cssi/SciSciGPT-SciSciNet huggingface dataset:
Poissonian pair correlation and discrepancy

Abstract A sequence ( x n ) n = 1 ∞ on the torus T ≅ [ 0 , 1 ] is said to exhibit Poissonian pair correlation if the local gaps behave like the spacings of a Poisson random variable, i.e. lim N → ∞ 1 N # 1 ≤ m ≠ n ≤ N : | x m − x n | ≤ s N = 2 s almost surely. We show that being close to Poissonian pair correlation for few values of s is enough to deduce global regularity statements: if, for some 0 δ 1 ∕ 2 , a set of points x 1 , … , x N satisfies 1 N # 1 ≤ m ≠ n ≤ N : | x m − x n | ≤ s N ≤ ( 1 + δ ) 2 s for all 1 ≤ s ≤ ( 8 ∕ δ ) log N , then the discrepancy D N of the set satisfies D N ≲ δ 1 ∕ 3 + N − 1 ∕ 3 δ − 1 ∕ 2 . We also show that distribution properties are reflected in the global deviation from the Poissonian pair correlation N 2 D N 5 ≲ 2 N ∫ 0 N ∕ 2 1 N # 1 ≤ m ≠ n ≤ N : | x m − x n | ≤ s N − 2 s 2 d s ≲ N 2 D N 2 , where the lower bound is conditioned on D N ≳ N − 1 ∕ 3 . The proofs use a connection between exponential sums, the heat kernel on T and spatial localization. Exponential sum estimates are obtained as a byproduct. We also describe a connection to diaphony and several open problems.
A general homological Kleiman-Bertini theorem

Let G be a smooth algebraic group acting on a variety X. Let F and E be coherent sheaves on X. We show that if all the higher Tor sheaves of F against G-orbits vanish, then for generic g in G, the sheaf Tor^X_j(gF, E) vanishes for all j >0. This generalizes a result of Miller and Speyer for transitive group actions and a result of Speiser, itself generalizing the classical Kleiman-Bertini theorem, on generic transversality, under a general group action, of smooth subvarieties over an algebraically closed field of characteristic 0.
Large Scale Distributed Semi-Supervised Learning Using Streaming Approximation

Traditional graph-based semi-supervised learning (SSL) approaches, even though widely applied, are not suited for massive data and large label scenarios since they scale linearly with the number of edges $|E|$ and distinct labels $m$. To deal with the large label size problem, recent works propose sketch-based methods to approximate the distribution on labels per node thereby achieving a space reduction from $O(m)$ to $O(\log m)$, under certain conditions. In this paper, we present a novel streaming graph-based SSL approximation that captures the sparsity of the label distribution and ensures the algorithm propagates labels accurately, and further reduces the space complexity per node to $O(1)$. We also provide a distributed version of the algorithm that scales well to large data sizes. Experiments on real-world datasets demonstrate that the new method achieves better performance than existing state-of-the-art algorithms with significant reduction in memory footprint. We also study different graph construction mechanisms for natural language applications and propose a robust graph augmentation strategy trained using state-of-the-art unsupervised deep learning architectures that yields further significant quality gains.
Cross-Domain Transfer in Reinforcement Learning Using Target Apprentice

In this paper, we present a new approach to transfer in Reinforcement Learning (RL) for cross-domain tasks. Unlike, available transfer approaches, where target task learning is accelerated through initialized learning from source, we propose to adapt and reuse the optimal source policy directly in the related domains. We show the optimal policy from a related source task can be near optimal in target domain provided an adaptive policy accounts for the model error between target and the projected source. A significant advantage of the proposed policy augmentation is in generalizing the policies across related domains without having to re-Iearn the new tasks. We demonstrate that, this architecture leads to better sample efficiency in the transfer, reducing sample complexity of target task learning to target apprentice learning.
A Morita theorem for dual operator algebras

