cssi/SciSciGPT-SciSciNet huggingface dataset:
Integration in algebraically closed valued fields

The first two steps of the construction of motivic integration in the fundamental work of Hrushovski and Kazhdan (2006) [8] have been presented in Yin (2010) [12]. In this paper we present the final third step. As in Yin (2010) [12], we limit our attention to the theory of algebraically closed valued fields of pure characteristic 0 expanded by a (V F,Γ)-generated substructure S in the language LRV. A canonical description of the kernel of the homomorphism L is obtained.
Ultralight repulsive dark matter and BEC

Abstract Ultralight scalar dark matter with mass at or below the eV scale and pressure from repulsive self-interaction could form a Bose–Einstein condensate in the early Universe and maybe in galaxies as well. It has been suggested to be a possible solution to the cusp/core problem or even to explain MOND phenomenology. In this paper, I initiate a study of possible self-interactions of ultralight scalar dark matter from the particle physics point of view. To protect its mass, the scalar dark matter is identified as a pseudo Nambu–Goldstone boson (pNGB). Quite a few pNGB models with different potentials such as the QCD axion and the dilaton lead to attractive self-interactions. Yet if an axion is a remnant of a 5D gauged U ( 1 ) symmetry, its self-interactions could be repulsive provided the masses and charges of the 5D matter contributing to its potential satisfy certain constraints. Collective symmetry breaking could also lead to a repulsive self-interaction yet with too large a strength that is ruled out by Bullet Cluster constraints. I also discuss cosmological and astrophysical constraints on ultralight repulsive dark matter in terms of a parametrization motivated by particle physics considerations.
A class of permutation binomials over finite fields

Let q be a prime power and f=tx+x2q−1, where t∈Fq⁎. It was recently conjectured that f is a permutation polynomial of Fq2 if and only if one of the following holds: (i) t=1, q≡1(mod4); (ii) t=−3, q≡±1(mod12); (iii) t=3, q≡−1(mod6). We confirm this conjecture in the present paper.
Riemannian Manifolds with Positive Yamabe Invariant and Paneitz Operator

For a Riemannian manifold with dimension at least six, we prove that the existence of a conformal metric with positive scalar and Q curvature is equivalent to the positivity of both the Yamabe invariant and the Paneitz operator.
Distribution‐preserving k‐anonymity

Preserving the privacy of individuals by protecting their sensitive attributes is an important consideration during microdata release. However, it is equally important to preserve the quality or ut...
Extension of PCA to Higher Order Data Structures: An Introduction to Tensors, Tensor Decompositions, and Tensor PCA

The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher order data with multiple aspects and high dimensionality. Data in the form of multidimensional arrays, also referred to as tensors, arise in a variety of applications including chemometrics, hyperspectral imaging, high-resolution videos, neuroimaging, biometrics, and social network analysis. Early multiway data analysis approaches reformatted such tensor data as large vectors or matrices and then resorted to dimensionality reduction methods developed for classical two-way analysis such as principal component analysis (PCA). However, one cannot discover hidden components within multiway data using conventional PCA. To this end, tensor decomposition methods which are flexible in the choice of the constraints and that extract more general latent components have been proposed. In this paper, we review the major tensor decomposition methods with a focus on problems targeted by classical PCA. In particular, we present tensor methods that aim to solve three important challenges typically addressed by PCA: dimensionality reduction, i.e., low-rank tensor approximation; supervised learning, i.e., learning linear subspaces for feature extraction; and robust low-rank tensor recovery. We also provide experimental results to compare different tensor models for both dimensionality reduction and supervised learning applications.
Numerical and Experimental Studies on the Separation Topology of the MVG Controlled Flow at M=2.5

In this paper, the implicitly implemented LES method and fifth order bandwidthoptimized WENO scheme are used to make comprehensive studies on the separation topology of the MVG controlled flow at M=2.5 and Reθ θ θ θ=5760. Experiments are also made to verify the prediction of the computation. Analyses are conducted on three categories of the topology: the surface separation, cross-section separation and the three dimensional structure of the vortices. A complete description about the separation topology and a series of new findings are obtained. Among them, a pair of spiral point is first predicted by the computation and verified by the experiment. A corresponding new vortex model with 7 vortex tubes is presented also.
Shockwaves from the Operator Product Expansion

We clarify and further explore the CFT dual of shockwave geometries in Anti-de Sitter. The shockwave is dual to a CFT state produced by a heavy local operator inserted at a complex point. It can also be created by light operators, smeared over complex positions. We describe the dictionary in both cases, and compare to various calculations, old and new. In CFT, we analyze the operator product expansion in the Regge limit, and find that the leading contribution is exactly the shockwave operator, ∫ duhuu, localized on a bulk geodesic. For heavy sources this is a simple consequence of conformal invariance, but for light operators it involves a smearing procedure that projects out certain double-trace contributions to the OPE. We revisit causality constraints in large-N CFT from this perspective, and show that the chaos bound in CFT coincides with a bulk condition proposed by Engelhardt and Fischetti. In particular states, this reproduces known constraints on CFT 3-point couplings, and confirms some assumptions about double-trace operators made in previous work.
Adversarial Training for Probabilistic Spiking Neural Networks

