula of the radio-faint gamma-ray pulsar PSR J1907+0602 discovered with Fermi. However, studies of the TeV morphology with VERITAS have shown that MGRO J1908+06 is somewhat larger than other pulsar wind nebulae of similar age and that the TeV spectrum does not soften with distance from the pulsar as is observed for other pulsar wind nebulae. Although MGRO J1908+06 is very bright in gamma rays with a flux corresponding to ∼80% of the Crab Nebula flux at 20 TeV, no extended emission at other energies has so far been detected. We report on our analysis of X-ray data obtained with XMM-Newton of the region near MGRO J1908+06. We searched the data for point-like sources and detected several hard-spectrum X-ray sources that could be associated with the TeV emission, including the gamma-ray pulsar PSR J1907+0602. We also performed an extended source analysis to search for diffuse emission from MGRO J1908+06 but found no evidence of diffuse X-ray emission coincident with the TeV source. We place an upper limit of 8.7× 1033 erg s−1 on the X-ray luminosity of MGRO J1908+06 in the 1–10 keV energy range. The corresponding limit on the ratio of gamma-ray to X-ray luminosity is consistent with the ratios found for other pulsar wind nebulae of similar age.
Hourly-Similarity Based Solar Forecasting Using Multi-Model Machine Learning Blending

With the increasing penetration of solar power into power systems, forecasting becomes critical in power system operations. In this paper, an hourly-similarity (HS) based method is developed for 1-hour-ahead (1HA) global horizontal irradiance (GHI) forecasting. This developed method utilizes diurnal patterns, statistical distinctions between different hours, and hourly similarities in solar data to improve the forecasting accuracy. The HS-based method is built by training multiple two-layer multi-model forecasting framework (MMFF) models independently with the same-hour subsets. The final optimal model is a combination of MMFF models with the best-performed blending algorithm at every hour. At the forecasting stage, the most suitable model is selected to perform the forecasting subtask of a certain hour. The HS-based method is validated by 1-year data with six solar features collected by the National Renewable Energy Laboratory (NREL). Results show that the HS-based method outperforms the non-HS (all-in-one) method significantly with the same MMFF architecture, wherein the optimal HS-based method outperforms the best all-in-one method by 10.94% and 7.74% based on the normalized mean absolute error and normalized root mean square error, respectively.
ON THE GAP OF HAMILTONIANS FOR THE ADIABATIC SIMULATION OF QUANTUM CIRCUITS

The time or cost of simulating a quantum circuit by adiabatic evolution is determined by the spectral gap of the Hamiltonians involved in the simulation. In "standard" constructions based on Feynman's Hamiltonian, such a gap decreases polynomially with the number of gates in the circuit, L. Because a larger gap implies a smaller cost, we study the limits of spectral gap amplification in this context. We show that, under some assumptions on the ground states and the cost of evolving with the Hamiltonians (which apply to the standard constructions), an upper bound on the gap of the order 1/L follows. In addition, if the Hamiltonians satisfy a frustration-free property, the upper bound is of the order 1/L2. Our proofs use recent results on adiabatic state transformations, spectral gap amplification, and the simulation of continuous-time quantum query algorithms. They also consider a reduction from the unstructured search problem, whose lower bound in the oracle cost translates into the upper bounds in the gaps. The impact of our results is that improving the gap beyond that of standard constructions (i.e. 1/L2), if possible, is challenging.
Random Eigenfunctions on Flat Tori: Universality for the Number of Intersections

We show that several statistics of the number of intersections between random eigenfunctions of general eigenvalues with a given smooth curve in flat tori are universal under various families of randomness.
Massively Parallel Algorithms for Finding Well-Connected Components in Sparse Graphs