Abstract We prove that two dual operator algebras are weak ∗ Morita equivalent in the sense of [D.P. Blecher, U. Kashyap, Morita equivalence of dual operator algebras, J. Pure Appl. Algebra 212 (2008) 2401–2412] if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weak ∗ -continuous on appropriate morphism spaces. Moreover, in a fashion similar to the operator algebra case, we characterize such functors as the module normal Haagerup tensor product with an appropriate weak ∗ Morita equivalence bimodule. We also develop the theory of the W ∗ -dilation, which connects the non-selfadjoint dual operator algebra with the W ∗ -algebraic framework. In the case of weak ∗ Morita equivalence, this W ∗ -dilation is a W ∗ -module over a von Neumann algebra generated by the non-selfadjoint dual operator algebra. The theory of the W ∗ -dilation is a key part of the proof of our main theorem.
The spt-crank for overpartitions

Bringmann, Lovejoy, and Osburn (14, 15) showed that the generating functions of the spt- overpartition functions spt (n), spt1 (n), spt2 (n), and M2spt(n) are quasimock theta functions, and satisfy a number of simple Ramanujan-like congruences. Andrews, Garvan, and Liang (7) defined an spt-crank in terms of weighted vector partitions which combinatorially explain simple congruences mod 5 and 7 for spt(n). Chen, Ji, and Zang (17) were able to define this spt-crank in terms of ordinary partitions. In this paper we define spt-cranks in terms of vector partitions that combinatorially explain the known simple congruences for all the spt-overpartition functions as well as new simple congruences. For all the overpartition functions except M2spt(n) we are able to define the spt-crank purely in terms of marked overpartitions. The proofs of the congruences depend on Bailey's Lemma and the difference formulas for the Dyson rank of an overpartition (24) and the M2-rank of a partition without repeated odd parts (25).
BIRACK MODULES AND THEIR LINK INVARIANTS

We extend the rack algebra ℤ[X] defined by Andruskiewitsch and Grana to the case of biracks, enabling a notion of birack modules. We use these birack modules to define an enhancement of the birack counting invariant generalizing the birack module counting invariant in [A. Haas, G. Heckel, S. Nelson, J. Yuen and Q. Zhang, Rack module enhancements of counting invariants, Osaka J. Math.49 (2012) 471–488]. We provide examples demonstrating that the enhanced invariant is not determined by the Jones or Alexander polynomials and is stronger than the unenhanced birack counting invariant.
Event Discovery in Time Series.

The discovery of events in time series can have important implications, such as identifying microlensing events in astronomical surveys, or changes in a patient’s electrocardiogram. Current methods for identifying events require a sliding window of a fixed size, which is not ideal for all applications and could overlook important events. In this work, we develop probability models for calculating the significance of an arbitrary-sized sliding window and use these probabilities to find areas of significance. Because a brute force search of all sliding windows and all window sizes would be computationally intractable, we introduce a method for quickly approximating the results. We apply our method to over 100,000 astronomical time series from the MACHO survey, in which 56 different sections of the sky are considered, each with one or more known events. Our method was able to recover 100% of these events in the top 1% of the results, essentially pruning 99% of the data. Interestingly, our method was able to identify events that do not pass traditional event discovery procedures.
In-depth exploration of single-snapshot lossy compression techniques for N-body simulations

In situ lossy compression allowing user-controlled data loss can significantly reduce the I/O burden. For large-scale N-body simulations where only one snapshot can be compressed at a time, the lossy compression ratio is very limited because of the fairly low spatial coherence of the particle data. In this work, we assess the state-of-the-art single-snapshot lossy compression techniques of two common N-body simulation models: cosmology and molecular dynamics. We design a series of novel optimization techniques based on the two representative real-world N-body simulation codes. For molecular dynamics simulation, we propose three compression modes (i.e., best speed, best tradeoff, best compression mode) that can refine the tradeoff between the compression rate (a.k.a., speed/throughput) and ratio. For cosmology simulation, we identify that our improved SZ is the best lossy compressor with respect to both compression ratio and rate. Its compression ratio is higher than the second-best compressor by 11% with comparable compression rate. Experiments with up to 1024 cores on the Blues supercomputer at Argonne show that our proposed lossy compression method can reduce I/O time by 80% compared with writing data directly to a parallel file system and outperforms the second-best solution by 60%. Moreover, our proposed lossy compression methods have the best rate-distortion with reasonable compression errors on the tested N-body simulation data compared with state-of-the-art compressors.
Uniqueness Properties of Hardy Space Functions

