cssi/SciSciGPT-SciSciNet huggingface dataset:
Numerical Study on Mechanism of Multiple Rings Formation

In this paper, the flow around each ring-like vortex is investigated by high order DNS including first sweep, first ejection, second sweep, second ejection, positive spike, momentum deficit, vortex shape, vortex location, strength of sweeps, etc. Meanwhile, the mechanism about formation of momentum deficit is deeply studied. A new mechanism on how the multiple rings are formed one by one found both by experiment and by DNS in late boundary layer transition is presented. It also reveals that the relation between streamwise vortex and spanvise vertex rings, and how the vorticity is transferred between them. Nomenclature ∞ M = Mach number Re = Reynolds number in δ = inflow displacement thickness w T = wall temperature ∞ T = free stream temperature in Lz = height at inflow boundary out Lz = height at outflow boundary Lx = length of computational domain along x direction Ly = length of computational domain along y direction in x = distance between leading edge of flat plate and upstream boundary of computational domain d A 2 = amplitude of 2D inlet disturbance d A 3 = amplitude of 3D inlet disturbance ω = frequency of inlet disturbance 2 3 d d , α α = two and three dimensional streamwise wave number of inlet disturbance β = spanwise wave number of inlet disturbance R = ideal gas constant γ = ratio of specific heats ∞ μ = viscosity
High-pressure, high-temperature molecular doping of nanodiamond

The development of color centers in diamond as the basis for emerging quantum technologies has been limited by the need for ion implantation to create the appropriate defects. We present a versatile method to dope diamond without ion implantation by synthesis of a doped amorphous carbon precursor and transformation at high temperatures and high pressures. To explore this bottom-up method for color center generation, we rationally create silicon vacancy defects in nanodiamond and investigate them for optical pressure metrology. In addition, we show that this process can generate noble gas defects within diamond from the typically inactive argon pressure medium, which may explain the hysteresis effects observed in other high-pressure experiments and the presence of noble gases in some meteoritic nanodiamonds. Our results illustrate a general method to produce color centers in diamond and may enable the controlled generation of designer defects.
Sentence Similarity Learning by Lexical Decomposition and Composition

Most conventional sentence similarity methods only focus on similar parts of two input sentences, and simply ignore the dissimilar parts, which usually give us some clues and semantic meanings about the sentences. In this work, we propose a model to take into account both the similarities and dissimilarities by decomposing and composing lexical semantics over sentences. The model represents each word as a vector, and calculates a semantic matching vector for each word based on all words in the other sentence. Then, each word vector is decomposed into a similar component and a dissimilar component based on the semantic matching vector. After this, a two-channel CNN model is employed to capture features by composing the similar and dissimilar components. Finally, a similarity score is estimated over the composed feature vectors. Experimental results show that our model gets the state-of-the-art performance on the answer sentence selection task, and achieves a comparable result on the paraphrase identification task.
Silicon micromachined high-contrast artificial dielectrics for millimeter-wave transformation optics antennas

Transformation optics methods and gradient index electromagnetic structures rely upon spatially varied arbitrary permittivity. This, along with recent interest in millimeter-wave lens-based antennas demands high spatial resolution dielectric variation. Perforated media have been used to fabricate gradient index structures from microwaves to THz but are often limited in contrast. We show that by employing regular polygon unit-cells (hexagon, square, and triangle) on matched lattices we can realize very high contrast permittivity ranging from 0.1–1.0 of the background permittivity. Silicon micromachining (Bosch process) is performed on high resistivity Silicon wafers to achieve a minimum permittivity of 1.25 (10% of Silicon) in the WR28 waveguide band, specifically targeting the proposed 39GHz 5G communications band. The method is valid into the THz band.
On the density of the odd values of the partition function, II: An infinite conjectural framework

Abstract We continue our study of a basic but seemingly intractable problem in integer partition theory, namely the conjecture that p ( n ) is odd exactly 50% of the time. Here, we greatly extend on our previous paper by providing a doubly-indexed, infinite framework of conjectural identities modulo 2, and show how to, in principle, prove each such identity. However, our conjecture remains open in full generality. A striking consequence is that, under suitable existence conditions, if any t-multipartition function is odd with positive density and t ≢ 0 ( mod 3 ) , then p ( n ) is also odd with positive density. These are all facts that appear virtually impossible to show unconditionally today. Our arguments employ a combination of algebraic and analytic methods, including certain technical tools recently developed by Radu in his study of the parity of the Fourier coefficients of modular forms.
Approximating the Held-Karp Bound for Metric TSP in Nearly-Linear Time