Massively parallel computation (MPC) algorithms for graph problems have witnessed a resurgence of interest in recent years. Despite major progress for numerous graph problems however, the complexity of the sparse graph connectivity problem in this model has remained elusive: While classical logarithmic-round PRAM algorithms for finding connected components in any n-vertex graph have been known for more than three decades (and imply the same bounds for MPC model), no o(log n)-round MPC algorithms are known for this task with truly sublinear in n memory per machine (which is the only interesting regime for sparse graphs with O(n) edges). It is conjectured that an o(log n)-round algorithm for connectivity on general sparse graphs with n1-Ω (1) per-machine memory may not exist, a conjecture that also forms the basis for multiple conditional hardness results on the round complexity of other problems in the MPC model.We take an opportunistic approach towards the sparse graph connectivity problem by designing an algorithm with improved performance in terms of the connectivity structure of the input graph. Formally, we design an MPC algorithm that finds all connected components with spectral gap at least λ in a graph in O(log log n + log(1/λ)) MPC rounds and nδ memory per machine for any constant δ ∈ (0,1). While this algorithm still requires Θ(log n) rounds in the worst-case, it achieves an exponential round reduction on "well-connected'' components with λ ≥ 1/polylog(n) using only nδ memory per machine and l(n) total memory, and still operates in o(log n)l rounds even when λ = 1/no(1).En-route to our main result, we design a new distributed data structure for performing independent random walks from all vertices simultaneously, as well as a new leader-election algorithm with exponentially faster round complexity on random graphs.
Uniqueness and Stability of Coexistence States in Two Species Models With/Without Chemotaxis on Bounded Heterogeneous Environments

The current paper is concerned with the asymptotic dynamics of two species competition systems with/without chemotaxis in heterogeneous media. In the previous work (Issa and Shen in Persistence, coexistence and extinction in two species chemotaxis models on bounded heterogeneous environments, 2017. https://arxiv.org/pdf/1709.10040.pdf), we find conditions on the parameters in such systems for the persistence of the two species and the existence of positive coexistence states. In this paper, we find conditions on the parameters for the uniqueness and stability of positive coexistence states of such systems. The established results are new even for the two species competition systems without chemotaxis but with space dependent coefficients.
Fully dynamic maximal independent set with sublinear update time

A maximal independent set (MIS) can be maintained in an evolving m-edge graph by simply recomputing it from scratch in O(m) time after each update. But can it be maintained in time sublinear in m in fully dynamic graphs? We answer this fundamental open question in the affirmative. We present a deterministic algorithm with amortized update time O(min{Δ,m3/4}), where Δ is a fixed bound on the maximum degree in the graph and m is the (dynamically changing) number of edges. We further present a distributed implementation of our algorithm with O(min{Δ,m3/4}) amortized message complexity, and O(1) amortized round complexity and adjustment complexity (the number of vertices that change their output after each update). This strengthens a similar result by Censor-Hillel, Haramaty, and Karnin (PODC’16) that required an assumption of a non-adaptive oblivious adversary.
Using Neural Networks to Generate Information Maps for Mobile Sensors

Target localization is a critical task for mobile sensors and has many applications. However, generating informative trajectories for these sensors is a challenging research problem. A common method uses information maps that estimate the value of taking measurements from any point in the sensor state space. These information maps are used to generate trajectories; for example, a trajectory might be designed so its distribution of measurements matches the distribution of the information map. Regardless of the trajectory generation method, generating information maps as new observations are made is critical. However, it can be challenging to compute these maps in real-time. We propose using convolutional neural networks to generate information maps from a target estimate and sensor model in real-time. Simulations show that maps are accurately rendered while offering orders of magnitude reduction in computation time.
A Rigidity Theorem for Surfaces in Schwarzschild Manifold

In this article, we prove a rigidity theorem for isometric embeddings into the Schwarzschild manifold, by using the variational formula of quasi-local mass.
Inducing Super-Approximation

Let $\Gamma_2\subseteq \Gamma_1$ be finitely generated subgroups of ${\rm GL}_{n_0}(\mathbb{Z}[1/q_0])$. For $i=1$ or $2$, let $\mathbb{G}_i$ be the Zariski-closure of $\Gamma_i$ in $({\rm GL}_{n_0})_{\mathbb{Q}}$, $\mathbb{G}_i^{\circ}$ be the Zariski-connected component of $\mathbb{G}_i$, and let $G_i$ be the closure of $\Gamma_i$ in $\prod_{p\nmid q_0}{\rm GL}_{n_0}(\mathbb{Z}_p)$. In this article we prove that, if $\mathbb{G}_1^{\circ}$ is the smallest closed normal subgroup of $\mathbb{G}_1^{\circ}$ which contains $\mathbb{G}_2^{\circ}$ and $\Gamma_2\curvearrowright G_2$ has spectral gap, then $\Gamma_1\curvearrowright G_1$ has spectral gap.
Nodal Sets of Smooth Functions with Finite Vanishing Order and p-Sweepouts