Classifiers trained using conventional empirical risk minimization or maximum likelihood methods are known to suffer dramatic performance degradations when tested over examples adversarially selected based on knowledge of the clas-sifier's decision rule. Due to the prominence of Artificial Neural Networks (ANNs) as classifiers, their sensitivity to adversarial examples, as well as robust training schemes, have been recently the subject of intense investigation. In this paper, for the first time, the sensitivity of spiking neural networks (SNNs), or third-generation neural networks, to adversarial examples is studied. The study considers rate and time encoding, as well as rate and first-to-spike decoding. Furthermore, a robust training mechanism is proposed that is demonstrated to enhance the performance of SNNs under white-box attacks.
Classification of expansive attractors on surfaces

We prove the conjecture of F. Rodriguez Hertz and J. Rodriguez Hertz [Expansive attractors on surfaces. Ergod. Th. & Dynam. Sys. 26 (1) (2006), 291–302; MR 2201950(2006j:37049)] that every non-trivial transitive expansive attractor of a homeomorphism of a compact surface is a derived from pseudo-Anosov attractor.
Programmatically Interpretable Reinforcement Learning

We present a reinforcement learning framework, called Programmatically Interpretable Reinforcement Learning (PIRL), that is designed to generate interpretable and verifiable agent policies. Unlike the popular Deep Reinforcement Learning (DRL) paradigm, which represents policies by neural networks, PIRL represents policies using a high-level, domain-specific programming language. Such programmatic policies have the benefits of being more easily interpreted than neural networks, and being amenable to verification by symbolic methods. We propose a new method, called Neurally Directed Program Search (NDPS), for solving the challenging nonsmooth optimization problem of finding a programmatic policy with maximal reward. NDPS works by first learning a neural policy network using DRL, and then performing a local search over programmatic policies that seeks to minimize a distance from this neural "oracle". We evaluate NDPS on the task of learning to drive a simulated car in the TORCS car-racing environment. We demonstrate that NDPS is able to discover human-readable policies that pass some significant performance bars. We also show that PIRL policies can have smoother trajectories, and can be more easily transferred to environments not encountered during training, than corresponding policies discovered by DRL.
The Schur–Horn theorem for operators with three point spectrum

Abstract We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with three points in the spectrum. Our result gives a Schur–Horn theorem for operators with three point spectrum analogous to Kadisonʼs Pythagorean theorem and carpenterʼs theorem, which characterize the diagonals of orthogonal projections.
Interactions of solitary pulses of E. coli in a one-dimensional nutrient gradient

Abstract We study the interaction of two bacterial pulses in a one-dimensional nutrient gradient. Simulations of the Keller–Segel chemotaxis model reveal two qualitatively distinct behaviors. As the two pulses approach one another, they either combine and move as a single pulse or, surprisingly, change direction and begin moving away from each other in the direction from which they originated. To study this phenomenon, we introduce a heuristic approximation to the spatial profiles of the pulses in the Keller–Segel model and derive a system of ordinary differential equations approximating the dynamics of the pulse centers of mass and widths. This approximation simplifies analysis of the global dynamics of the bacterial system and allows us to efficiently explore qualitative behavior changes under a range of parameter variations. We end by presenting experimental data showing that populations of E. coli display behavior that qualitatively agrees with our theoretical results.
Derivations of quantizations in characteristic p

Let k be an algebraically closed field of odd characteristic. We describe derivations of a large class of quantizations of affine normal Poisson varieties over k.
A characterization of maximal operators associated with radial fourier multipliers

We give a simple necessary and sufficient condition for maximal operators associated with radial Fourier multipliers to be bounded on $L^p_{rad}$ and $L^p$ for certain $p$ greater than $2$. The range of exponents obtained for the $L^p_{rad}$ characterization is optimal for the given condition. The $L^p$ characterization is derived from an inequality of Heo, Nazarov, and Seeger regarding a characterization of radial Fourier multipliers.
Searching for Multiple Objects in Multiple Locations

Abstract Many practical search problems concern the search for multiple hidden objects or agents, such as earthquake survivors. In such problems, knowing only the list of possible locations, the Searcher needs to find all the hidden objects by visiting these locations one by one. To study this problem, we formulate new game-theoretic models of discrete search between a Hider and a Searcher. The Hider hides k balls in n boxes, and the Searcher opens the boxes one by one with the aim of finding all the balls. Every time the Searcher opens a box she must pay its search cost, and she either finds one of the balls it contains or learns that it is empty. If the Hider is an adversary, an appropriate payoff function may be the expected total search cost paid to find all the balls, while if the Hider is Nature, a more appropriate payoff function may be the difference between the total amount paid and the amount the Searcher would have to pay if she knew the locations of the balls a priori (the regret). We give a full solution to the regret version of this game, and a partial solution to the search cost version. We also consider variations on these games for which the Hider can hide at most one ball in each box. The search cost version of this game has already been solved in previous work, and we give a partial solution in the regret version.
Integrating NOE and RDC using sum-of-squares relaxation for protein structure determination