We give a nearly linear-time randomized approximation scheme for the Held-Karp bound [22] for Metric-TSP. Formally, given an undirected edge-weighted graph G = (V,E) on m edges and &#x03B5; 0, the algorithm outputs in O(m log^4 n/&#x03B5;^2) time, with high probability, a (1 + &#x03B5;)-approximation to the Held-Karp bound on the Metric-TSP instance induced by the shortest path metric on G. The algorithm can also be used to output a corresponding solution to the Subtour Elimination LP. We substantially improve upon the O(m^2 log^2(m)/&#x03B5;^2) running time achieved previously by Garg and Khandekar.
A variational method for analyzing stochastic limit cycle oscillators

We introduce a variational method for analyzing limit cycle oscillators in $\mathbb{R}^d$ driven by Gaussian noise. This allows us to derive exact stochastic differential equations for the amplitud...
Computing bases of modular forms using the graded algebra structure

We develop a new algorithm to compute a basis for $$M_k(\Gamma _0(N))$$ , the space of weight k holomorphic modular forms on $$\Gamma _0(N)$$ , in the case when the graded algebra of modular forms over $$\Gamma _0(N)$$ is generated at weight two. Our tests show that this algorithm significantly outperforms a commonly used algorithm which relies more heavily on modular symbols.
A Systematic Analysis for State-of-the-Art 3D Lung Nodule Proposals Generation

Abstract Lung nodule proposals generation is the primary step of lung nodule detection and has received much attention in recent years. In this paper, we first construct a model of 3-dimension Convolutional Neural Network (3D CNN) to generate lung nodule proposals, which can achieve the state-of-the-art performance. Then, we analyze a series of key problems concerning the training performance and efficiency. Firstly, we train the 3D CNN model with data in different resolutions and find out that models trained by high resolution input data achieve better lung nodule proposals generation performances especially for nodules in too small sizes, while consumes much more memory at the same time. Then, we analyze the memory consumptions on different platforms and the experimental results indicate that CPU architecture can provide us with larger memory and enables us to explore more possibilities of 3D applications. We implement the 3D CNN model on CPU platform and propose an Intel Extended-Caffe framework which supports many highly-efficient 3D computations, which is opened source at https://github.com/extendedcaffe/extended-caffe .
Dialog Structure Through the Lens of Gender, Gender Environment, and Power

Understanding how the social context of an interaction affects our dialog behavior is of great interest to social scientists who study human behavior, as well as to computer scientists who build automatic methods to infer those social contexts. In this paper, we study the interaction of power, gender, and dialog behavior in organizational interactions. In order to perform this study, we first construct the Gender Identified Enron Corpus of emails, in which we semi-automatically assign the gender of around 23,000 individuals who authored around 97,000 email messages in the Enron corpus. This corpus, which is made freely available, is orders of magnitude larger than previously existing gender identified corpora in the email domain. Next, we use this corpus to perform a largescale data-oriented study of the interplay of gender and manifestations of power. We argue that, in addition to one’s own gender, the “gender environment” of an interaction, i.e., the gender makeup of one’s interlocutors, also affects the way power is manifested in dialog. We focus especially on manifestations of power in the dialog structure — both, in a shallow sense that disregards the textual content of messages (e.g., how often do the participants contribute, how often do they get replies etc.), as well as the structure that is expressed within the textual content (e.g., who issues requests and how are they made, whose requests get responses etc.). We find that both gender and gender environment affect the ways power is manifested in dialog, resulting in patterns that reveal the underlying factors. Finally, we show the utility of gender information in the problem of automatically predicting the direction of power between pairs of participants in email interactions.
Quantum simulations of one dimensional quantum systems

We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the quantum harmonic oscillator (QHO) based on a refined analysis of the Trotter-Suzuki formula that exploits the Lie algebra structure. For total evolution time t and precision e > 0, the complexity of our method is O(exp(γ√log(N/e))), where γ > 0 is a constant and N is the quantum number associated with an "energy cutoff" of the initial state. Remarkably, this complexity is subpolynomial in N/e. We also provide a method to prepare discrete versions of the eigenstates of the QHO of complexity polynomial in log(N)/e, where N is the dimension or number of points in the discretization. Next, we consider a system with a quartic potential. Our numerical simulations suggest a method for simulating the evolution of sublinear complexity O(N1/3+o(1)), for constant t and e. We also analyze complex one-dimensional systems and prove a complexity bound O(N), under fairly general assumptions. Our quantum algorithms may find applications in other problems. As an example, we discuss a generalization of the Fourier transform that is useful for signal analysis and can be formulated in terms of the evolution of the QHO.
Endomorphism fields of abelian varieties

We give a sharp divisibility bound, in terms of g, for the degree of the field extension required to realize the endomorphisms of an abelian variety of dimension g over an arbitrary number field; this refines a result of Silverberg. This follows from a stronger result giving the same bound for the order of the component group of the Sato–Tate group of the abelian variety, which had been proved for abelian surfaces by Fite–Kedlaya–Rotger–Sutherland. The proof uses Minkowski’s reduction method, but with some care required in the extremal cases when p equals 2 or a Fermat prime.
A geometric multigrid method for isogeometric compatible discretizations of the generalized Stokes and Oseen problems