We study the boundary uniqueness properties of Hardy space functions in several complex variables. Along the way, we develop properties of the Lumer Hardy space.
Entanglement is not enough

This is the written version of a lecture given at KITP in Oct 2014 on Black Holes and quantum complexity. I've included (in boldface) various questions that came up during the lecture and discussions the following day, as well as the quantitative calculations that form the basis of the arguments.
Totaro’s question for tori of low rank

Let $G$ be a smooth connected linear algebraic group and $X$ be a $G$-torsor. Totaro asked: if $X$ admits a zero-cycle of degree $d \geq 1$, then does $X$ have a closed \'etale point of degree dividing $d$? This question is entirely unexplored in the literature for algebraic tori. We settle Totaro's question affirmatively for algebraic tori of rank $\leq 2$.
Pathogen evasion of chemokine response through suppression of CXCL10

Clearance of intracellular pathogens, such as Leishmania (L.) major, depends on an immune response with well-regulated cytokine signaling. Here we describe a pathogen-mediated mechanism of evading CXCL10, a chemokine with diverse antimicrobial functions, including T cell recruitment. Infection with L. major in a human monocyte cell line induced robust CXCL10 transcription without increasing extracellular CXCL10 protein concentrations. We found that this transcriptionally independent suppression of CXCL10 is mediated by the virulence factor and protease, glycoprotein-63 (gp63). Specifically, GP63 cleaves CXCL10 after amino acid A81 at the base of a C-terminal alpha-helix. Cytokine cleavage by GP63 demonstrated specificity, as GP63 cleaved CXCL10 and its homologues, which all bind the CXCR3 receptor, but not distantly related chemokines, such as CXCL8 and CCL22. Further characterization demonstrated that CXCL10 cleavage activity by GP63 was produced by both extracellular promastigotes and intracellular amastigotes. Crucially, CXCL10 cleavage impaired T cell chemotaxis in vitro, indicating that cleaved CXCL10 cannot signal through CXCR3. Ultimately, we propose CXCL10 suppression is a convergent mechanism of immune evasion, as Salmonella enterica and Chlamydia trachomatis also suppress CXCL10. This commonality suggests that counteracting CXCL10 suppression may provide a generalizable therapeutic strategy against intracellular pathogens.
Models for mock homotopy categories of projectives

Let $R$ be a ring and Ch($R$) the category of chain complexes of $R$-modules. We put an abelian model structure on Ch($R$) whose homotopy category is equivalent to $K(Proj)$, the homotopy category of all complexes of projectives. However, the cofibrant objects are not complexes of projectives, but rather all complexes of flat modules. The trivial objects are what Positselski calls contraacyclic complexes and so the homotopy category coincides with his contraderived category. We in fact construct this model on the category of chain complexes of quasi-coherent sheaves on any scheme $X$ admitting a flat generator. In this case the homotopy category recovers what Murfet calls the mock homotopy category of projectives. In the same way we construct a model for the (mock) projective stable derived category, and we use model category methods to recover the recollement of Murfet. Finally, we consider generalizations by replacing the flat cotorsion pair with other complete hereditary cotorsion pairs in Grothendieck categories.
Integrability of scalar curvature and normal metric on conformally flat manifolds

Abstract On a manifold ( R n , e 2 u | d x | 2 ) , we say u is normal if the Q-curvature equation that u satisfies ( − Δ ) n 2 u = Q g e n u can be written as the integral form u ( x ) = 1 c n ∫ R n log ⁡ | y | | x − y | Q g ( y ) e n u ( y ) d y + C . In this paper, we show that the integrability assumption on the negative part of the scalar curvature implies the metric is normal. As an application, we prove a bi-Lipschitz equivalence theorem for conformally flat metrics.
Super-Resolution of Complex Exponentials From Modulations With Unknown Waveforms