We show that on a compact Riemannian manifold (M, g), nodal sets of linear combinations of any $$p+1$$ smooth functions form an admissible p-sweepout provided these linear combinations have uniformly bounded vanishing order. This applies in particular to finite linear combinations of Laplace eigenfunctions. As a result, we obtain a new proof of the Gromov, Guth, Marques–Neves upper bounds on the min–max p-widths of M. We also prove that close to a point at which a smooth function on $$\mathbb {R}^{n+1}$$ vanishes to order k, its nodal set is contained in the union of $$k\,W^{1,p}$$ graphs for some $$p > 1$$ . This implies that the nodal set is locally countably n-rectifiable and has locally finite $$\mathcal {H}^n$$ measure, facts which also follow from a previous result of Bar. Finally, we prove the continuity of the Hausdorff measure of nodal sets under heat flow.
Indices of inseparability in towers of field extensions

Let K be a local field whose residue field has characteristic p and let L/K be a finite separable totally ramified extension of degree n=apν. The indices of inseparability i0,i1,…,iν of L/K were defined by Fried in the case char(K)=p and by Heiermann in the case char(K)=0; they give a refinement of the usual ramification data for L/K. The indices of inseparability can be used to construct “generalized Hasse–Herbrand functions” ϕL/Kj for 0≤j≤ν. In this paper we give an interpretation of the values ϕL/Kj(c) for nonnegative integers c. We use this interpretation to study the behavior of generalized Hasse–Herbrand functions in towers of field extensions.
Characterization of the equivalence of robustification and regularization in linear and matrix regression

Abstract The notion of developing statistical methods in machine learning which are robust to adversarial perturbations in the underlying data has been the subject of increasing interest in recent years. A common feature of this work is that the adversarial robustification often corresponds exactly to regularization methods which appear as a loss function plus a penalty. In this paper we deepen and extend the understanding of the connection between robustification and regularization (as achieved by penalization) in regression problems. Specifically, (a) In the context of linear regression, we characterize precisely under which conditions on the model of uncertainty used and on the loss function penalties robustification and regularization are equivalent. (b) We extend the characterization of robustification and regularization to matrix regression problems (matrix completion and Principal Component Analysis).
Improved Approximation of Storage-Rate Tradeoff for Caching With Multiple Demands

Caching at the network edge has emerged as a viable solution for alleviating the severe capacity crunch in modern content centric wireless networks by leveraging network load-balancing in the form of localized content storage and delivery. In this paper, we consider a cache-aided network, where the cache storage phase is assisted by a central server and users can demand multiple files at each transmission interval. To service these demands, we consider two delivery models: 1) centralized content delivery, where user demands at each transmission interval are serviced by the central server via multicast transmissions; and 2) device-to-device assisted distributed delivery, where users multicast to each other in order to service file demands. For such cache-aided networks, we present new results on the fundamental cache storage versus transmission rate tradeoff. Specifically, we develop a new technique for characterizing information theoretic lower bounds on the storage-rate tradeoff and show that the new lower bounds are strictly tighter than cut-set bounds from literature. Furthermore, using the new lower bounds, we improve the constant factor approximation of the optimal storage-rate tradeoff for cache-aided systems under both delivery models.
Single crystal functional oxides on silicon

Single-crystalline thin films of complex oxides show a rich variety of functional properties such as ferroelectricity, piezoelectricity, ferro and antiferromagnetism and so on that have the potential for completely new electronic applications. Direct synthesis of such oxides on silicon remains challenging because of the fundamental crystal chemistry and mechanical incompatibility of dissimilar interfaces. Here we report integration of thin (down to one unit cell) single crystalline, complex oxide films onto silicon substrates, by epitaxial transfer at room temperature. In a field-effect transistor using a transferred lead zirconate titanate layer as the gate insulator, we demonstrate direct reversible control of the semiconductor channel charge with polarization state. These results represent the realization of long pursued but yet to be demonstrated single-crystal functional oxides on-demand on silicon.
Partitions and conservativity