In this paper, we present a geometric multigrid methodology for the solution of matrix systems associated with isogeometric compatible discretizations of the generalized Stokes and Oseen problems. The methodology provably yields a pointwise divergence-free velocity field independent of the number of pre-smoothing steps, post-smoothing steps, grid levels, or cycles in a V-cycle implementation. The methodology relies upon Scwharz-style smoothers in conjunction with specially defined overlapping subdomains that respect the underlying topological structure of the generalized Stokes and Oseen problems. Numerical results in both two- and three-dimensions demonstrate the robustness of the methodology through the invariance of convergence rates with respect to grid resolution and flow parameters for the generalized Stokes problem as well as the generalized Oseen problem provided it is not advection-dominated.
Closure operations that induce big Cohen–Macaulay algebras

Abstract We study closure operations over a local domain R that satisfy a set of axioms introduced by Geoffrey Dietz. The existence of a closure operation satisfying the axioms (called a Dietz closure) is equivalent to the existence of a big Cohen–Macaulay module for R. When R is complete and has characteristic p > 0 , tight closure and plus closure satisfy the axioms. We give an additional axiom (the Algebra Axiom), such that the existence of a Dietz closure satisfying this axiom is equivalent to the existence of a big Cohen–Macaulay algebra. We prove that many closure operations satisfy the Algebra Axiom, whether or not they are Dietz closures. We discuss the smallest big Cohen–Macaulay algebra closure on a given ring, and show that every Dietz closure satisfying the Algebra Axiom is contained in a big Cohen–Macaulay algebra closure. This leads to proofs that in rings of characteristic p > 0 , every Dietz closure satisfying the Algebra Axiom is contained in tight closure, and there exist Dietz closures that do not satisfy the Algebra Axiom.
Towards a classification of finite-dimensional representations of rational Cherednik algebras of type D

Using a combinatorial description due to Jacon and Lecouvey of the wall crossing bijections for cyclotomic rational Cherednik algebras, we show that the irreducible representations Lc(λ±) of the ra...
An effective estimate for the Lebesgue measure of preimages of iterates of the Farey map

Abstract Using techniques from infinite ergodic theory, Kessebohmer and Stratmann determined the asymptotic behavior of the Lebesgue measure of sets of the form F − n [ α , β ] , where [ α , β ] ⊆ ( 0 , 1 ] and F is the Farey map. In this paper, we provide an effective version of this result, employing mostly basic properties of the transfer operator of the Farey map and an application of Freud's effective version of Karamata's Tauberian theorem.
Twisted virtual biracks and their twisted virtual link invariants

Abstract A virtual link can be understood as a link in a trivial I-bundle over an orientable compact surface with genus. A twisted virtual link is a link in a trivial I-bundle over a not-necessarily orientable compact surface. A twisted virtual birack is an algebraic structure with axioms derived from the twisted virtual Reidemeister moves. We extend a method previously used with racks and biracks to the twisted case to define computable invariants of twisted virtual links using finite twisted virtual biracks with birack rank N ⩾ 1 . As an application, we classify twist structures on the virtual Hopf link.
On the Distribution of Monochromatic Complete Subgraphs and Arithmetic Progressions

We investigate the distributions of the number of: (1) monochromatic complete subgraphs over edgewise 2-colorings of complete graphs; and (2) monochromatic arithmetic progressions over 2-colorings ...
Pseudo knots and an obstruction to cosmetic crossings

Pseudo links have two crossing types: classical crossings and indeterminate crossings. They were first introduced by Hanaki as a possible tool for analyzing images produced by electron microscopy of DNA. A normalized bracket polynomial is defined for pseudo links and then used to construct an obstruction to cosmetic crossings in classical links.
Dissipation anomaly and energy cascade in 3D incompressible flows

Abstract The purpose of this Note is to present a mathematical evidence of the dissipation anomaly in 3D turbulent flows within a general setting for the study of energy cascade in physical scales of 3D incompressible flows recently introduced by the authors.
A Coupled Compressive Sensing Scheme for Unsourced Multiple Access

This article introduces a novel paradigm for the unsourced multiple-access communication problem. This divide-and-conquer approach leverages recent advances in compressive sensing and forward error correction to produce a computationally efficient algorithm. Within the proposed framework, every active device first partitions its data into several subblocks, and subsequently adds redundancy using a systematic linear block code. Compressive sensing techniques are then employed to recover sub-blocks, and the original messages are obtained by connecting pieces together using a low-complexity tree-based algorithm. Numerical results suggest that the proposed scheme outperforms other existing practical coding schemes. Measured performance lies approximately 4.3 dB away from the Polyanskiy achievability limit, which is obtained in the absence of complexity constraints.
Grothendieck’s trace map for arithmetic surfaces via residues and higher adèles