Super-resolution is generally referred to as the task of recovering fine details from coarse information. Motivated by applications, such as single-molecule imaging, radar imaging, etc., we consider parameter estimation of complex exponentials from their modulations with unknown waveforms, allowing for non-stationary blind super-resolution. This problem, however, is ill-posed since both the parameters associated with the complex exponentials and the modulating waveforms are unknown. To alleviate this, we assume that the unknown waveforms live in a common low-dimensional subspace. Using a lifting trick, we recast the blind super-resolution problem as a structured low-rank matrix recovery problem. Atomic norm minimization is then used to enforce the structured low-rankness, and is reformulated as a semidefinite program that is solvable in polynomial time. We show that, up to scaling ambiguities, exact recovery of both of the complex exponential parameters and the unknown waveforms is possible when the waveform subspace is random and the number of measurements is proportional to the number of degrees of freedom in the problem. Numerical simulations support our theoretical findings, showing that non-stationary blind super-resolution using atomic norm minimization is possible.
The free boundary of variational inequalities with gradient constraints

Abstract In this paper we prove that the free boundary of the minimizer of I ( v ) ≔ ∫ U 1 2 | D v | 2 − η v d x , subject to the pointwise gradient constraint | D v | p ≤ 1 , is as regular as the tangent bundle of the boundary of the domain. To this end, we study a generalized notion of ridge of a domain in the plane, which is the set of singularity of the distance function in the p -norm to the boundary of the domain.
AACT: Application-Aware Cooperative Time Allocation for Internet of Things

As the number of Internet of Things (IoT) devices keeps increasing, data is required to be communicated and processed by these devices at unprecedented rates. Cooperation among wireless devices by exploiting Device- to-Device (D2D) connections is promising, where aggregated resources in a cooperative setup can be utilized by all devices, which would increase the total utility of the setup. In this paper, we focus on the resource allocation problem for cooperating IoT devices with multiple heterogeneous applications. In particular, we develop Application-Aware Cooperative Time allocation (AACT) framework, which optimizes the time that each application utilizes the aggregated system resources by taking into account heterogeneous device constraints and application requirements. AACT is grounded on the concept of Rolling Horizon Control (RHC) where decisions are made by iteratively solving a convex optimization problem over a moving control window of estimated system parameters. The simulation results demonstrate significant performance gains.
A Fully Convolutional Tri-Branch Network (FCTN) for Domain Adaptation

A domain adaptation method for urban scene segmentation is proposed in this work. We develop a fully convolutional tri-branch network, where two branches assign pseudo labels to images in the unlabeled target domain while the third branch is trained with supervision based on images in the pseudo-labeled target domain. The re-labeling and re-training processes alternate. With this design, the tri-branch network learns target-specific discriminative representations progressively and, as a result, the cross-domain capability of the segmenter improves. We evaluate the proposed network on large-scale domain adaptation experiments using both synthetic (GTA) and real (Cityscapes) images. It is shown that our solution achieves the state-of-the-art performance and it outperforms previous methods by a significant margin.
Rank and crank moments for partitions without repeated odd parts

Using quasimodular forms with respect to Γ0(4) we find exact relations between the M2-rank for partitions without repeated odd parts and three residual cranks. From these identities we are able to deduce various congruences mod 3 and 5 between the rank and crank moments. In turn, these congruences give congruences for M2spt(n), the number of occurrences of smallest parts in the partitions of n with smallest part even and without repeated odd parts, and for the higher-order analog M2spt2(n).
Hermitian harmonic maps and non-degenerate curvatures