Abstract We study the partition properties enjoyed by the “next best thing to a P-point” ultrafilters introduced recently in joint work with Dobrinen and Raghavan. That work established some finite-exponent partition relations, and we now analyze the connections between these relations for different exponents and the notion of conservativity introduced much earlier by Phillips. In addition, we establish some infinite-exponent partition relations for these ultrafilters and also for sums of non-isomorphic selective ultrafilters indexed by selective ultrafilters.
Density matrix minimization with $\ell_1$ regularization

We propose a convex variational principle to find sparse representation of low-lying eigenspace of symmetric matrices. In the context of electronic structure calculation, this corresponds to a sparse density matrix minimization algorithm with $\ell_1$ regularization. The minimization problem can be efficiently solved by a split Bergman iteration type algorithm. We further prove that from any initial condition, the algorithm converges to a minimizer of the variational principle.
Phase retrieval from coded diffraction patterns

Abstract This paper considers the question of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray crystallography and related disciplines. We study a physically realistic setup where one can modulate the signal of interest and then collect the intensity of its diffraction pattern, each modulation thereby producing a sort of coded diffraction pattern. We show that PhaseLift, a recent convex programming technique, recovers the phase information exactly from a number of random modulations, which is polylogarithmic in the number of unknowns. Numerical experiments with noiseless and noisy data complement our theoretical analysis and illustrate our approach.
Quasi-exceptional sets and equivariant coherent sheaves on the nilpotent cone

In math.AG/0005152 a certain $t$-structure on the derived category of equivariant coherent sheaves on the nil-cone of a simple complex algebraic group was introduced (the so-called perverse $t$-structure corresponding to the middle perversity). In the present note we show that the same $t$-structure can be obtained from a natural quasi-exceptional set generating this derived category. As a consequence we obtain a bijection between the sets of dominant weights and pairs consisting of a nilpotent orbit, and an irreducible representation of the centralizer of this element, conjectured by Lusztig and Vogan (and obtained by other means in math.RT/0010089).
The F-pure threshold of a Calabi-Yau hypersurface

We compute the \(F\)-pure threshold of the affine cone over a Calabi–Yau hypersurface, and relate it to the order of vanishing of the Hasse invariant on the versal deformation space of the hypersurface.
Free Stein kernels and an improvement of the free logarithmic Sobolev inequality

We introduce a free version of the Stein kernel, relative to a semicircular law. We use it to obtain a free counterpart of the HSI inequality of Ledoux, Peccatti and Nourdin, which is an improvement of the free logarithmic Sobolev inequality of Biane and Speicher, as well as a rate of convergence in the (multivariate) entropic free Central Limit Theorem. We also compute the free Stein kernels for several relevant families of self-adjoint operators.
Communication Complexity for Algorithm Designers

This text collects the lecture notes from the author's course "Communication Complexity for Algorithm Designers," taught at Stanford in the winter quarter of 2015. The two primary goals of the text are:1 Learn several canonical problems in communication complexity that are useful for proving lower bounds for algorithms disjointness, index, gap-hamming, etc..2 Learn how to reduce lower bounds for fundamental algorithmic problems to communication complexity lower bounds.Along the way, readers will also:3 Get exposure to lots of cool computational models and some famous results about them — data streams and linear sketches, compressive sensing, space-query time trade-offs in data structures, sublinear-time algorithms, and the extension complexity of linear programs.4 Scratch the surface of techniques for proving communication complexity lower bounds fooling sets, corruption arguments, etc..
MEC-aware cell association for 5G heterogeneous networks

The need for efficient use of network resources is continuously increasing with the grow of traffic demand, however, current mobile systems have been planned and deployed so far with the mere aim of enhancing radio coverage and capacity. Unfortunately, this approach is not sustainable anymore, as 5G communication systems will have to cope with huge amounts of traffic, heterogeneous in terms of latency among other Quality-of-Service (QoS) requirements. Moreover, the advent of Multi-access Edge Computing (MEC) brings up the need to more efficiently plan and dimension network deployment by means of jointly exploiting the available radio and processing resources. From this standpoint, advanced cell association of users can play a key role for 5G systems. Focusing on a Heterogeneous Network (HetNet), this paper proposes a comparison between state-of-the-art (i.e., radio-only) and MEC-aware cell association rules, taking the scenario of task offloading in the Uplink (UL) as an example. Numerical evaluations show that the proposed cell association rule provides nearly 60% latency reduction, as compared to its standard, radio-exclusive counterpart.
Differential Privacy for Growing Databases

