cssi/SciSciGPT-SciSciNet huggingface dataset:
Noncoherent compressive channel estimation for mm-wave massive MIMO

Millimeter (mm) wave massive MIMO has the potential for delivering orders of magnitude increases in mobile data rates, with compact antenna arrays providing narrow steerable beams for unprecedented levels of spatial reuse. A fundamental technical bottleneck, however, is rapid spatial channel estimation and beam adaptation in the face of mobility and blockage. Recently proposed compressive techniques which exploit the sparsity of mm wave channels are a promising approach to this problem, with overhead scaling linearly with the number of dominant paths and logarithmically with the number of array elements. Further, they can be implemented with RF beamforming with low-precision phase control. However, these methods make implicit assumptions on long-term phase coherence that are not satisfied by existing hardware. In this paper, we propose and evaluate a noncoherent compressive channel estimation technique which can estimate a sparse spatial channel based on received signal strength (RSS) alone, and is compatible with off-the-shelf hardware. The approach is based on cascading phase retrieval (i.e., recovery of complex-valued measurements from RSS measurements, up to a scalar multiple) with coherent compressive estimation. While a conventional cascade scheme would multiply two measurement matrices to obtain an overall matrix whose entries are in a continuum, a key novelty in our scheme is that we constrain the overall measurement matrix to be implementable using coarsely quantized pseudorandom phases, employing a virtual decomposition of the matrix into a product of measurement matrices for phase retrieval and compressive estimation. Theoretical and simulation results show that our noncoherent method scales almost as well with array size as its coherent counterpart, thus inheriting the scalability and low overhead of the latter.
Pairing between zeros and critical points of random polynomials with independent roots

Let $p_n$ be a random, degree $n$ polynomial whose roots are chosen independently according to the probability measure $\mu$ on the complex plane. For a deterministic point $\xi$ lying outside the support of $\mu$, we show that almost surely the polynomial $q_n(z):=p_n(z)(z - \xi)$ has a critical point at distance $O(1/n)$ from $\xi$. In other words, conditioning the random polynomials $p_n$ to have a root at $\xi$, almost surely forces a critical point near $\xi$. More generally, we prove an analogous result for the critical points of $q_n(z):=p_n(z)(z - \xi_1)\cdots (z - \xi_k)$, where $\xi_1, \ldots, \xi_k$ are deterministic. In addition, when $k=o(n)$, we show that the empirical distribution constructed from the critical points of $q_n$ converges to $\mu$ in probability as the degree tends to infinity, extending a recent result of Kabluchko.
Longitudinal phase space manipulation in energy recovering linac-driven free-electron lasers

Energy recovering [1] an electron beam after it has participated in a free-electron laser (FEL) interaction can be quite challenging because of the substantial FEL-induced energy spread and the energy anti-damping that occurs during deceleration. In the Jefferson Lab infrared FEL driver-accelerator, such an energy recovery scheme was implemented by properly matching the longitudinal phase space throughout the recirculation transport by employing the so-called energy compression scheme [2]- In the present paper, after presenting a single-particle dynamics approach of the method used to energy-recover the electron beam, we report on experimental validation of the method obtained by measurements of the so-called--compression efficiency--and--momentum compaction--lattice transfer maps at different locations in the recirculation transport line. We also compare these measurements with numerical tracking simulations.
Advanced geometrical constructs in a Pueblo ceremonial site, c 1200 CE

Abstract Summer 2015 marked the 100th anniversary of the excavation by J.W. Fewkes of the Sun Temple in Mesa Verde National Park, Colorado; an ancient complex prominently located atop a mesa, constructed by the ancestral Pueblo peoples approximately 800 years ago. While the D-shaped structure is generally recognized by modern Pueblo peoples as a ceremonial complex, the exact uses of the site are unknown, although the site has been shown to have key solar and lunar alignments. In this study, we examined the potential that the site was laid out using advanced knowledge of geometrical constructs. Using aerial imagery in conjunction with ground measurements, we performed a survey of key features of the site. We found apparent evidence that the ancestral Pueblo peoples laid out the site using the Golden rectangle, Pythagorean 3:4:5 triangles, equilateral triangles, and 45° right triangles. The survey also revealed that a single unit of measurement, L = 30.5 ± 0.5 cm, or one third of that, appeared to be associated with many key features of the site. Further study is needed to determine if this unit of measurement is common to other ancestral Pueblo sites, and also if geometric constructs are apparent at other sites. These findings represent the first potential quantitative evidence of knowledge of advanced geometrical constructs in a prehistoric North American society, which is particularly remarkable given that the ancestral Pueblo peoples had no written language or number system.
Latent voter model on locally tree-like random graphs

Abstract In the latent voter model, individuals who have just changed their choice have a latent period, which is exponential with rate λ , during which they will not change their opinion. We study this model on random graphs generated by a configuration model with degrees 3 ≤ d ( x ) ≤ M . We show that if the number of vertices n → ∞ and log n ≪ λ n ≪ n then there is a quasi-stationary state in which each opinion has probability ≈ 1 ∕ 2 and persists in this state for a time that is ≥ n m for any m ∞ .
Conditional End-to-End Audio Transforms.