In this paper, we study the existence of various harmonic maps from Hermitian manifolds to Kaehler, Hermitian and Riemannian manifolds respectively. By using refined Bochner formulas on Hermitian (possibly non-Kaehler) manifolds, we derive new rigidity results on Hermitian harmonic maps from compact Hermitian manifolds to Riemannian manifolds, and we also obtain the complex analyticity of pluri-harmonic maps from compact complex manifolds to compact Kaehler manifolds (and Riemannian manifolds) with non-degenerate curvatures, which are analogous to several fundamental results in [28,Siu], [14,Jost-Yau] and [26, Sampson].
Free probability, Planar algebras, Subfactors and Random Matrices

To a planar algebra P in the sense of Jones we associate a natural noncommutative ring, which can be viewed as the ring of non-commutative polynomials in several indeterminates, invariant under a symmetry encoded by P. We show that this ring carries a natural structure of a non-commutative probability space. Non-commutative laws on this space turn out to describe random matrix ensembles possessing special symmetries. As application, we give a canonical construction of a subfactor and its symmetric enveloping algebra associated to a given planar algebra P. This talk is based on joint work with A. Guionnet and V. Jones.
An arc graph distance formula for the flip graph

Using existing technology, we prove a Masur-Minsky style distance formula for flip- graph distance between two triangulations, expressed as a sum of the distances of the projections of these triangulations into arc graphs of the suitable subsurfaces of S.
Black Box FDR

Analyzing large-scale, multi-experiment studies requires scientists to test each experimental outcome for statistical significance and then assess the results as a whole. We present Black Box FDR (BB-FDR), an empirical-Bayes method for analyzing multi-experiment studies when many covariates are gathered per experiment. BB-FDR learns a series of black box predictive models to boost power and control the false discovery rate (FDR) at two stages of study analysis. In Stage 1, it uses a deep neural network prior to report which experiments yielded significant outcomes. In Stage 2, a separate black box model of each covariate is used to select features that have significant predictive power across all experiments. In benchmarks, BB-FDR outperforms competing state-of-the-art methods in both stages of analysis. We apply BB-FDR to two real studies on cancer drug efficacy. For both studies, BB-FDR increases the proportion of significant outcomes discovered and selects variables that reveal key genomic drivers of drug sensitivity and resistance in cancer.
Optimum basis of finite convex geometry

Abstract Convex geometries form a subclass of closure systems with unique criticals, or U C -systems. We show that the F -basis introduced in Adaricheva and Nation (2014) for U C -systems, becomes optimum in convex geometries, in two essential parts of the basis: right sides (conclusions) of binary implications and left sides (premises) of non-binary ones. The right sides of non-binary implications can also be optimized, when the convex geometry either satisfies the Carousel property, or does not have D -cycles. The latter generalizes a result of P.L. Hammer and A. Kogan for acyclic Horn Boolean functions. Convex geometries of order convex subsets in a poset also have tractable optimum basis. The problem of tractability of optimum basis in convex geometries in general remains to be open.
Minimal reductions and cores of edge ideals

Abstract We study minimal reductions of edge ideals of graphs and determine restrictions on the coefficients of the generators of these minimal reductions. We prove that when I is not basic, then core I ⊂ m I , where I is an edge ideal in the corresponding localized polynomial ring and m is the maximal ideal of this ring. We show that the inclusion is an equality for the edge ideal of an even cycle with an arbitrary number of whiskers. Moreover, we show that the core is obtained as a finite intersection of homogeneous minimal reductions in the case of even cycles. The formula for the core does not hold in general for the edge ideal of any graph and we provide a counterexample. In particular, we show in this example that the core is not obtained as a finite intersection of general minimal reductions.
Shortened Regenerating Codes

For general exact repair regenerating codes, the optimal trade-offs between the storage size and repair bandwidth remain undetermined. Various outer bounds and partial results have been proposed. Using a simple chain rule argument, we identify nonnegative differences between the functional repair and the exact repair outer bounds, and one of the differences is then bounded from below by the repair data of a shortened subcode. Our main result is a new outer bound for an exact repair regenerating code in terms of its shortened subcodes. In general, the new outer bound is implicit and depends on the choice of shortened subcodes. For the linear case, we obtain explicit bounds.
Intermittency fronts for space-time fractional stochastic partial differential equations in (d+1) dimensions