We revisit the problem of protein structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program (SDP). However, often the NOE distance restraints are too imprecise and sparse for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing framework. In this paper, we model the protein backbone as an articulated structure composed of rigid units. Determining the rotation of each rigid unit gives the full protein structure. We propose solving the non-convex optimization problems using the sum-of-squares (SOS) hierarchy, a hierarchy of convex relaxations with increasing complexity and approximation power. Unlike classical global optimization approaches, SOS optimization returns a certificate of optimality if the global optimum is found. Based on the SOS method, we proposed two algorithms—RDC-SOS and RDC–NOE-SOS, that have polynomial time complexity in the number of amino-acid residues and run efficiently on a standard desktop. In many instances, the proposed methods exactly recover the solution to the original non-convex optimization problem. To the best of our knowledge this is the first time SOS relaxation is introduced to solve non-convex optimization problems in structural biology. We further introduce a statistical tool, the Cramer–Rao bound (CRB), to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy measurements using any unbiased estimator. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise of realistic variance, both SOS based algorithms attain the CRB. We successfully apply our method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental NOE and RDC measurements obtained in two alignment media, achieving more accurate and faster reconstructions compared to the current state of the art.
Effect of Retransmissions on Optimal Caching in Cache-Enabled Small Cell Networks

Caching popular content in the storage of small cells is being considered as an efficient technique to complement limited backhaul of small cells in ultradense heterogeneous cellular networks. Limited storage capacity of the small cells renders it important to determine the optimal set of files (cache) to be placed on each small cell. In contrast to prior works on optimal caching, in this work we study the effect of retransmissions on the optimal cache placement policy for both static and mobile user scenarios. With the popularity of files modeled as a Zipf distribution and a maximum $n$ transmissions, i.e., $n-1$ retransmissions, allowed to receive each file, we determine the optimal caching probability of the files that maximizes the hit probability . Our closed-form optimal solutions concretely demonstrate that the optimal caching probabilities are very sensitive to the number of retransmissions.
An Accurate Globally Conservative Subdomain Discontinuous Least-Squares Scheme for Solving Neutron Transport Problems

In this work, we present a subdomain discontinuous least-squares (SDLS) scheme for neutronics problems. Least-squares (LS) methods are known to be inaccurate for problems with sharp total cross-sec...
1-Bounded entropy and regularity problems in von Neumann algebras

We investigate the singular subspace of an inclusion of tracial von Neumann algebras. The singular subspace is a canonical N-N subbimodule of L^{2}(M) and it contains the quasinormalizer introduced by Popa, one-sided quasinormalizer introduced by Fang-Gao-Smith, and wq-normalizer introduced in Galatan-Popa (following upon work in Ioana-Peterson-Popa and Popa). We then obtain a weak notion of regularity (called spectral regularity) by demanding that the singular subspace of N in M generates M. By abstracting Voiculescu's original proof of absence of Cartan subalgebras, we show that there can be no diffuse, hyperfinite subalgebra of L(\FF_{n}) which is spectrally regular. Our techniques are robust enough to repeat this process by transfinite induction and rule out chains of spectrally regular inclusions of algebras starting from a diffuse, hyperfinite algebra and ending in L(\FF_{n}). We use this to prove some conjectures made by Galatan-Popa in their study of smooth cohomology of II_{1}-factors. Our results may be regarded as a consistency check for the possibility of existence of a "good" cohomology theory of II_{1}-factors. Lastly, we deduce nonisomorphism results for crossed products of q-deformed free group factors by Bogoliubov actions, as well as for the continuous core of q-deformed Free Araki-Woods algebras. This extends work of Houdayer-Shlyakhtenko as well as Shlyakhtenko.
Physical-Layer Security: Does it Work in a Real Environment?

This paper applies channel sounding measurements to enable physical-layer security coding. The channel measurements were acquired in an indoor environment and used to assess the secrecy capacity as a function of physical location. A variety of Reed-Muller wiretap codes were applied to the channel measurements to determine the most effective code for the environment. The results suggest that deploying physical-layer security coding is a three-point design process, where channel sounding data guides 1) the physical placement of the antennas, 2) the power settings of the transmitter, and 3) the selection of wiretap coding.
Learning schizophrenia imaging genetics data via Multiple Kernel Canonical Correlation Analysis