The large majority of differentially private algorithms focus on the static setting, where queries are made on an unchanging database. This is unsuitable for the myriad applications involving databases that grow over time. To address this gap in the literature, we consider the dynamic setting, in which new data arrive over time. Previous results in this setting have been limited to answering a single non-adaptive query repeatedly as the database grows. In contrast, we provide tools for richer and more adaptive analysis of growing databases. Our first contribution is a novel modification of the private multiplicative weights algorithm, which provides accurate analysis of exponentially many adaptive linear queries (an expressive query class including all counting queries) for a static database. Our modification maintains the accuracy guarantee of the static setting even as the database grows without bound. Our second contribution is a set of general results which show that many other private and accurate algorithms can be immediately extended to the dynamic setting by rerunning them at appropriate points of data growth with minimal loss of accuracy, even when data growth is unbounded.
Diffusion-Convolutional Neural Networks

We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from graph-structured data and used as an effective basis for node classification. DCNNs have several attractive qualities, including a latent representation for graphical data that is invariant under isomorphism, as well as polynomial-time prediction and learning that can be represented as tensor operations and efficiently implemented on a GPU. Through several experiments with real structured datasets, we demonstrate that DCNNs are able to outperform probabilistic relational models and kernel-on-graph methods at relational node classification tasks.
Convolutional Neural Network Achieves Human-level Accuracy in Music Genre Classification

Music genre classification is one example of content-based analysis of music signals. Traditionally, human-engineered features were used to automatize this task and 61% accuracy has been achieved in the 10-genre classification. However, it's still below the 70% accuracy that humans could achieve in the same task. Here, we propose a new method that combines knowledge of human perception study in music genre classification and the neurophysiology of the auditory system. The method works by training a simple convolutional neural network (CNN) to classify a short segment of the music signal. Then, the genre of a music is determined by splitting it into short segments and then combining CNN's predictions from all short segments. After training, this method achieves human-level (70%) accuracy and the filters learned in the CNN resemble the spectrotemporal receptive field (STRF) in the auditory system.
Inverse Density as an Inverse Problem: the Fredholm Equation Approach

We address the problem of estimating the ratio q/p where p is a density function and q is another density, or, more generally an arbitrary function. Knowing or approximating this ratio is needed in various problems of inference and integration often referred to as importance sampling in statistical inference. It is also closely related to the problem of covariate shift in transfer learning. Our approach is based on reformulating the problem of estimating the ratio as an inverse problem in terms of an integral operator corresponding to a kernel, known as the Fredholm problem of the first kind. This formulation, combined with the techniques of regularization leads to a principled framework for constructing algorithms and for analyzing them theoretically. The resulting family of algorithms (FIRE, for Fredholm Inverse Regularized Estimator) is flexible, simple and easy to implement. We provide detailed theoretical analysis including concentration bounds and convergence rates for the Gaussian kernel for densities defined on ℝd and smooth d-dimensional sub-manifolds of the Euclidean space. Model selection for unsupervised or semi-supervised inference is generally a difficult problem. It turns out that in the density ratio estimation setting, when samples from both distributions are available, simple completely unsupervised model selection methods are available. We call this mechanism CD-CV for Cross-Density Cross-Validation. We show encouraging experimental results including applications to classification within the covariate shift framework.
Learning selectively conditioned forest structures with applications to DBNs and classification