We establish the reciprocity law along a vertical curve for residues of differential forms on arithmetic surfaces, and describe Grothendieck’s trace map of the surface as a sum of residues. Points at infinity are then incorporated into the theory and the reciprocity law is extended to all curves on the surface. Applications to adelic duality for the arithmetic surface are discussed. MSC2010: 14H25, 14B15, 14F10.
Dihedral Rigidity and Deformation

We consider defining the embedding of a triangle mesh into $R^3$, up to translation, rotation, and scale, by its vector of dihedral angles. Theoretically, we show that locally, almost everywhere, the map from realizable vectors of dihedrals to mesh embeddings is one-to-one. We experiment with a heuristic method for mapping straight-line interpolations in dihedral space to interpolations between mesh embeddings and produce smooth and intuitively appealing morphs between three-dimensional shapes.
FRIST - Flipping and rotation invariant sparsifying transform learning and applications

Features based on sparse representation, especially using the synthesis dictionary model, have been heavily exploited in signal processing and computer vision. However, synthesis dictionary learning typically involves NP-hard sparse coding and expensive learning steps. Recently, sparsifying transform learning received interest for its cheap computation and its optimal updates in the alternating algorithms. In this work, we develop a methodology for learning Flipping and Rotation Invariant Sparsifying Transforms, dubbed FRIST, to better represent natural images that contain textures with various geometrical directions. The proposed alternating FRIST learning algorithm involves efficient optimal updates. We provide a convergence guarantee, and demonstrate the empirical convergence behavior of the proposed FRIST learning approach. Preliminary experiments show the promising performance of FRIST learning for sparse image representation, segmentation, denoising, robust inpainting, and compressed sensing-based magnetic resonance image reconstruction.
On an isomorphic Banach–Mazur rotation problem and maximal norms in Banach spaces

Abstract We prove that the spaces l p , 1 p ∞ , p ≠ 2 , and all infinite-dimensional subspaces of their quotient spaces do not admit equivalent almost transitive renormings. This is a step towards the solution of the Banach–Mazur rotation problem, which asks whether a separable Banach space with a transitive norm has to be isometric or isomorphic to a Hilbert space. We obtain this as a consequence of a new property of almost transitive spaces with a Schauder basis, namely we prove that in such spaces the unit vector basis of l 2 2 belongs to the two-dimensional asymptotic structure and we obtain some information about the asymptotic structure in higher dimensions. Further, we prove that the spaces l p , 1 p ∞ , p ≠ 2 , have continuum different renormings with 1-unconditional bases each with a different maximal isometry group, and that every symmetric space other than l 2 has at least a countable number of such renormings. On the other hand we show that the spaces l p , 1 p ∞ , p ≠ 2 , have continuum different renormings each with an isometry group which is not contained in any maximal bounded subgroup of the group of isomorphisms of l p .
Slow and Stale Gradients Can Win the Race: Error-Runtime Trade-offs in Distributed SGD.

Distributed Stochastic Gradient Descent (SGD) when run in a synchronous manner, suffers from delays in waiting for the slowest learners (stragglers). Asynchronous methods can alleviate stragglers, but cause gradient staleness that can adversely affect convergence. In this work we present a novel theoretical characterization of the speed-up offered by asynchronous methods by analyzing the trade-off between the error in the trained model and the actual training runtime (wallclock time). The novelty in our work is that our runtime analysis considers random straggler delays, which helps us design and compare distributed SGD algorithms that strike a balance between stragglers and staleness. We also present a new convergence analysis of asynchronous SGD variants without bounded or exponential delay assumptions, and a novel learning rate schedule to compensate for gradient staleness.
On a linearization trick

In several situations, mainly involving a self-adjoint set of unitary generators of a $C^*$-algebra, we show that any matrix polynomial in the generators and the unit that is in the open unit ball can be written as a product of matrix polynomials of degree 1 also in the open unit ball.
Building a telescope to look into high-dimensional image spaces

An image pattern can be represented by a probability distribution whose density is concentrated on different low-dimensional subspaces in the high-dimensional image space. Such probability densities have an astronomical number of local modes corresponding to typical pattern appearances. Related groups of modes can join to form macroscopic image basins that represent pattern concepts. Recent works use neural networks that capture high-order image statistics to learn Gibbs models capable of synthesizing realistic images of many patterns. However, characterizing a learned probability density to uncover the Hopfield memories of the model, encoded by the structure of the local modes, remains an open challenge. In this work, we present novel computational experiments that map and visualize the local mode structure of Gibbs densities. Efficient mapping requires identifying the global basins without enumerating the countless modes. Inspired by Grenander's jump-diffusion method, we propose a new MCMC tool called Attraction-Diffusion (AD) that can capture the macroscopic structure of highly non-convex densities by measuring metastability of local modes. AD involves altering the target density with a magnetization potential penalizing distance from a known mode and running an MCMC sample of the altered density to measure the stability of the initial chain state. Using a low-dimensional generator network to facilitate exploration, we map image spaces with up to 12,288 dimensions (64 $\times$ 64 pixels in RGB). Our work shows: (1) AD can efficiently map highly non-convex probability densities, (2) metastable regions of pattern probability densities contain coherent groups of images, and (3) the perceptibility of differences between training images influences the metastability of image basins.
Convexity estimates for mean curvature flow with free boundary