We present an end-to-end method for transforming audio from one style to another. For the case of speech, by conditioning on speaker identities, we can train a single model to transform words spoken by multiple people into multiple target voices. For the case of music, we can specify musical instruments and achieve the same result. Architecturally, our method is a fully-differentiable sequence-to-sequence model based on convolutional and hierarchical recurrent neural networks. It is designed to capture long-term acoustic dependencies, requires minimal post-processing, and produces realistic audio transforms. Ablation studies confirm that our model can separate speaker and instrument properties from acoustic content at different receptive fields. Empirically, our method achieves competitive performance on community-standard datasets.
Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun

We present a simplified proof for a recent theorem by Junyan Cao and Mihai Paun, confirming a special case of Iitaka's conjecture: if $f \colon X\to Y$ is an algebraic fiber space, and if the Albanese mapping of $Y$ is generically finite over its image, then we have the inequality of Kodaira dimensions $\kappa (X)\geq \kappa (Y)+\kappa (F)$, where $F$ denotes a general fiber of $f$. We include a detailed survey of the main algebraic and analytic techniques, especially the construction of singular hermitian metrics on pushforwards of adjoint bundles (due to Berndtsson, Paun, and Takayama).
Resilience of locally routed network flows: More capacity is not always better

In this paper, we are concerned with the resilience of locally routed network flows with finite link capacities. In this setting, an external inflow is injected to the so-called origin nodes. The total inflow arriving at each node is routed locally such that none of the outgoing links are overloaded unless the node receives an inflow greater than its total outgoing capacity. A link irreversibly fails if it is overloaded or if there is no operational link in its immediate downstream to carry its flow. For such systems, resilience is defined as the minimum amount of reduction in the link capacities that would result in the failure of all the outgoing links of an origin node. We show that such networks do not necessarily become more resilient as additional capacity is built in the network. Moreover, when the external inflow does not exceed the network capacity, selective reductions of capacity at certain links can actually help averting the cascading failures, without requiring any change in the local routing policies. This is an attractive feature as it is often easier in practice to reduce the available capacity of some critical links than to add physical capacity or to alter routing policies, e.g., when such policies are determined by social behavior, as in the case of road traffic networks. The results can thus be used for real-time monitoring of distance-to-failure in such networks and devising a feasible course of actions to avert systemic failures.
Length, Weight, and Yield in Channel Catfish, Lake Diane, MI

Background: Channel catfish (Ictalurus punctatus) are important to both commercial aquaculture and recreational fisheries. Little published data is available on length-weight relationships of channel catfish in Michigan. Though there is no record of public or private stocking, channel catfish appeared in Lake Diane between 1984 and 1995 and it has developed into an excellent fishery.Materials and Methods: Sport angling provided 38 samples which were weighed and measured (fork length). Fillets were also weighed. The best fit estimates of parameters a and b in the model, W(L) = aLb, were obtained by both linear least-squares (LLS) regression (log(W) = log(a) + b log(L)) and non-linear least-squares (NLLS) regression. Best-fit parameters of an improved model, W(L) = (L/L1)^b, were also determined by NLLS regression; the parameter L1 is the typical length of a fish weighing 1 kg. The resulting best-fit parameters, parameter standard errors, and covariances are compared between the two models. The average relative weight for this sample of channel catfish is also determined, along with the typical meat yield obtained by filleting.Results: NLLS regression yields parameter estimates of b = 3.2293 and a = 0.00522. The improved model yields the same estimate for the exponent, b, and a length estimate (parameter L1) of 45.23 cm. Estimates of uncertainty and covariance are smaller for the improved model, but the correlation coefficient is r = 0.995 in both cases. LLS regression produced different parameter values, a = 0.01356 and b = 2.9726, and a smaller correlation coefficient, r = 0.980. On average, catfish in the sample weighed 106.0% of the standard weight, (Brown et al.) and the linear regression (no slope) of fillet yield vs. total weight suggests a typical fillet yield of 28.1% with r = 0.989.Conclusion: Most of the fish in the sample were above the standard weight, heavier than the 75th percentile for their length. Channel catfish are doing well in Lake Diane and the population is well matched to the food supply. Management should attempt to maintain current population levels. In this case, the improved length-weight model, W(L) = (L/L1)^b, provided lower uncertainties in parameter estimates and smaller covariance than the traditional model.
Einstein metrics and Yamabe invariants of weighted projective spaces

An orbifold version of the Hitchin-Thorpe inequality is used to prove that certain weighted projective spaces do not admit orbifold Einstein metrics. Also, several estimates for the orbifold Yamabe invariants of weighted projective spaces are proved.
Distributed Nonparametric Regression under Communication Constraints