Dealing with uncertainty in Bayesian Network structures using maximum a posteriori (MAP) estimation or Bayesian Model Averaging (BMA) is often intractable due to the superexponential number of possible directed, acyclic graphs. When the prior is decomposable, two classes of graphs where efficient learning can take place are tree-structures, and fixed-orderings with limited in-degree. We show how MAP estimates and BMA for selectively conditioned forests (SCF), a combination of these two classes, can be computed efficiently for ordered sets of variables. We apply SCFs to temporal data to learn Dynamic Bayesian Networks having an intra-timestep forest and inter-timestep limited in-degree structure, improving model accuracy over DBNs without the combination of structures. We also apply SCFs to Bayes Net classification to learn selective forest-augmented Naive Bayes classifiers. We argue that the built-in feature selection of selective augmented Bayes classifiers makes them preferable to similar non-selective classifiers based on empirical evidence.
Spatial Statistics of Apollonian Gaskets

Apollonian gaskets are formed by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We experimentally study the nearest neighbor spacing, pair co...
Movement-Efficient Sensor Deployment in Wireless Sensor Networks With Limited Communication Range

We study a mobile wireless sensor network (MWSN) consisting of multiple mobile sensors or robots. Three key factors in MWSNs, such as sensing quality, energy consumption, and connectivity, have attracted plenty of attention, but the interaction of these factors is not well studied. To take all the three factors into consideration, we model the sensor deployment problem as a constrained optimization problem. Our goal is to find an optimal sensor deployment (or relocation) to optimize the sensing quality with a limited communication range and a specific network lifetime constraint. We derive necessary conditions for the optimal sensor deployment in both homogeneous and heterogeneous MWSNs. According to our derivation, some sensors are idle in the optimal deployment of heterogeneous MWSNs. Using these necessary conditions, we design both the centralized and distributed algorithms to provide a flexible and explicit tradeoff between sensing uncertainty and network lifetime. The proposed algorithms are successfully extended to more applications, such as area coverage and target coverage, via properly selected density functions. The simulation results show that our algorithms outperform the existing relocation algorithms.
Accelerated carrier recombination by grain boundary/edge defects in MBE grown transition metal dichalcogenides

Defect-carrier interaction in transition metal dichalcogenides (TMDs) plays important roles in carrier relaxation dynamics and carrier transport, which determines the performance of electronic devices. With femtosecond laser time-resolved spectroscopy, we investigated the effect of grain boundary/edge defects on the ultrafast dynamics of photoexcited carrier in molecular beam epitaxy (MBE)-grown MoTe2 and MoSe2. We found that, comparing with exfoliated samples, the carrier recombination rate in MBE-grown samples accelerates by about 50 times. We attribute this striking difference to the existence of abundant grain boundary/edge defects in MBE-grown samples, which can serve as effective recombination centers for the photoexcited carriers. We also observed coherent acoustic phonons in both exfoliated and MBE-grown MoTe2, indicating strong electron-phonon coupling in this materials. Our measured sound velocity agrees well with the previously reported result of theoretical calculation. Our findings provide a ...
A categorification of the square root of $-1$

We give a graphical calculus for a monoidal DG category $\cal{I}$ whose Grothendieck group is isomorphic to the ring $\mathbb{Z}[\sqrt{-1}]$. We construct a categorical action of $\cal{I}$ which lifts the action of $\mathbb{Z}[\sqrt{-1}]$ on $\mathbb{Z}^2$.
Synthesizing Distributed Energy Resources in Microgrids with Temporal Logic Specifications

Grid supportive (GS) modes integrated within distributed energy resources (DERs) can improve the frequency response. However, synthesis of GS modes for guaranteed performance is challenging. Moreover, a tool is needed to handle sophisticated specifications from grid codes and protection relays. This paper proposes a model predictive control (MPC)-based mode synthesis methodology, which can accommodate the temporal logic specifications (TLSs). The TLSs allow richer descriptions of control specifications addressing both magnitude and time at the same time. The proposed controller will compute a series of Boolean control signals to synthesize the GS mode of DERs by solving the MPC problem under the normal condition, where the frequency response predicted by a reduced-order model satisfies the defined specifications. Once a sizable disturbance is detected, the pre-calculated signals are applied to the DERs. The proposed synthesis methodology is verified on the full nonlinear model in Simulink. A robust factor is imposed on the specifications to compensate the response mismatch between the reduce-order model and nonlinear model so that the nonlinear response satisfies the required TLS.
Polynomial approximation on a compact subset of the real line

Abstract We prove an analogue of the classical Bernstein theorem concerning the rate of polynomial approximation of piecewise analytic functions on a compact subset of the real line.
Adaptive learning rates and parallelization for stochastic, sparse, non-smooth gradients