Kernel and Multiple Kernel Canonical Correlation Analysis (CCA) are employed to classify schizophrenic and healthy patients based on their SNPs, DNA Methylation and fMRI data. Kernel and Multiple Kernel CCA are popular methods for finding nonlinear correlations between high-dimensional datasets. Data was gathered from 183 patients, 79 with schizophrenia and 104 healthy controls. Kernel and Multiple Kernel CCA represent new avenues for studying schizophrenia, because, to our knowledge, these methods have not been used on these data before. Classification is performed via k nearest neighbors on the kernel matrix outputs of the Kernel and Multiple Kernel CCA algorithm. Accuracies of the Kernel and Multiple Kernel CCA classification are compared to that of the regularized linear CCA algorithm classification, and are found to be significantly more accurate. Both algorithms demonstrate maximal accuracies when the combination of DNA methylation and fMRI data are used, and experience lower accuracies when the SNP data are incorporated.
Julius and Julia: Mastering the Art of the Schwarz Lemma

This article discusses classical versions of the Schwarz lemma at the boundary of the unit disk in the complex plane. The exposition includes commentary on the history, the mathematics, and the app...
A reduced upper bound for an edge-coloring problem from relation algebra

Starting with the Johnson scheme J(14, 7), we construct an edge-coloring of $$K_{N}$$ (for $$N = 3432$$ ) in colors red, dark blue, and light blue, such that there are no monochromatic blue triangles and such that the coloring satisfies a certain strong universal-existential property. The edge-coloring of $$K_{N}$$ depends on a cyclic coloring of $$K_{17}$$ whose two color classes contain no monochromatic $$K_{4}$$ , $$K_{4,3}$$ , or $$K_{5,2}$$ subgraphs. This construction yields the smallest known representation of the relation algebra $$32_{65}$$ , reducing the upper bound from 8192 to 3432.
Nonlinear differential inequality

A nonlinear differential inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations in Banach spaces. It is applied to a study of global existence of solutions to nonlinear partial differential equations. Mathematics subject classification (2010): 26D10, 37L05, 47J35, 65J15.
Partial Sublinear Time Approximation and Inapproximation for Maximum Coverage

We develop a randomized approximation algorithm for the classical maximum coverage problem, which given a list of sets \(A_1,A_2,\cdots \), \(A_{m}\) and integer parameter k, select k sets \(A_{i_1}, A_{i_2},\cdots , A_{i_k}\) for maximum union \(A_{i_1}\cup A_{i_2}\cup \cdots \cup A_{i_k}\). In our algorithm, each input set \(A_i\) is a black box that can provide its size \(|A_i|\), generate a random element of \(A_i\), and answer the membership query \((x\in A_i?)\) in O(1) time. Our algorithm gives \((1-{1\over e})\)-approximation for maximum coverage problem in \(O(\mathrm{poly}(k)m\cdot \log m)\) time, which is independent of the sizes of the input sets. No existing \(\mathrm{O}(p(m)n^{1-\epsilon })\) time \((1-{1\over e})\)-approximation algorithm for the maximum coverage has been found for any function \(p(m)\) that only depends on the number of sets, where \(n=\max (|A_1|,\cdots ,| A_{m}|)\) (the largest size of input sets). The notion of partial sublinear time algorithm is introduced. For a computational problem with input size controlled by two parameters \(n\) and \(m\), a partial sublinear time algorithm for it runs in a \(O(p(m)n^{1-\epsilon })\) time or \(O(q(n)m^{1-\epsilon })\) time. The maximum coverage has a partial sublinear time \(O(\mathrm{poly}(m))\) constant factor approximation since \(k\le m\). On the other hand, we show that the maximum coverage problem has no partial sublinear \(O(q(n)m^{1-\epsilon })\) time constant factor approximation algorithm.
Club isomorphisms on higher Aronszajn trees

Abstract We prove the consistency, assuming an ineffable cardinal, of the statement that CH holds and any two normal countably closed ω 2 -Aronszajn trees are club isomorphic. This work generalizes to higher cardinals the property of Abraham–Shelah [1] that any two normal ω 1 -Aronszajn trees are club isomorphic, which follows from PFA . The statement that any two normal countably closed ω 2 -Aronszajn trees are club isomorphic implies that there are no ω 2 -Suslin trees, so our proof also expands on the method of Laver–Shelah [5] for obtaining the ω 2 -Suslin hypothesis.
Discriminative Recurrent Sparse Auto-Encoders

Abstract: We present the discriminative recurrent sparse auto-encoder model, comprising a recurrent encoder of rectified linear units, unrolled for a fixed number of iterations, and connected to two linear decoders that reconstruct the input and predict its supervised classification. Training via backpropagation-through-time initially minimizes an unsupervised sparse reconstruction error; the loss function is then augmented with a discriminative term on the supervised classification. The depth implicit in the temporally-unrolled form allows the system to exhibit all the power of deep networks, while substantially reducing the number of trainable parameters. From an initially unstructured network the hidden units differentiate into categorical-units, each of which represents an input prototype with a well-defined class; and part-units representing deformations of these prototypes. The learned organization of the recurrent encoder is hierarchical: part-units are driven directly by the input, whereas the activity of categorical-units builds up over time through interactions with the part-units. Even using a small number of hidden units per layer, discriminative recurrent sparse auto-encoders achieve excellent performance on MNIST.
Free Pick functions: Representations, asymptotic behavior and matrix monotonicity in several noncommuting variables