This paper studies the problem of nonparametric estimation of a smooth function with data distributed across multiple machines. We assume an independent sample from a white noise model is collected at each machine, and an estimator of the underlying true function needs to be constructed at a central machine. We place limits on the number of bits that each machine can use to transmit information to the central machine. Our results give both asymptotic lower bounds and matching upper bounds on the statistical risk under various settings. We identify three regimes, depending on the relationship among the number of machines, the size of the data available at each machine, and the communication budget. When the communication budget is small, the statistical risk depends solely on this communication bottleneck, regardless of the sample size. In the regime where the communication budget is large, the classic minimax risk in the non-distributed estimation setting is recovered. In an intermediate regime, the statistical risk depends on both the sample size and the communication budget.
The Minimum Size of Signed Sumsets

For a finite abelian group $G$ and positive integers $m$ and $h$, we let $$\rho(G, m, h) = \min \{ |hA| \; : \; A \subseteq G, |A|=m\}$$ and $$\rho_{\pm} (G, m, h) = \min \{ |h_{\pm} A| \; : \; A \subseteq G, |A|=m\},$$ where $hA$ and $h_{\pm} A$ denote the $h$-fold sumset and the $h$-fold signed sumset of $A$, respectively. The study of $\rho(G, m, h)$ has a 200-year-old history and is now known for all $G$, $m$, and $h$. Here we prove that $\rho_{\pm}(G, m, h)$ equals $\rho (G, m, h)$ when $G$ is cyclic, and establish an upper bound for $\rho_{\pm} (G, m, h)$ that we believe gives the exact value for all $G$, $m$, and $h$.
On the mathematics and physics of high genus invariants of $[C^3/Z_3]$

This paper wishes to foster communication between mathematicians and physicists working in mirror symmetry and orbifold Gromov-Witten theory. We provide a reader friendly review of the physics computation in [arXiv:hep-th/0607100] that predicts Gromov-Witten invariants of [C^3/Z_3] in arbitrary genus, and of the mathematical framework for expressing these invariants as Hodge integrals. Using geometric properties of the Hodge classes, we compute the unpointed invariants for g=2,3, thus providing the first high genus mathematical check of the physics predictions.
Linear-Memory and Decomposition-Invariant Linearly Convergent Conditional Gradient Algorithm for Structured Polytopes

Recently, several works have shown that natural modifications of the classical conditional gradient method (aka Frank-Wolfe algorithm) for constrained convex optimization, provably converge with a linear rate when the feasible set is a polytope, and the objective is smooth and strongly-convex. However, all of these results suffer from two significant shortcomings: i) large memory requirement due to the need to store an explicit convex decomposition of the current iterate, and as a consequence, large running-time overhead per iteration ii) the worst case convergence rate depends unfavorably on the dimension In this work we present a new conditional gradient variant and a corresponding analysis that improves on both of the above shortcomings. In particular, both memory and computation overheads are only linear in the dimension, and in addition, in case the optimal solution is sparse, the new convergence rate replaces a factor which is at least linear in the dimension in previous works, with a linear dependence on the number of non-zeros in the optimal solution At the heart of our method, and corresponding analysis, is a novel way to compute decomposition-invariant away-steps. While our theoretical guarantees do not apply to any polytope, they apply to several important structured polytopes that capture central concepts such as paths in graphs, perfect matchings in bipartite graphs, marginal distributions that arise in structured prediction tasks, and more. Our theoretical findings are complemented by empirical evidence that shows that our method delivers state-of-the-art performance.
HIGHER RANK STABLE PAIRS ON K3 SURFACES

We define and compute higher rank analogs of Pandharipande– Thomas stable pair invariants in primitive classes for K3 surfaces. Higher rank stable pair invariants for Calabi–Yau threefolds have been defined by Sheshmani [26, 27] using moduli of pairs of the form O^n →F for F purely one-dimensional and computed via wall-crossing techniques. These invariants may be thought of as virtually counting embedded curves decorated with a (n − 1)- dimensional linear system. We treat invariants counting pairs O^n → E on a K3 surface for E an arbitrary stable sheaf of a fixed numerical type (“coherent systems” in the language of [16]) whose first Chern class is primitive, and fully compute them geometrically. The ordinary stable pair theory of K3 surfaces is treated by [22]; there they prove the KKV conjecture in primitive classes by showing the resulting partition functions are governed by quasimodular forms. We prove a “higher” KKV conjecture by showing that our higher rank partition functions are modular forms.
On a theorem of Bishop and commutants of Toeplitz operators in $\mathbb{C}^n$

We prove an approximation theorem on a class of domains in $$\mathbb {C}^n$$ on which the $$\overline{\partial }$$ -problem is solvable in $$L^{\infty }$$ . Furthermore, as a corollary, we obtain a version of the Axler–Cuckovic–Rao theorem in higher dimensions.
The complexity of the classification problem of continua

We prove that the homeomorphism problem for connected compact metric spaces is Borel bireducible with a universal orbit equivalence relation induced by a Borel action of a Polish group.
Spatial-mode-interaction-induced dispersive-waves and their active tuning in microresonators