Abstract We consider time fractional stochastic heat type equation ∂ t β u t ( x ) = − ν ( − Δ ) α / 2 u t ( x ) + I t 1 − β [ σ ( u ) W ⋅ ( t , x ) ] in ( d + 1 ) dimensions, where ν > 0 , β ∈ ( 0 , 1 ) , α ∈ ( 0 , 2 ] , d min { 2 , β − 1 } α , ∂ t β is the Caputo fractional derivative, − ( − Δ ) α / 2 is the generator of an isotropic stable process, W ⋅ ( t , x ) is space-time white noise, and σ : R → R is Lipschitz continuous. Mijena and Nane proved in (Mijena and Nane, 2016) that: (i) absolute moments of the solutions of this equation grow exponentially; and (ii) the distances to the origin of the farthest high peaks of those moments grow exactly linearly with time. The last result was proved under the assumptions α = 2 and d = 1 . In this paper we extend this result to the case α = 2 and d ∈ { 1 , 2 , 3 } .
How Do Fairness Definitions Fare?: Examining Public Attitudes Towards Algorithmic Definitions of Fairness

What is the best way to define algorithmic fairness? While many definitions of fairness have been proposed in the computer science literature, there is no clear agreement over a particular definition. In this work, we investigate ordinary people's perceptions of three of these fairness definitions. Across two online experiments, we test which definitions people perceive to be the fairest in the context of loan decisions, and whether fairness perceptions change with the addition of sensitive information (i.e., race of the loan applicants). Overall, one definition (calibrated fairness) tends to be more pre- ferred than the others, and the results also provide support for the principle of affirmative action.
A Note on rings of finite rank

The rank rk(R) of a ring R is the supremum of minimal cardinalities of generating sets of I as I ranges over ideals of R. Matsuda and Matson showed that every n∈ℤ+ (the positive integers) occurs as...
Ill-posedness for the Incompressible Euler Equations in Critical Sobolev Spaces

For the 2D Euler equation in vorticity formulation, we construct localized smooth solutions whose critical Sobolev norms become large in a short period of time, and solutions which initially belong to $$L^\infty \cap H^1$$ but escapes $$H^1$$ immediately for $$t>0$$ . Our main observation is that a localized chunk of vorticity bounded in $$L^\infty \cap H^1$$ with odd-odd symmetry is able to generate a hyperbolic flow with large velocity gradient at least for a short period of time, which stretches the vorticity gradient.
An information-theoretic external cluster-validity measure

In this paper we propose a measure of similarity/ association between two partitions of a set of objects. Our motivation is the desire to use the measure to characterize the quality or accuracy of clustering algorithms by somehow comparing the clusters they produce with "ground truth" consisting of classes assigned by manual means or some other means in whose veracity there is confidence. Such measures are referred to as "external". Our measure also allows clusterings with different numbers of clusters to be compared in a quantitative and principled way. Our evaluation scheme quantitatively measures how useful the cluster labels are as predictors of their class labels. It computes the reduction in the number of bits that would be required to encode (comress) the class labels if both the encoder and decoder have free access to the cluster labels. To achieve this encoding the estimated conditional probabilities of the class labels given the cluster labels must also be encoded. In addition to defining the measure we compare it to other commonly used external measures and demonstrate its superiority as judged by certain criteria.
Pattern characterization of rationally smooth affine Schubert varieties of type A

Abstract Schubert varieties in finite dimensional flag manifolds G / P are a well-studied family of projective varieties indexed by elements of the corresponding Weyl group W. In particular, there are many tests for smoothness and rational smoothness of these varieties. One key result due to Lakshmibai and Sandhya is that in type A the smooth Schubert varieties are precisely those that are indexed by permutations that avoid the patterns 4231 and 3412. Recently, there has been a flurry of research related to the infinite dimensional analogs of flag manifolds corresponding with G being a Kac–Moody group and W being an affine Weyl group or parabolic quotient. In this paper we study the case when W is the affine Weyl group of type A or the affine permutations. We develop the notion of pattern avoidance for affine permutations. Our main result is a characterization of the rationally smooth Schubert varieties corresponding to affine permutations in terms of the patterns 4231 and 3412 and the twisted spiral permutations.
Sum capacity of K user Gaussian degraded interference channels