Abstract We prove the estimates of [3] and [2] for finite-time singularities of mean-convex, mean curvature flow with free boundary in a barrier S. Here S can be any embedded, oriented surface in R n + 1 of bounded geometry and positive inscribed radius. We also prove the estimate [4] in the case of convex flows and S = S n , which gives an alternative proof to [6] .
Sacks of Dice with Fair Totals

A fair sack is a finite set of independent dice, not required to be fair and allowed to have any number of sides, for which all totals are equally likely. These have been studied for over 60 years....
Apollonian circle packings of the half-plane

We consider Apollonian circle packings of a half Euclidean plane. We give necessary and sufficient conditions for two such packings to be related by a Euclidean similarity (that is, by translations, reflections, rotations and dilations) and describe explicitly the group of self-similarities of a given packing. We observe that packings with a non-trivial self-similarity correspond to positive real numbers that are the roots of quadratic polynomials with rational coefficients. This is reflected in a close connection between Apollonian circle packings and continued fractions which allows us to completely classify such packings up to similarity.
Low-Thrust Trajectory Design Using Reachability Sets near Asteroid 4769 Castalia

We present a computational approach for the design of continuous low thrust transfers around an asteroid. These transfers are computed through the use of a reachability set generated on a lower dimensional Poincare surface. Complex, long duration transfer trajectories are highly sensitive to the initial guess and generally have a small region of convergence. Computation of the reachable set alleviates the need to generate an accurate initial guess for optimization. From the reachable set, we chose a trajectory which minimizes a distance metric towards the desired target. Successive computation of the reachable set allows for the design of general transfer trajectories which iteratively approach the target. We demonstrate this method by determining a transfer trajectory about the asteroid 4769 Castalia.
Rescaled Pure Greedy Algorithm for convex optimization

We suggest a new greedy strategy for convex optimization in Banach spaces and prove its convergence rates under a suitable behavior of the modulus of uniform smoothness of the objective function. We show that this algorithm is a generalization of the recently discovered Rescaled Pure Greedy Algorithm for approximation in Hilbert spaces.
Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves

We prove a theorem giving the asymptotic number of binary quartic forms having bounded invariants; this extends, to the quartic case, the classical results of Gauss and Davenport in the quadratic and cubic cases, respectively. Our techniques are quite general and may be applied to counting integral orbits in other representations of algebraic groups. We use these counting results to prove that the average rank of elliptic curves over Q, when ordered by their heights, is bounded. In particular, we show that when elliptic curves are ordered by height, the mean size of the 2-Selmer group is 3. This implies that the limsup of the average rank of elliptic curves is at most 1:5.
A Numerical Methodology for Enforcing Maximum Principles and the Non-Negative Constraint for Transient Diffusion Equations

Transient diffusion equations arise in many branches of engineering and applied sciences (e.g., heat transfer and mass transfer), and are parabolic partial differential equations. It is well-known that these equations satisfy important mathematical properties like maximum principles and the non-negative constraint, which have implications in mathematical modeling. However, existing numerical formulations for these types of equations do not, in general, satisfy maximum principles and the non-negative constraint. In this paper, we present a methodology for enforcing maximum principles and the non-negative constraint for transient anisotropic diffusion equation. The proposed methodology is based on the method of horizontal lines in which the time is discretized first. This results in solving steady anisotropic diffusion equation with decay equation at every discrete time-level. We also present other plausible temporal discretizations, and illustrate their shortcomings in meeting maximum principles and the non-negative constraint. The proposed methodology can handle general computational grids with no additional restrictions on the time-step. We illustrate the performance and accuracy of the proposed methodology using representative numerical examples. We also perform a numerical convergence analysis of the proposed methodology. For comparison, we also present the results from the standard single-field semi-discrete formulation and the results from a popular software package, which all will violate maximum principles and the non-negative constraint.
Additional waves and additional boundary conditions in local quartic metamaterials

Additional electromagnetic waves and additional boundary conditions (ABCs) in non-local materials attract a lot of attention. Here we report the possibility of additional propagating and evanescent waves in local anisotropic and bi-anisotropic linear materials if non-reciprocity is present. We also show that additional waves cannot propagate in local reciprocal bi-anisotropic materials. We investigate the possible options for ABCs and describe how to complement the conventional 4 Maxwell’s boundary conditions in the situations when there are more than 4 waves that need to be matched at the boundary of local and linear quartic metamaterials. We show that these ABCs must depend on the properties of the interface and require the introduction of the additional effective material parameters describing this interface, such as surface conductivities.
Simplified equations for gravitational field in the vector theory of gravity and new insights into dark energy