The nonlinear propagation of optical pulses in dielectric waveguides and resonators induces a wide range of remarkable interactions. One example is dispersive-wave generation, the optical analog of Cherenkov radiation. These waves play an essential role in the fiber-optic spectral broadeners used in spectroscopy and metrology. Dispersive waves form when a soliton pulse begins to radiate power as a result of higher-order dispersion. Recently, dispersive-wave generation in microcavities has been reported by phase matching the waves to dissipative Kerr solitons. Here, it is shown that spatial mode interactions within a microcavity can be used to induce dispersive waves. The soliton self-frequency shift is also shown to enable fine tuning control of the dispersive-wave frequency. Both this mechanism and spatial mode interactions allow spectral control of these important waves in microresonators.
Iterative Variable-Blaschke Factorization

Blaschke factorization allows us to write any holomorphic function F as a formal series $$\begin{aligned} F = a_0 B_0 + a_1 B_0 B_1 + a_2 B_0 B_1 B_2 + \cdots \end{aligned}$$ where $$a_i \in \mathbb {C}$$ and $$B_i$$ is a Blaschke product. We introduce a more general variation of the canonical Blaschke product and study the resulting formal series. We prove that the series converges exponentially in the Dirichlet space given a suitable choice of parameters if F is a polynomial and we provide explicit conditions under which this convergence can occur. Finally, we derive analogous properties of Blaschke factorization using our new variable framework.
Fractal and multifractal analysis of the rise of oxygen in Earth’s early atmosphere

Abstract The rise of oxygen in Earth’s atmosphere that occurred 2.4–2.2 billion years ago is known as the Earth’s Great Oxidation, and its impact on the development of life on Earth has been profound. Thereafter, the increase in Earth’s oxygen level persisted, though at a more gradual pace. The proposed underlying mathematical models for these processes are based on physical parameters whose values are currently not well-established owing to uncertainties in geological and biological data. In this paper, a previously developed model of Earth’s atmosphere is modified by adding different strengths of noise to account for the parameters’ uncertainties. The effects of the noise on the time variations of oxygen, carbon and methane for the early Earth are investigated by using fractal and multifractal analysis. We show that the time variations following the Great Oxidation cannot properly be described by a single fractal dimension because they exhibit multifractal characteristics. The obtained results demonstrate that the time series as obtained exhibit multifractality caused by long-range time correlations.
Maximum Selection and Ranking under Noisy Comparisons

We consider $(\epsilon,\delta)$-PAC maximum-selection and ranking for general probabilistic models whose comparisons probabilities satisfy strong stochastic transitivity and stochastic triangle inequality. Modifying the popular knockout tournament, we propose a maximum-selection algorithm that uses $\mathcal{O}\left(\frac{n}{\epsilon^2}\log \frac{1}{\delta}\right)$ comparisons, a number tight up to a constant factor. We then derive a general framework that improves the performance of many ranking algorithms, and combine it with merge sort and binary search to obtain a ranking algorithm that uses $\mathcal{O}\left(\frac{n\log n (\log \log n)^3}{\epsilon^2}\right)$ comparisons for any $\delta\ge\frac1n$, a number optimal up to a $(\log \log n)^3$ factor.
A wonderful embedding of the loop group

I describe the wonderful compactification of loop groups. These compactifications are obtained by adding normal-crossing boundary divisors to the group LG of loops in a reductive group G (or more accurately, to the semi-direct product C×⋉LG) in a manner equivariant for the left and right C×⋉LG-actions. The analogue for a torus group T is the theory of toric varieties; for an adjoint group G, this is the wonderful compactification of De Concini and Procesi. The loop group analogue is suggested by work of Faltings in relation to the compactification of moduli of G-bundles over nodal curves.
Over-rotation numbers for unimodal maps

We introduce twist unimodal maps of the interval and describe their structure. Sufficient conditions for the growth of over-rotation interval in families of maps are given.
Immersed self-shrinkers

We construct infinitely many complete, immersed self-shrinkers with rotational symmetry for each of the following topological types: the sphere, the plane, the cylinder, and the torus.
Identifying the Canonical Component for the Whitehead Link

In this paper we determine topologically the canonical component of the SL2(C) character variety of the Whitehead link complement.
Bottleneck Conditional Density Estimation

We introduce a new framework for training deep generative models for high-dimensional conditional density estimation. The Bottleneck Conditional Density Estimator (BCDE) is a variant of the conditional variational autoencoder (CVAE) that employs layer(s) of stochastic variables as the bottleneck between the input $x$ and target $y$, where both are high-dimensional. Crucially, we propose a new hybrid training method that blends the conditional generative model with a joint generative model. Hybrid blending is the key to effective training of the BCDE, which avoids overfitting and provides a novel mechanism for leveraging unlabeled data. We show that our hybrid training procedure enables models to achieve competitive results in the MNIST quadrant prediction task in the fully-supervised setting, and sets new benchmarks in the semi-supervised regime for MNIST, SVHN, and CelebA.
A Stabilized Separation of Variables Method for the Modified Biharmonic Equation