Abstract: Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on stationary problems, and permitting learning rates to grow appropriately in non-stationary tasks. Here, we extend the idea in three directions, addressing proper minibatch parallelization, including reweighted updates for sparse or orthogonal gradients, improving robustness on non-smooth loss functions, in the process replacing the diagonal Hessian estimation procedure that may not always be available by a robust finite-difference approximation. The final algorithm integrates all these components, has linear complexity and is hyper-parameter free.
Automatic Identification of AltLexes using Monolingual Parallel Corpora

The automatic identification of discourse relations is still a challenging task in natural language processing. Discourse connectives, such as since or but, are the most informative cues to identify explicit relations; however discourse parsers typically use a closed inventory of such connectives. As a result, discourse relations signalled by markers outside these inventories (i.e. AltLexes) are not detected as effectively. In this paper, we propose a novel method to leverage parallel corpora in text simplification and lexical resources to automatically identify alternative lexicalizations that signal discourse relation. When applied to the Simple Wikipedia and Newsela corpora along with WordNet and the PPDB, the method allowed the automatic discovery of 91 AltLexes.
Edge detecting new physics the Voronoi way

Edge detection is an important tool in the search for and exploration of physics beyond the standard model. Ideally one would be able to perform edge detection in a relatively model-independent way, however most analyses rely on more detailed properties (i.e. "shapes" or likelihood distributions) of the variable(s) of interest. We therefore present a sketch of how edge detection can be accomplished using Voronoi tessellations, focusing on the case of two-dimensional distributions for simplicity. After deriving some useful properties of the Voronoi tessellations of simplified distributions containing edges, we propose several algorithms for tagging the Voronoi cells in the vicinity of kinematic edges in real data and show that the efficiency of our methods is improved by the addition of a few Voronoi relaxation steps via Lloyd's method. Our results suggest specifically that Voronoi-based methods should be useful for relatively model-independent edge detection, and, more generally, that the wider adaptation of Voronoi tessellations may be useful in collider physics.
The k -tacnode process

The tacnode process is a universal behavior arising in nonintersecting particle systems and tiling problems. For Dyson Brownian bridges, the tacnode process describes the grazing collision of two packets of walkers. We consider such a Dyson sea on the unit circle with drift. For any $$k\in \mathbb {Z}$$ , we show that an appropriate double scaling of the drift and return time leads to a generalization of the tacnode process in which k particles are expected to wrap around the circle. We derive winding number probabilities and an expression for the correlation kernel in terms of functions related to the generalized Hastings–McLeod solutions to the inhomogeneous Painleve-II equation. The method of proof is asymptotic analysis of discrete orthogonal polynomials with a complex weight.
The effect of stellar evolution on migrating warm jupiters

Warm jupiters are an unexpected population of extrasolar planets that are too near to their host to have formed in situ, but distant enough to retain a significant eccentricity in the face of tidal damping. These planets are curiously absent around stars larger than two solar radii. We hypothesize that the warm jupiters are migrating due to Kozai-Lidov oscillations, which leads to transient episodes of high eccentricity and a consequent tidal decay. As their host evolves, such planets would be rapidly dragged in or engulfed at minimum periapse, leading to a rapid depletion of the population with increasing stellar radius, as is observed. Using numerical simulations, we determine the relationship between periapse distance and orbital migration rate for planets 0.1 to 10 Jupiter masses and with orbital periods between 10 and 100 days. We find that Kozai-Lidov oscillations effectively result in planetary removal early in the evolution of the host star, possibly accounting for the observed deficit. While the observed eccentricity distribution is inconsistent with the simulated distribution for an oscillating and migrating warm jupiter population, observational biases may explain the discrepancy.
Range separation: The divide between local structures and field theories

This work presents parallel histories of the development of two modern theories of condensed matter: the theory of electron structure in quantum mechanics, and the theory of liquid structure in statistical mechanics. Comparison shows that key revelations in both are not only remarkably similar, but even follow along a common thread of controversy that marks progress from antiquity through to the present. This theme appears as a creative tension between two competing philosophies, that of short range structure (atomistic models) on the one hand, and long range structure (continuum or density functional models) on the other. The timeline and technical content are designed to build up a set of key relations as guideposts for using density functional theories together with atomistic simulation.
The Rest Mass of an Asymptotically Anti-de Sitter Spacetime