R. Nevanlinna showed that elements of the Pick class, the set of complex analytic functions taking the upper half plane into itself, have certain integral representations which reflect their asymptotic behavior at infinity. Later, Lowner connected the Pick class to matrix monotone functions. We generalize the Nevanlinna representation theorems and Lowner's theorem on matrix monotone functions to the free Pick class, the collection of functions that map tuples of matrices with positive imaginary part into the matrices with positive imaginary part which obey the free functional calculus.
Coding-theoretic methods for sparse recovery

We review connections between coding-theoretic objects and sparse learning problems. In particular, we show how seemingly different combinatorial objects such as error-correcting codes, combinatorial designs, spherical codes, compressed sensing matrices and group testing designs can be obtained from one another. The reductions enable one to translate upper and lower bounds on the parameters attainable by one object to another. We survey some of the well-known reductions in a unified presentation, and bring some existing gaps to attention. New reductions are also introduced; in particular, we bring up the notion of minimum L-wise distance of codes and show that this notion closely captures the combinatorial structure of RIP-2 matrices. Moreover, we show how this weaker variation of the minimum distance is related to combinatorial list-decoding properties of codes.
AN AFFINE INDEX POLYNOMIAL INVARIANT OF VIRTUAL KNOTS

This paper describes a polynomial invariant of virtual knots that is defined in terms of an integer labeling of the virtual knot diagram. This labeling is seen to derive from an essentially unique structure of affine flat biquandle for flat virtual diagrams. The invariant is discussed in detail with many examples, including its relation to previous invariants of this type and we show how to construct Vassiliev invariants from the same data.
On Learning Markov Chains

The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence measures. Surprisingly, an equally important problem, estimating an unknown Markov chain from its samples, is still far from understood. We consider two problems related to the min-max risk (expected loss) of estimating an unknown k-state Markov chain from its n sequential samples: predicting the conditional distribution of the next sample with respect to the KL-divergence, and estimating the transition matrix with respect to a natural loss induced by KL or a more general f-divergence measure. For the first measure, we determine the min-max prediction risk to within a linear factor in the alphabet size, showing it is \Omega(k\log\log n/n) and O(k^2\log\log n/n). For the second, if the transition probabilities can be arbitrarily small, then only trivial uniform risk upper bounds can be derived. We therefore consider transition probabilities that are bounded away from zero, and resolve the problem for essentially all sufficiently smooth f-divergences, including KL-, L_2-, Chi-squared, Hellinger, and Alpha-divergences.
Positivity Of Equivariant Gromov–Witten Invariants

We show that the equivariant Gromov-Witten invariants of a projective homogeneous space G/P exhibit Graham-positivity: when expressed as polynomials in the positive roots, they have nonnegative coefficients.
Using TPA to count linear extensions

Abstract A linear extension of a poset P is a permutation of the elements of the set that respects the partial order. Let L ( P ) be the set of linear extensions. It is a #P complete problem to determine the size of L ( P ) exactly for an arbitrary poset, and so randomized approximation algorithms are used that employ samples that are uniformly drawn from the set of linear extensions. In this work, a new randomized approximation algorithm is proposed where the linear extensions are not uniformly drawn, but instead come from a distribution indexed by a continuous parameter β. The introduction of β allows for the use of a more efficient method for approximating # L ( P ) called TPA . Our primary result is that it is possible to sample from this continuous embedding in time that as fast or faster than the best known methods for sampling uniformly from linear extensions. For a poset containing n elements, this means we can approximate L ( P ) to within a factor of 1 + ϵ with probability at least 1 − δ using O ( n 3 ( ln ⁡ n ) ( ln ⁡ # L ( P ) ) 2 ϵ − 2 ln ⁡ δ − 1 ) expected number of random uniforms and comparisons.
Hard Sard: Quantitative Implicit Function and Extension Theorems for Lipschitz Maps