The modified biharmonic equation is encountered in a variety of application areas, including streamfunction formulations of the Navier–Stokes equations. We develop a separation of variables representation for this equation in polar coordinates, for either the interior or exterior of a disk, and derive a new class of special functions which makes the approach stable. We discuss how these functions can be used in conjunction with fast algorithms to accelerate the solution of the modified biharmonic equation or the “bi-Helmholtz” equation in more complex geometries.
Super-rigidity for CR embeddings of real hypersurfaces into hyperquadrics☆

We consider holomorphic mappings sending a given Levi-nondegenerate pseudoconcave hypersurface M in into a nondegenerate hyperquadric of the same signature in and show that if M is sufficiently close to a hyperquadric in a certain sense, then any two such mappings differ only by an automorphism of the hyperquadric.
Reading between the pixels: Photographic steganography for camera display messaging

We exploit human color metamers to send light-modulated messages decipherable by cameras, but camouflaged to human vision. These time-varying messages are concealed in ordinary images and videos. Unlike previous methods which rely on visually obtrusive intensity modulation, embedding with color reduces visible artifacts. The mismatch in human and camera spectral sensitivity creates a unique opportunity for hidden messaging. Each color pixel in an electronic display image is modified by shifting the base color along a particular color gradient. The challenge is to find the set of color gradients that maximizes camera response and minimizes human response. Our approach does not require a priori measurement of these sensitivity curves. We learn an ellipsoidal partitioning of the 6-dimensional space of base colors and color gradients. This partitioning creates metamer sets defined by the base color of each display pixel and the corresponding color gradient for message encoding. We sample from the learned metamer sets to find optimal color steps for arbitrary base colors. Ordinary displays and cameras are used, so there is no need for high speed cameras or displays. Our primary contribution is a method to map pixels in an arbitrary image to metamer pairs for steganographic camera-display messaging.
Picard Groups of Moduli Spaces of Curves with Symmetry

We study the Picard groups of moduli spaces of smooth complex projective curves that have a group of automorphisms with a prescribed topological action. One of our main tools is the theory of symmetric mapping class groups. In the first part of the paper, we show that, under mild restrictions, the moduli spaces of smooth curves with an abelian group of automorphisms of a fixed topological type have finitely generated Picard groups. In certain special cases, we are able to compute them exactly. In the second part of the paper, we show that finite abelian level covers of the hyperelliptic locus in the moduli space of smooth curves have finitely generated Picard groups. We also compute the Picard groups of the moduli spaces of hyperelliptic curves of compact type.
Off-Ramp Coupling Conditions Devoid of Spurious Blocking and Re-Routing:

When modeling vehicular traffic flow on highway networks via macroscopic models, suitable coupling conditions at the network nodes are crucial. Frequently, the evolution of traffic flow on each network edge is described in a lane-averaged fashion using a single-class Lighthill-Whitham-Richards model. At off-ramps, split ratios (i.e., what percentage of traffic exits the highway) are prescribed that can be drawn from historical data. In this situation, classic FIFO coupling conditions yield unrealistic results, in that a clogged off-ramp yields zero flux through the node. As a remedy, non-FIFO conditions have been proposed. However, as we demonstrate here, those lead to spurious re-routing of vehicles. A new coupling model, FIFO with queue (FIFOQ), is presented which preserves the desirable properties of non-FIFO models while not leading to any spurious re-routing.
Spherical space forms revisited

We give a simplified proof of J. A. Wolf’s classification of groups that can act freely and isometrically on a round sphere of some dimension. We also remove a small amount of redundancy from his list. The classification is the same as the classification of Frobenius complements in finite group theory. In chapters 4–7 of his famous Spaces of Constant Curvature [7], J. A. Wolf classified the spherical space forms: connected Riemannian manifolds locally isometric to the n-sphere S. By passing to the action of the fundamental group on the universal covering space, this is equivalent to classifying the possible free isometric actions of finite groups on S. Then, by embedding S in Euclidean space, this is equivalent to classifying the real representations of finite groups that are “free” in the sense that no element except the identity fixes any vector except 0. This allowed Wolf to use the theory of finite groups and their representations. In this paper we classify anew the finite groups that can act freely and isometrically on spheres. Wolf’s main result on this was a list of all such groups, as presentations (theorems 6.1.11 and 6.3.1 of [7]). Our approach to his theorem relies on a trick (lemma 3.10) that leads to the most interesting example, the binary icosahedral group, with very little case analysis and no complicated character-theoretic inequalities. There are some finite groups which appear several times on Wolf’s list, because different presentations can define isomorphic groups (see example 5.1). Therefore we have classified the possible groups in an “intrinsic” manner. Namely, a finite group G acts freely and isometrically on a sphere if and only if it has one of 6 possible “structures”, in which case it has a unique such “structure”, up to conjugation. (See theorems 1.1 and 1.2.) This approach makes it easy to enumerate the possible G without redundancy, in terms of a fairly simple set of invariants. Namely: a type I–VI, two numbers |G| and a, and a subgroup of Date: 16 November 2015. 1991 Mathematics Subject Classification. 20B10(57S17, 57S25).
Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism

To any finite group Γ⊂Sp(V) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ of the algebra ℂ[V]#Γ, smash product of Γ with the polynomial algebra on V. The parameter κ runs over points of ℙ r , where r=number of conjugacy classes of symplectic reflections in $Γ$. The algebra Hκ, called a symplectic reflection algebra, is related to the coordinate ring of a Poisson deformation of the quotient singularity V/Γ. This leads to a symplectic analogue of McKay correspondence, which is most complete in case of wreath-products. If Γ is the Weyl group of a root system in a vector space ? and V=?⊕?*, then the algebras Hκ are certain ‘rational’ degenerations of the double affine Hecke algebra introduced earlier by Cherednik. Let $Γ=S n , the Weyl group of ?=?? n . We construct a 1-parameter deformation of the Harish-Chandra homomorphism from ?(?)?, the algebra of invariant polynomial differential operators on ?? n , to the algebra of S n -invariant differential operators with rational coefficients on the space ℂ n of diagonal matrices. The second order Laplacian on ? goes, under the deformed homomorphism, to the Calogero-Moser differential operator on ℂ n , with rational potential. Our crucial idea is to reinterpret the deformed Harish-Chandra homomorphism as a homomorphism: ?(?)? ↠ spherical subalgebra in Hκ, where Hκ is the symplectic reflection algebra associated to the group Γ=S n . This way, the deformed Harish-Chandra homomorphism becomes nothing but a description of the spherical subalgebra in terms of ‘quantum’ Hamiltonian reduction. In the ‘classical’ limit κ→∞, our construction gives an isomorphism between the spherical subalgebra in H∞ and the coordinate ring of the Calogero-Moser space. We prove that all simple H∞-modules have dimension n!, and are parametrised by points of the Calogero-Moser space. The family of these modules forms a distinguished vector bundle on the Calogero-Moser space, whose fibers carry the regular representation of S n . Moreover, we prove that the algebra $H∞ is isomorphic to the endomorphism algebra of that vector bundle.
Radial symmetry of large solutions of semilinear elliptic equations with convection

We study the radial symmetry of large solutions of the semilinear elliptic problem Δu + ∇h · ∇u = f (∣x∣, u), and we provide sharp conditions under which the problem has a radial solution. The result is independent of the rate of growth of the solution at infinity.
Perverse bundles and Calogero-Moser spaces

We present a simple description of moduli spaces of torsion-free 𝒟-modules (𝒟-bundles) on general smooth complex curves, generalizing the identification of the space of ideals in the Weyl algebra with Calogero–Moser quiver varieties. Namely, we show that the moduli of 𝒟-bundles form twisted cotangent bundles to moduli of torsion sheaves on X, answering a question of Ginzburg. The corresponding (untwisted) cotangent bundles are identified with moduli of perverse vector bundles on T*X, which contain as open subsets the moduli of framed torsion-free sheaves (the Hilbert schemes T*X[n] in the rank-one case). The proof is based on the description of the derived category of 𝒟-modules on X by a noncommutative version of the Beilinson transform on P1.
Learning One Convolutional Layer with Overlapping Patches

We give the first provably efficient algorithm for learning a one hidden layer convolutional network with respect to a general class of (potentially overlapping) patches. Additionally, our algorithm requires only mild conditions on the underlying distribution. We prove that our framework captures commonly used schemes from computer vision, including one-dimensional and two-dimensional "patch and stride" convolutions. Our algorithm-- $Convotron$ -- is inspired by recent work applying isotonic regression to learning neural networks. Convotron uses a simple, iterative update rule that is stochastic in nature and tolerant to noise (requires only that the conditional mean function is a one layer convolutional network, as opposed to the realizable setting). In contrast to gradient descent, Convotron requires no special initialization or learning-rate tuning to converge to the global optimum. We also point out that learning one hidden convolutional layer with respect to a Gaussian distribution and just $one$ disjoint patch $P$ (the other patches may be arbitrary) is $easy$ in the following sense: Convotron can efficiently recover the hidden weight vector by updating $only$ in the direction of $P$.
Stratification and enumeration of Boolean functions by canalizing depth

Abstract Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The canalizing depth of a function describes how many canalizing variables can be recursively “picked off”, until a non-canalizing function remains. In this paper, we show how every Boolean function has a unique algebraic form involving extended monomial layers and a well-defined core polynomial. This generalizes recent work on the algebraic structure of nested canalizing functions, and it yields a stratification of all Boolean functions by their canalizing depth. As a result, we obtain closed formulas for the number of n -variable Boolean functions with depth k , which simultaneously generalizes enumeration formulas for canalizing, and nested canalizing functions.
Equivariant complete Segal spaces

In this paper we give a model for equivariant $(\infty, 1)$-categories. We modify an approach of Shimakawa for equivariant $\Gamma$-spaces to the setting of simplicial spaces. We then adapt Rezk's Segal and completeness conditions to fit with this setting.
On rationalizing divisors