We study the space of Killing fields on the four dimensional AdS spacetime $$AdS^{3,1}$$ . Two subsets $${\mathcal {S}}$$ and $${\mathcal {O}}$$ are identified: $${\mathcal {S}}$$ (the spinor Killing fields) is constructed from imaginary Killing spinors, and $${\mathcal {O}}$$ (the observer Killing fields) consists of all hypersurface orthogonal, future timelike unit Killing fields. When the cosmology constant vanishes, or in the Minkowski spacetime case, these two subsets have the same convex hull in the space of Killing fields. In presence of the cosmology constant, the convex hull of $$ {\mathcal {O}}$$ is properly contained in that of $${\mathcal {S}}$$ . This leads to two different notions of energy for an asymptotically AdS spacetime, the spinor energy and the observer energy. Chruściel et al. (J High Energy Phys 2006(11):084, 2006) proved the positivity of the spinor energy and derived important consequences among the related conserved quantities. We show that the positivity of the observer energy follows from the positivity of the spinor energy. A new notion called the “rest mass” of an asymptotically AdS spacetime is then defined by minimizing the observer energy and is shown to be evaluated in terms of the adjoint representation of the Lie algebra of Killing fields. It is proved that the rest mass has the desirable rigidity property that characterizes the AdS spacetime.
Using Large Ensembles of Control Variates for Variational Inference

Variational inference is increasingly being addressed with stochastic optimization. In this setting, the gradient's variance plays a crucial role in the optimization procedure, since high variance gradients lead to poor convergence. A popular approach used to reduce gradient's variance involves the use of control variates. Despite the good results obtained, control variates developed for variational inference are typically looked at in isolation. In this paper we clarify the large number of control variates that are available by giving a systematic view of how they are derived. We also present a Bayesian risk minimization framework in which the quality of a procedure for combining control variates is quantified by its effect on optimization convergence rates, which leads to a very simple combination rule. Results show that combining a large number of control variates this way significantly improves the convergence of inference over using the typical gradient estimators or a reduced number of control variates.
Cutoff on all Ramanujan graphs

We show that on every Ramanujan graph $${G}$$ , the simple random walk exhibits cutoff: when $${G}$$ has $${n}$$ vertices and degree $${d}$$ , the total-variation distance of the walk from the uniform distribution at time $${t=\frac{d}{d-2} \log_{d-1} n + s\sqrt{\log n}}$$ is asymptotically $${{\mathbb{P}}(Z > c \, s)}$$ where $${Z}$$ is a standard normal variable and $${c=c(d)}$$ is an explicit constant. Furthermore, for all $${1 \leq p \leq \infty}$$ , $${d}$$ -regular Ramanujan graphs minimize the asymptotic $${L^p}$$ -mixing time for SRW among all $${d}$$ -regular graphs. Our proof also shows that, for every vertex $${x}$$ in $${G}$$ as above, its distance from $${n-o(n)}$$ of the vertices is asymptotically $${\log_{d-1} n}$$ .
Comparative Causal Mediation and Relaxing the Assumption of No Mediator-Outcome Confounding: An Application to International Law and Audience Costs

Experiments often include multiple treatments, with the primary goal to compare the causal effects of those treatments. This study focuses on comparing the causal anatomies of multiple treatments through the use of causal mediation analysis. It proposes a novel set of comparative causal mediation (CCM) estimands that compare the mediation effects of different treatments via a common mediator. Further, it derives the properties of a set of estimators for the CCM estimands and shows these estimators to be consistent (or conservative) under assumptions that do not require the absence of unobserved confounding of the mediator–outcome relationship, which is a strong and nonrefutable assumption that must typically be made for consistent estimation of individual causal mediation effects. To illustrate the method, the study presents an original application investigating whether and how the international legal status of a foreign policy commitment can increase the domestic political “audience costs” that democratic governments suffer for violating such a commitment. The results provide novel evidence that international legalization can enhance audience costs via multiple causal channels, including by amplifying the perceived immorality of violating the commitment.