Abstract Recently, a new alternative vector theory of gravity has been proposed which assumes that universe has fixed background Euclidean geometry and gravity is a vector field that alters this geometry (Svidzinsky, 2017). It has been shown that vector gravity passes all available gravitational tests and yields, with no free parameters, the value of cosmological constant in agreement with observations. Here we obtain substantially simplified gravitational field equations of vector gravity which are more suitable for analytical and numerical analyses. We also provide a detailed explanation why in vector gravity in the reference frame of observer that takes a snapshot of the universe at time t 0 the ratio of the cosmological constant to the critical density is equal to 2 ∕ 3 at t = t 0 . We also show that dark energy does not affect universe evolution in the co-evolving reference frame. Thus, in reality, universe is expanding at a continually decelerating rate, with expansion asymptotically approaching zero.
On the minimum mean p-th error in Gaussian noise channels and its applications

The problem of estimating an arbitrary random variable from its observation corrupted by additive white Gaussian noise, where the cost function is taken to be the minimum mean p-th error (MMPE), is considered. The classical minimum mean square error (MMSE) is a special case of the MMPE. Several bounds and properties of the MMPE are derived and discussed. As applications of the new MMPE bounds, this paper presents: (a) a new upper bound for the MMSE that complements the ‘single-crossing point property’ for all SNR values below a certain value at which the MMSE is known, (b) an improved characterization of the phase-transition phenomenon which manifests, in the limit as the length of the capacity achieving code goes to infinity, as a discontinuity of the MMSE, and (c) new bounds on the second derivative of mutual information, or the first derivative of MMSE, that tighten previously known bounds.
Improved Bounds for Relaxed Graceful Trees

We introduce left and right-layered trees as trees with a specific representation and define the excess of a tree. Applying these ideas, we show a range-relaxed graceful labeling which improves on the upper bound for maximum vertex label given by Van Bussel. For the case when the tree is a lobster of size m and diameter d, the labeling produces vertex labels no greater than $$\frac{3}{2}m-\frac{1}{2}d$$32m-12d. Furthermore, we show that any lobster T with m edges and diameter d has an edge-relaxed graceful bipartite labeling with at least $$\max \{\frac{3m-d+6}{4},\frac{5m+d+15}{8}\}$$max{3m-d+64,5m+d+158} of the edge weights distinct, which is an improvement on a bound given by Rosa and ?ira? on the $$\alpha $$?-size of trees, for $$d 5m-657. We also show that there exists an edge-relaxed graceful labeling (not necessarily bipartite) with at least $$\max \left\{ \frac{3}{4}m+\frac{d-\nu }{8}+\frac{3}{2},\nu \right\} $$max34m+d-?8+32,? of the edge weights distinct, where $$\nu $$? is twice the size of a partial matching of T. This is an improvement on the best known gracesize bound, for certain values of $$\nu $$? and d. We view these results as a step towards Bermond's conjecture that all lobsters are graceful.
Overlimiting Current and Shock Electrodialysis in Porous Media

Most electrochemical processes, such as electrodialysis, are limited by diffusion, but in porous media, surface conduction and electroosmotic flow also contribute to ionic flux. In this article, we report experimental evidence for surface-driven overlimiting current (faster than diffusion) and deionization shocks (propagating salt removal) in a porous medium. The apparatus consists of a silica glass frit (1 mm thick with a 500 nm mean pore size) in an aqueous electrolyte (CuSO4 or AgNO3) passing ionic current from a reservoir to a cation-selective membrane (Nafion). The current–voltage relation of the whole system is consistent with a proposed theory based on the electroosmotic flow mechanism over a broad range of reservoir salt concentrations (0.1 mM to 1.0 M) after accounting for (Cu) electrode polarization and pH-regulated silica charge. Above the limiting current, deionized water (≈10 μM) can be continuously extracted from the frit, which implies the existence of a stable shock propagating against the...
Optimal Network Control in Partially-Controllable Networks

The effectiveness of many optimal network control algorithms (e.g., BackPressure) relies on the premise that all of the nodes are fully controllable. However, these algorithms may yield poor performance in a partially-controllable network where a subset of nodes are uncontrollable and use some unknown policy. Such a partially-controllable model is of increasing importance in real-world networked systems such as overlay-underlay networks. In this paper, we design optimal network control algorithms that can stabilize a partially-controllable network. We first study the scenario where uncontrollable nodes use a queue-agnostic policy, and propose a low-complexity throughput-optimal algorithm, called Tracking-MaxWeight (TMW), which enhances the original MaxWeight algorithm with an explicit learning of the policy used by uncontrollable nodes. Next, we investigate the scenario where uncontrollable nodes use a queue-dependent policy and the problem is formulated as an MDP with unknown queueing dynamics. We propose a new reinforcement learning algorithm, called Truncated Upper Confidence Reinforcement Learning (TUCRL), and prove that TUCRL achieves tunable three-way tradeoffs between throughput, delay and convergence rate.
Near-Optimal Joint Object Matching via Convex Relaxation