Rational pairs generalize the notion of rational singularities to reduced pairs (X, D). In this paper we deal with the problem of determining whether a normal variety X has a rationalizing divisor, i.e., a reduced divisor D such that (X, D) is a rational pair. We give a criterion for cones to have a rationalizing divisor, and relate the existence of such a divisor to the locus of rational singularities of a variety.
Truncated Back-propagation for Bilevel Optimization

Bilevel optimization has been recently revisited for designing and analyzing algorithms in hyperparameter tuning and meta learning tasks. However, due to its nested structure, evaluating exact gradients for high-dimensional problems is computationally challenging. One heuristic to circumvent this difficulty is to use the approximate gradient given by performing truncated back-propagation through the iterative optimization procedure that solves the lower-level problem. Although promising empirical performance has been reported, its theoretical properties are still unclear. In this paper, we analyze the properties of this family of approximate gradients and establish sufficient conditions for convergence. We validate this on several hyperparameter tuning and meta learning tasks. We find that optimization with the approximate gradient computed using few-step back-propagation often performs comparably to optimization with the exact gradient, while requiring far less memory and half the computation time.
Detecting speech act types in developer question/answer conversations during bug repair

This paper targets the problem of speech act detection in conversations about bug repair. We conduct a ``Wizard of Oz'' experiment with 30 professional programmers, in which the programmers fix bugs for two hours, and use a simulated virtual assistant for help. Then, we use an open coding manual annotation procedure to identify the speech act types in the conversations. Finally, we train and evaluate a supervised learning algorithm to automatically detect the speech act types in the conversations. In 30 two-hour conversations, we made 2459 annotations and uncovered 26 speech act types. Our automated detection achieved 69% precision and 50% recall. The key application of this work is to advance the state of the art for virtual assistants in software engineering. Virtual assistant technology is growing rapidly, though applications in software engineering are behind those in other areas, largely due to a lack of relevant data and experiments. This paper targets this problem in the area of developer Q/A conversations about bug repair.
Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks

Deep neural networks, in particular convolutional neural networks, have become highly effective tools for compressing images and solving inverse problems including denoising, inpainting, and reconstruction from few and noisy measurements. This success can be attributed in part to their ability to represent and generate natural images well. Contrary to classical tools such as wavelets, image-generating deep neural networks have a large number of parameters---typically a multiple of their output dimension---and need to be trained on large datasets. In this paper, we propose an untrained simple image model, called the deep decoder, which is a deep neural network that can generate natural images from very few weight parameters. The deep decoder has a simple architecture with no convolutions and fewer weight parameters than the output dimensionality. This underparameterization enables the deep decoder to compress images into a concise set of network weights, which we show is on par with wavelet-based thresholding. Further, underparameterization provides a barrier to overfitting, allowing the deep decoder to have state-of-the-art performance for denoising. The deep decoder is simple in the sense that each layer has an identical structure that consists of only one upsampling unit, pixel-wise linear combination of channels, ReLU activation, and channelwise normalization. This simplicity makes the network amenable to theoretical analysis, and it sheds light on the aspects of neural networks that enable them to form effective signal representations.
A Saak Transform Approach to Efficient, Scalable and Robust Handwritten Digits Recognition

An efficient, scalable and robust approach to the handwritten digits recognition problem based on the Saak transform is proposed in this work. First, multi-stage Saak transforms are used to extract a family of joint spatial-spectral representations of input images. Then, the Saak coefficients are used as features and fed into the SVM classifier for the classification task. In order to control the size of Saak coefficients, we adopt a lossy Saak transform that uses the principal component analysis (PCA) to select a smaller set of transform kernels. The handwritten digits recognition problem is well solved by the convolutional neural network (CNN) such as the LeNet-5. We conduct a comparative study on the performance of the LeNet-5 and the Saak-transform-based solutions in terms of scalability and robustness as well as the efficiency of lossless and lossy Saak transforms under a comparable accuracy level.
Identifying Species Network Features from Gene Tree Quartets Under the Coalescent Model

We show that many topological features of level-1 species networks are identifiable from the distribution of the gene tree quartets under the network multi-species coalescent model. In particular, every cycle of size at least 4 and every hybrid node in a cycle of size at least 5 are identifiable. This is a step toward justifying the inference of such networks which was recently implemented by Solis-Lemus and Ane. We show additionally how to compute quartet concordance factors for a network in terms of simpler networks, and explore some circumstances in which cycles of size 3 and hybrid nodes in 4-cycles can be detected.
A comparison of two complexes

Abstract We prove the conjecture of Lusztig in [5, Section 4] . Given a reductive group over F q ‾ [ e ] / ( e r ) for some r ≥ 2 , there is a notion of a character sheaf defined in [4, Section 8] . On the other hand, there is also a geometric analogue of the character constructed by Gerardin [2] . The conjecture in [5, Section 4] states that the two constructions are equivalent, which Lusztig also proved for r = 2 , 3 , 4 . Here we generalize his method to prove this conjecture for general r. As a corollary we prove that the characters derived from these two complexes are equal.
Social Influence Makes Self-Interested Crowds Smarter: An Optimal Control Perspective