We prove a global implicit function theorem. In particular we show that any Lipschitz map $${f : \mathbb{R}^{n} \times \mathbb{R}^{m} \rightarrow \mathbb{R}^{n}}$$ (with n-dim. image) can be precomposed with a bi-Lipschitz map $${\bar{g} : \mathbb{R}^{n} \times \mathbb{R}^{m} \rightarrow \mathbb{R}^{n} \times \mathbb{R}^{m}}$$ such that $${f \circ \bar{g}}$$ will satisfy, when we restrict to a large portion of the domain $${E \subset \mathbb{R}^{n} \times \mathbb{R}^{m}}$$ , that $${f \circ \bar{g}}$$ is bi-Lipschitz in the first coordinate, and constant in the second coordinate. Geometrically speaking, the map $${\bar{g}}$$ distorts $${\mathbb{R}^{n+m}}$$ in a controlled manner so that the fibers of f are straightened out. Furthermore, our results stay valid when the target space is replaced by any metric space. A main point is that our results are quantitative: the size of the set E on which behavior is good is a significant part of the discussion. Our estimates are motivated by examples such as Kaufman’s 1979 construction of a C 1 map from [0, 1]3 onto [0, 1]2 with rank ≤ 1 everywhere. On route we prove an extension theorem which is of independent interest. We show that for any D ≥ n, any Lipschitz function $${f : [0,1]^{n} \rightarrow \mathbb{R}^{D}}$$ gives rise to a large (in an appropriate sense) subset $${E \subset [0,1]^{n}}$$ such that $${f|_E}$$ is bi-Lipschitz and may be extended to a bi-Lipschitz function defined on all of $${\mathbb{R}^{n}}$$ . This extends results of Jones and David, from 1988. As a simple corollary, we show that n-dimensional Ahlfors–David regular spaces lying in $${\mathbb{R}^{D}}$$ having big pieces of bi-Lipschitz images also have big pieces of big pieces of Lipschitz graphs in $${\mathbb{R}^{D}}$$ . This was previously known only for D ≥ 2n + 1 by a result of David and Semmes.
Ramsey numbers of trees and unicyclic graphs versus fans

The generalized Ramsey number R(H,K) is the smallest positive integer n such that for any graph G with n vertices either G contains H as a subgraph or its complement G contains K as a subgraph. Let Tn be a tree with n vertices and Fm be a fan with 2m+1 vertices consisting of m triangles sharing a common vertex. We prove a conjecture of Zhang, Broersma and Chen for m9 that R(Tn,Fm)=2n1 for all nm2m+1. Zhang, Broersma and Chen showed that R(Sn,Fm)2n for nm2m where Sn is a star on n vertices, implying that the lower bound we show is in some sense tight. We also extend this result to unicyclic graphs UCn, which are connected graphs with n vertices and a single cycle. We prove that R(UCn,Fm)=2n1 for all nm2m+1 where m18. In proving this conjecture and extension, we present several methods for embedding trees in graphs, which may be of independent interest.
Fixed points of symplectic periodic flows

The study of fixed points is a classical subject in geometry and dynamics. If the circle acts in a Hamiltonian fashion on a compact symplectic manifold M, then it is classically known that there are at least fixed points; this follows from Morse theory for the momentum map of the action. In this paper we use Atiyah–Bott–Berline–Vergne (ABBV) localization in equivariant cohomology to prove that this conclusion also holds for symplectic circle actions with non-empty fixed sets, as long as the Chern class map is somewhere injective—the Chern class map assigns to a fixed point the sum of the action weights at the point. We complement this result with less sharp lower bounds on the number of fixed points, under no assumptions; from a dynamical systems viewpoint, our results imply that there is no symplectic periodic flow with exactly one or two equilibrium points on a compact manifold of dimension at least eight.
Do Experiment and the Correspondence Principle Oblige Revision of Relativistic Quantum Theory

Recent preliminary data gathered by the Fermilab MINOS Collaboration suggest with 95% confidence that the mass of the muon neutrino differs from that of its antineutrino partner, which contradicts the entrenched relativistic quantum theory notion that a free antiparticle is a negativeenergy free particle compelled to travel backwards in time. Also a discrepancy of about five standard deviations in the value of the proton charge radius recently obtained from muonic hydrogen versus that previously obtained from electronic hydrogen casts doubt on the calculation of the dominant relativistic QED contributions to the effects that are actually measured (e.g., the Lamb shift): these QED contributions dominate proton charge radius contributions less in muonic hydrogen than in electronic hydrogen. The negative-energy “free particles” of entrenched relativistic quantum theory are well-known features of the Klein-Gordon and Dirac equations, which are shown to have many other unphysical features as well. The correspondence principle for relativistic particles is incompatible with these two equations, produces no unphysical features and implies only positive energies for free particles, which eliminates the very basis of the entrenched notion of antiparticles, as well as of the CPT theorem. This principle thus requires antiparticles to arise from charge conjugation (or more generally CP) invariance, whose known breaking is naturally expected to produce mass splitting between particle and antiparticle, in consonance with the preliminary MINOS data. It also requires revamping of relativistic QED, which is in accord with the doubt cast on it by the proton charge radius results, and implies that QED is nonlocal, i.e. has no Hamiltonian density.
Strong sums of projections in von Neumann factors

Abstract This paper presents necessary and sufficient conditions for a positive bounded operator on a separable Hilbert space to be the sum of a finite or infinite collection of projections (not necessarily mutually orthogonal), with the sum converging in the strong operator topology if the collection is infinite. A similar necessary condition is given when the operator and the projections are taken in a type II von Neumann factor, and the condition is proven to be also sufficient if the operator is “diagonalizable”. A simpler necessary and sufficient condition is given in the type III factor case.
Source-channel secrecy with causal disclosure