Joint object matching aims at aggregating information from a large collection of similar instances (e.g. images, graphs, shapes) to improve the correspondences computed between pairs of objects, typically by exploiting global map compatibility. Despite some practical advances on this problem, from the theoretical point of view, the error-correction ability of existing algorithms are limited by a constant barrier -- none of them can provably recover the correct solution when more than a constant fraction of input correspondences are corrupted. Moreover, prior approaches focus mostly on fully similar objects, while it is practically more demanding and realistic to match instances that are only partially similar to each other. In this paper, we propose an algorithm to jointly match multiple objects that exhibit only partial similarities, where the provided pairwise feature correspondences can be densely corrupted. By encoding a consistent partial map collection into a 0-1 semidefinite matrix, we attempt recovery via a two-step procedure, that is, a spectral technique followed by a parameter-free convex program called MatchLift. Under a natural randomized model, MatchLift exhibits nearoptimal error-correction ability, i.e. it guarantees the recovery of the ground-truth maps even when a dominant fraction of the inputs are randomly corrupted. We evaluate the proposed algorithm on various benchmark data sets including synthetic examples and real-world examples, all of which confirm the practical applicability of the proposed algorithm.
The probability that a character value is zero for the symmetric group

Let be chosen at random from the irreducible characters of the symmetric group Sn and let g be chosen at random from the group itself. What is the probability that .g/ D 0? In this short note we give a remarkable asymptotic answer of one. Throughout the paper “at random” means uniformly at random. Theorem 1. If is chosen at random from the irreducible characters of Sn and g is chosen at random from Sn, then .g/ D 0 with probability P.Sn/ ! 1 as n ! 1. It will follow that the same must be true for the alternating group An. Theorem 2. If is chosen at random from the irreducible characters ofAn and g is chosen at random from An, then .g/ D 0 with probability P.An/ ! 1 as n ! 1. We prove these results in Section 1 and make some remarks in Section 2.
Mining Features Associated with Effective Tweets

What tweet features are associated with higher effectiveness in tweets? Through the mining of 122 million engagements of 2.5 million original tweets, we present a systematic review of tweet time, entities, composition, and user account features. We show that the relationship between various features and tweeting effectiveness is non-linear; for example, tweets that use a few hashtags have higher effectiveness than using no or too many hashtags. This research closely relates to various industrial applications that are based on tweet features, including the analysis of advertising campaigns, the prediction of user engagement, the extraction of signals for automated trading, etc.
Competitive Resource Allocation in HetNets: The Impact of Small-Cell Spectrum Constraints and Investment Costs

Heterogeneous wireless networks with small-cell deployments in licensed and unlicensed spectrum bands are a promising approach for expanding wireless connectivity and service. As a result, wireless service providers (SPs) are adding small-cells to augment their existing macro-cell deployments. This added flexibility complicates network management, in particular, service pricing and spectrum allocations across macro- and small-cells. Further, these decisions depend on the degree of competition among SPs. Restrictions on shared spectrum access imposed by regulators, such as low power constraints that lead to small-cell deployments, along with the investment cost needed to add small cells to an existing network, also impact strategic decisions and market efficiency. If the revenue generated by small-cells does not cover the investment cost, then there will be no deployment even if it increases social welfare. We study the implications of such spectrum constraints and investment costs on resource allocation and pricing decisions by competitive SPs, along with the associated social welfare. Our results show that while the optimal resource allocation taking constraints and investment into account can be uniquely determined, adding those features with strategic SPs can have a substantial effect on the equilibrium market structure.
Injections into function spaces over compacta

Abstract We study the topology of X given that C p ( X ) injects into C p ( Y ) , where Y is compact. We first show that if C p over a GO-space injects into C p over a compactum, then the Dedekind remainder of the GO-space is hereditarily paracompact. Also, for each ordinal τ of uncountable cofinality, we construct a continuous bijection of C p ( τ , { 0 , 1 } ) onto a subgroup of C p ( τ + 1 , { 0 , 1 } ) , which is in addition a group isomorphism.
CW-resolutions of monomial ideals that are supported on face posets

ABSTRACTGiven a monomial ideal I with minimal free resolution ℱ supported in characteristic p>0 on a CW-complex X with regular 2-skeleton, in general it is not the case that the face poset of X, P(X), also supports ℱ in the sense of Clark and Tchernev. We construct a (not necessarily regular) CW-complex Y that also supports ℱ and such that the face poset P(Y) also supports ℱ.
Principal differences analysis: interpretable characterization of differences between distributions