It is very common to observe crowds of individuals solving similar problems with similar information in a largely independent manner. We argue here that crowds can become “smarter,” i.e., more efficient and robust, by partially following the average opinion. This observation runs counter to the widely accepted claim that the wisdom of crowds deteriorates with social influence. The key difference is that individuals are self-interested, and hence, can reject feedback that does not improve performance. We propose a control-theoretic methodology to compute the degree of social influence, i.e., the level to which one accepts the population feedback, that optimizes performance. We conducted an experiment with human subjects ( $N=194$ ), where the participants were first asked to solve an optimization problem independently, i.e., with no social influence. Our theoretical methodology estimates a 30% degree of social influence to be optimal, resulting in a 29% improvement in the crowd’s performance. We then let the same cohort solve a new problem and have access to the average opinion. Surprisingly, we find the average degree of social influence in the cohort to be 32% with a 29% improvement in performance: In other words, the crowd self-organized into a near-optimal setting. We believe this new paradigm for making crowds “smarter” has the potential for significant impact on a diverse set of fields from population health to government planning. We include a case study to show how a crowd of states potentially could collectively learn the level of taxation and expenditure that optimizes economic growth.
Regularity of Milne problem with geometric correction in 3D

Consider the Milne problem with geometric correction in a 3D convex domain. Via bootstrapping arguments, we establish W1,∞-regularity for its solutions. Combined with a uniform L6-estimate, such regularity leads to the validity of diffusive expansion for the neutron transport equation with diffusive boundary conditions.
A sharp bilinear restriction estimate for paraboloids

Recently Wolff [W3] obtained a sharp L 2 bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of “elliptic surfaces” such as paraboloids. Except for an endpoint, this answers a conjecture of Machedon and Klainerman, and also improves upon the known restriction theory for the paraboloid and sphere.
Multi-dueling Bandits with Dependent Arms

The dueling bandits problem is an online learning framework for learning from pairwise preference feedback, and is particularly well-suited for modeling settings that elicit subjective or implicit human feedback. In this paper, we study the problem of multi-dueling bandits with dependent arms, which extends the original dueling bandits setting by simultaneously dueling multiple arms as well as modeling dependencies between arms. These extensions capture key characteristics found in many real-world applications, and allow for the opportunity to develop significantly more efficient algorithms than were possible in the original setting. We propose the \selfsparring algorithm, which reduces the multi-dueling bandits problem to a conventional bandit setting that can be solved using a stochastic bandit algorithm such as Thompson Sampling, and can naturally model dependencies using a Gaussian process prior. We present a no-regret analysis for multi-dueling setting, and demonstrate the effectiveness of our algorithm empirically on a wide range of simulation settings.
Detecting LTE-U duty cycling misbehavior for fair sharing with Wi-Fi in shared bands

Coexistence of Wi-Fi and LTE Unlicensed (LTE-U) in shared or unlicensed bands has drawn growing attention from both academia and industry. An important consideration is fairness between Wi-Fi and duty cycled LTE-U, which is often defined in terms of channel access time, as adopted by the LTE-U Forum. Despite many studies on duty cycle adaptation design for fair sharing, one crucial fact has often been neglected: LTE-U systems unilaterally control LTE-U duty cycles; hence, as selfinterested users, they have incentives to misbehave, e.g., transmitting with a larger duty cycle that exceeds a given limit, so as to gain a greater share in channel access time and throughput. In this paper, we propose a scheme that allows the spectrum manager managing the shared bands to estimate the duty cycle of a target LTE-U cell based on PHY layer observations from a nearby Wi-Fi AP, without interrupting normal Wi-Fi operations. We further propose a thresholding scheme to detect duty cycling misbehavior (i.e., determining if the duty cycle exceeds the assigned limit), and analyze its performance in terms of detection and false alarm probabilities. The proposed schemes are implemented in ns3 and evaluated with extensive simulations. Our results show that the proposed scheme provides an estimate within ± 1% of the true duty cycle, and detects misbehavior with a duty cycle 2.8% higher than the limit with a detection probability of at least 95%, while keeping the false alarm probability less than or equal to 1%.
Excluding subdivisions of bounded degree graphs

Abstract Let H be a fixed graph. What can be said about graphs G that have no subgraph isomorphic to a subdivision of H? Grohe and Marx proved that such graphs G satisfy a certain structure theorem that is not satisfied by graphs that contain a subdivision of a (larger) graph H 1 . Dvořak found a clever strengthening—his structure is not satisfied by graphs that contain a subdivision of a graph H 2 , where H 2 has “similar embedding properties” as H. Building upon Dvořak's theorem, we prove that said graphs G satisfy a similar structure theorem. Our structure is not satisfied by graphs that contain a subdivision of a graph H 3 that has similar embedding properties as H and has the same maximum degree as H. This will be important in a forthcoming application to well-quasi-ordering.