Imperfect secrecy in communication systems is investigated. Instead of using equivocation as a measure of secrecy, the distortion that an eavesdropper incurs in producing an estimate of the source sequence is examined. The communication system consists of a source and a broadcast (wiretap) channel, and lossless reproduction of the source sequence at the legitimate receiver is required. A key aspect of this model is that the eavesdropper's actions are allowed to depend on the past behavior of the system. Achievability results are obtained by studying the performance of source and channel coding operations separately, and then linking them together digitally. Although the problem addressed here has been solved when the secrecy resource is shared secret key, it is found that substituting secret key for a wiretap channel brings new insights and challenges: the notion of weak secrecy provides just as much distortion at the eavesdropper as strong secrecy, and revealing public messages freely is detrimental.
Adaptive linear programming decoding of polar codes

Polar codes are high density parity check codes and hence the sparse factor graph, instead of the parity check matrix, has been used to practically represent an LP polytope for LP decoding. Although LP decoding on this polytope has the MLcertificate property, it performs poorly over a BAWGN channel. In this paper, we propose modifications to adaptive cut generation based LP decoding techniques and apply the modified-adaptive LP decoder to polar codes over a BAWGN channel. The proposed decoder provides significant FER performance gain compared to the previously proposed LP decoder and its performance approaches that of ML decoding at high SNRs. We also present an algorithm to obtain a smaller factor graph from the original sparse factor graph of a polar code. This reduced factor graph preserves the small check node degrees needed to represent the LP polytope in practice. We show that the fundamental polytope of the reduced factor graph can be obtained from the projection of the polytope represented by the original sparse factor graph and the frozen bit information. Thus, the LP decoding time complexity is decreased without changing the FER performance by using the reduced factor graph representation.
Accelerating light with metasurfaces

It has been recently shown that specially engineered light beams have the remarkable ability to propagate along curved trajectories in vacuum. Current methods for generating accelerating beams use phase modulators and lenses, leading to length scales on the order of tens of centimeters or larger. This poses constraints and severely limits their applicability inside materials. Here, we accelerate light inside glass using a metasurface consisting of plasmonic nanoantennas. Highly bending beams with radii of curvature on the order of a hundred micrometers were generated, and the imaged intensities agree well with theory. Our approach for generating accelerating beams allows for their integration into on-chip photonic systems.
The prisoner's dilemma as a cancer model.

Tumor development is an evolutionary process in which a heterogeneous population of cells with different growth capabilities compete for resources in order to gain a proliferative advantage. What are the minimal ingredients needed to recreate some of the emergent features of such a developing complex ecosystem? What is a tumor doing before we can detect it? We outline a mathematical model, driven by a stochastic Moran process, in which cancer cells and healthy cells compete for dominance in the population. Each are assigned payoffs according to a Prisoner’s Dilemma evolutionary game where the healthy cells are the cooperators and the cancer cells are the defectors. With point mutational dynamics, heredity, and a fitness landscape controlling birth and death rates, natural selection acts on the cell population and simulated ‘cancer-like’ features emerge, such as Gompertzian tumor growth driven by heterogeneity, the log-kill law which (linearly) relates therapeutic dose density to the (log) probability of cancer cell survival, and the Norton-Simon hypothesis which (linearly) relates tumor regression rates to tumor growth rates. We highlight the utility, clarity, and power that such models provide, despite (and because of) their simplicity and built-in assumptions.
New mapping properties of the time domain electric field integral equation

We show some improved mapping properties of the Time Domain Electric Field Integral Equation and of its Galerkin semidiscretization in space. We relate the weak distributional framework with a stronger class of solutions using a group of strongly continuous operators. The stability and error estimates we derive are sharper than those in the literature.
Computing Maximal Layers Of Points in $E^{f(n)}$

In this paper we present a randomized algorithm for computing the collection of maximal layers for a point set in \(E^{k}\) (\(k = f(n)\)). The input to our algorithm is a point set \(P = \{p_1,\ldots ,p_n\}\) with \(p_i \in E^{k}\). The proposed algorithm achieves a runtime of \(O\left( kn^{2 - {1 \over \log {k}} + \log _k{\left( 1 + {2 \over {k+1}}\right) }}\log {n}\right) \) when P is a random order and a runtime of \(O(k^2 n^{3/2 + (\log _{k}{(k-1)})/2}\log {n})\) for an arbitrary P. Both bounds hold in expectation. Additionally, the run time is bounded by \(O(kn^2)\) in the worst case. This is the first non-trivial algorithm whose run-time remains polynomial whenever f(n) is bounded by some polynomial in n while remaining sub-quadratic in n for constant k (in expectation). The algorithm is implemented using a new data-structure for storing and answering dominance queries over the set of incomparable points.
Non-singular Cyclic Cosmology without Phantom Menace