We introduce principal differences analysis (PDA) for analyzing differences between high-dimensional distributions. The method operates by finding the projection that maximizes the Wasserstein divergence between the resulting univariate populations. Relying on the Cramer-Wold device, it requires no assumptions about the form of the underlying distributions, nor the nature of their inter-class differences. A sparse variant of the method is introduced to identify features responsible for the differences. We provide algorithms for both the original minimax formulation as well as its semidefinite relaxation. In addition to deriving some convergence results, we illustrate how the approach may be applied to identify differences between cell populations in the somatosensory cortex and hippocampus as manifested by single cell RNA-seq. Our broader framework extends beyond the specific choice of Wasserstein divergence.
Monotone operator theory in convex optimization

Several aspects of the interplay between monotone operator theory and convex optimization are presented. The crucial role played by monotone operators in the analysis and the numerical solution of convex minimization problems is emphasized. We review the properties of subdifferentials as maximally monotone operators and, in tandem, investigate those of proximity operators as resolvents. In particular, we study new transformations which map proximity operators to proximity operators, and establish connections with self-dual classes of firmly nonexpansive operators. In addition, new insights and developments are proposed on the algorithmic front.
On the Local Existence for the Characteristic Initial Value Problem in General Relativity

Given a truncated incoming null cone and a truncated outgoing null cone intersecting at a two sphere $S$ with smooth characteristic initial data, a theorem of Rendall shows that the vacuum Einstein equations can be solved in a small neighborhood of $S$ in the future of $S$. We show that in fact the vacuum Einstein equations can be solved in a neighborhood in the future of the cones, as long as the constraint equations are initially satisfied on the null cones. The proof is based on energy type estimates and relies heavily on the null structure of the Einstein equations in the double null foliation.
DC decomposition of nonconvex polynomials with algebraic techniques

We consider the problem of decomposing a multivariate polynomial as the difference of two convex polynomials. We introduce algebraic techniques which reduce this task to linear, second order cone, and semidefinite programming. This allows us to optimize over subsets of valid difference of convex decompositions (dcds) and find ones that speed up the convex–concave procedure. We prove, however, that optimizing over the entire set of dcds is NP-hard.
Finding $k$ Simple Shortest Paths and Cycles

We present algorithms and techniques for several problems related to finding multiple simple shortest paths and cycles in a graph. Our main result is a new algorithm for finding k simple shortest paths for all pairs of vertices in a weighted directed graph G = (V, E). For k = 2 our algorithm runs in O(mn + n^2 log n) time where m and n are the number of edges and vertices in G. For k = 3 our algorithm runs in O(mn^2 + n^3 log n) time, which is almost a factor of n faster than the best previous algorithm. Our approach is based on forming suitable path extensions to find simple shortest paths; this method is different from the 'detour finding' technique used in most of the prior work on simple shortest paths, replacement paths, and distance sensitivity oracles. We present new algorithms for generating simple cycles and simple paths in G in non-decreasing order of their weight. The algorithm for generating simple paths is much faster,and uses another variant of path extensions.
Advanced EMT and Phasor-Domain Hybrid Simulation With Simulation Mode Switching Capability for Transmission and Distribution Systems

Conventional electromagnetic transient (EMT) and phasor-domain hybrid simulation approaches presently exist for transmission system level studies. Their simulation efficiency is generally constrained by the EMT simulation. With an increasing number of distributed energy resources and nonconventional loads being installed in distribution systems, it is imperative to extend the hybrid simulation application to include distribution systems and integrated transmission and distribution systems. Meanwhile, it is equally important to improve the simulation efficiency as the modeling scope and complexity of the detailed system in the EMT simulation increases. To meet both requirements, this paper introduces an advanced EMT and phasor-domain hybrid simulation approach. This approach has two main features: first, a comprehensive phasor-domain modeling and simulation framework which supports positive-sequence, three-sequence, three-phase, and mixed three-sequence/three-phase representations and second, a robust and flexible simulation mode switching scheme. The developed scheme enables simulation switching from hybrid simulation mode back to pure phasor-domain dynamic simulation mode to achieve significantly improved simulation efficiency. The proposed method has been tested on integrated transmission and distribution systems. The results show that with the developed simulation switching feature, the total computational time is significantly reduced compared to running the hybrid simulation for the whole simulation period while maintaining good simulation accuracy.
Action of Complex Symplectic Matrices on the Siegel Upper Half Space

Abstract The Siegel upper half space, S n , the space of complex symmetric matrices, Z with positive definite imaginary part, is the generalization of the complex upper half plane in higher dimensions. In this paper, we study a generalization of linear fractional transformations, Φ S , where S is a complex symplectic matrix, on the Siegel upper half space. We partially classify the complex symplectic matrices for which Φ S ( Z ) is well defined. We also consider S n and S ‾ n as metric spaces and discuss distance properties of the map Φ S from S n to S n and S ‾ n respectively.