In this article we review recent developments of cyclic cosmology. A typical non-singular cyclic model within General Relativity requires a non-conventional fluid with negative effective energy density, in order to cancel the matter component and lead to a non-singular bounce. However, the existence of such a non-conventional fluid usually leads to quantum instabilities and makes the theory ill-defined. In the present work we follow the alternative way, obtaining two scenarios of non-singular cyclic cosmological evolutions in the context of gravitational theories beyond General Relativity. The degrees-of-freedom examination reveals that these two models are free of the Phantom Menace. Our analysis illustrates that, if cyclic cosmology describes overall universe, a theory of gravity beyond Einstein may be expected.
Evaluating memento service optimizations

Services and applications based on the Memento Aggregator can suffer from slow response times due to the federated search across web archives performed by the Memento infrastructure. In an effort to decrease the response times, we established a cache system and experimented with machine learning models to predict archival holdings. We reported on the experimental results in previous work and can now, after these optimizations have been in production for two years, evaluate their efficiency, based on long-term log data. During our investigation we find that the cache is very effective with a 70 -- 80% cache hit rate for human-driven services. The machine learning prediction operates at an acceptable average recall level of 0.727 but our results also show that a more frequent retraining of the models is needed to further improve prediction accuracy.
Convolutional neural network for seismic impedance inversion

ABSTRACTWe have addressed the geophysical problem of obtaining an elastic model of the subsurface from recorded normal-incidence seismic data using convolutional neural networks (CNNs). We train th...
Classification of solitons for pluriclosed flow on complex surfaces

We give a classification of compact solitons for the pluriclosed flow on complex surfaces. First, by exploiting results from the Kodaira classification of surfaces, we show that the complex surface underlying a soliton must be Kahler except for the possibility of steady solitons on minimal Hopf surfaces. Then, we construct steady solitons on all class 1 Hopf surfaces by exploiting a symmetry ansatz.
A New Approach for Distributed Hypothesis Testing with Extensions to Byzantine-Resilience

We study a setting where a group of agents, each receiving partially informative private observations, seek to collaboratively learn the true state (among a set of hypotheses) that explains their joint observation profiles over time. To solve this problem, we propose a distributed learning rule that differs fundamentally from existing approaches, in the sense that it does not employ any form of “belief-averaging”. Specifically, every agent maintains a local belief on each hypothesis that is updated in a Bayesian manner without any network influence, and an actual belief that is updated (up to normalization) as the minimum of its own local belief and the actual beliefs of its neighbors. Under minimal requirements on the signal structures of the agents and the underlying communication graph, we establish consistency of the proposed belief update rule, i.e., we show that the actual beliefs of the agents asymptotically concentrate on the true state almost surely. As one of the key benefits of our approach, we show that our learning rule can be extended to scenarios that capture misbehavior on the part of certain agents in the network, modeled via the Byzantine adversary model. In particular, we prove that each non-adversarial agent can asymptotically learn the true state of the world almost surely, under appropriate conditions on the observation model and the network topology.
Salient Speech Representations Based on Cloned Networks.

We define salient features as features that are shared by signals that are defined as being equivalent by a system designer. The definition allows the designer to contribute qualitative information. We aim to find salient features that are useful as conditioning for generative networks. We extract salient features by jointly training a set of clones of an encoder network. Each network clone receives as input a different signal from a set of equivalent signals. The objective function encourages the network clones to map their input into a set of features that is identical across the clones. It additionally encourages feature independence and, optionally, reconstruction of a desired target signal by a decoder. As an application, we train a system that extracts a time-sequence of feature vectors of speech and uses it as a conditioning of a WaveNet generative system, facilitating both coding and enhancement.
Energy-efficient Rate Adaptation MAC Protocol for Ad Hoc Wireless Networks

In this paper, two novel energy-efficient rate adaptation schemes are presented. The proposed protocols use the Distributed Power Control (DPC) algorithm to predict the channel state and determine the necessary transmission power which optimizes the energy consumption. The first proposed rate adaptation scheme heuristically alters the modulation rate to balance the energy-efficiency and the required throughput which is estimated with queue fill ratio. Moreover, the back-off scheme is incorporated to mitigate congestion and reduce packet losses due to buffer overflows thus minimizing energy consumption. Consequently, the nodes will conserve energy when the traffic is low, offer higher throughput when needed and save energy during congestion by limiting transmission rates. The second rate adaptation scheme employs dynamic programming (DP) principle to analytically select modulation rate and a burst size to be used during transmission. The proposed quadratic cost-function minimizes the energy consumption while alleviating network congestions and buffer overflows. The proposed DP solution renders a Riccati equation ultimately providing an optimal rate selection. The simulation results indicate that an increase in throughput by 96% and energy-efficiency by 131% is observed when compared to other available protocols, for example Receiver Based AutoRate (RBAR).