This paper studies a family of genie-MAC (multiple access channel) outer bounds for K-user Gaussian interference channels. This family is inspired by existing genie-aided bounding mechanisms, but differs from current approaches in its optimization problem formulation and application. The fundamental idea behind these bounds is to create a group of genie receivers that form multiple access channels that can decode a subset of the original interference channel's messages. The MAC sum capacity of each of the genie receivers provides an outer bound on the sum of rates for this subset. The genie-MAC outer bounds are used to derive new sum-capacity results. In particular, this paper derives sum-capacity in closed-form for the class of K-user Gaussian degraded interference channels. The sum-capacity achieving scheme is shown to be a successive interference cancellation scheme. This result generalizes a known result for two-user channels to K-user channels.
Fundamentals of Modeling Finite Wireless Networks Using Binomial Point Process

Modeling the locations of nodes as a uniform binomial point process, we present a generic mathematical framework to characterize the performance of an arbitrarily located reference receiver in a finite wireless network. Different from most of the prior works where the serving transmitter (TX) is located at the fixed distance from the reference receiver, we consider two general TX-selection policies: 1) uniform TX-selection : the serving node is chosen uniformly at random from amongst all transmitting nodes and 2) $k$ -closest TX-selection : the serving node is the $k$ th closest node (out of all transmitting nodes) to the reference receiver. The key intermediate step in our analysis is the derivation of a new set of distance distributions that lead not only to the tractable analysis of coverage probability but also enable the analysis of wide range of classical and currently trending problems in wireless networks. Using this new set of distance distributions, we further investigate the diversity loss due to $\mathtt {SIR}$ correlation in a finite network. We then obtain the optimal number of links that can be simultaneously activated to maximize network spectral efficiency. Finally, we evaluate optimal caching probability to maximize the total hit probability in cache-enabled finite networks.
Dynamics of Large Femtosecond Filament Arrays: Possibilities, Limitations, and Trade-Offs

Stable propagation of large, multifilament arrays over long distances in air paves new ways for microwave-radiation manipulation. Although the dynamics of a single or a few filaments has been discussed in previous studies, we show that the stability of large plasma-filament arrays is significantly more complicated and is constrained by several trade-offs. Here, we analyze the stability properties of rectangular arrays as a function of four parameters: relative phase of the generating beams, number of filaments, separation between them, and initial power. We find that arrays with an alternating filament phase are more stable than similar arrays with all beams in phase. Additionally, we show that increasing the size of an array increases its stability and that a proper choice of the beam separation and the initial power has to be made in order to obtain a dense and regular array of filaments.
Convergence of a mass-lumped finite element method for the Landau-Lifshitz equation

The dynamics of the magnetic distribution in a ferromagnetic material is governed by the Landau-Lifshitz equation, which is a nonlinear geometric dispersive equation with a nonconvex constraint that requires the magnetization to remain of unit length throughout the domain. In this article, we present a mass-lumped finite element method for the Landau-Lifshitz equation. This method preserves the nonconvex constraint at each node of the finite element mesh, and is energy nonincreasing. We show that the numerical solution of our method for the Landau-Lifshitz equation converges to a weak solution of the Landau-Lifshitz-Gilbert equation using a simple proof technique that cancels out the product of weakly convergent sequences. Numerical tests for both explicit and implicit versions of the method on a unit square with periodic boundary conditions are provided for structured and unstructured meshes.
Synthesis of shared control protocols with provable safety and performance guarantees

We formalize synthesis of shared control protocols with correctness guarantees for temporal logic specifications. More specifically, we introduce a modeling formalism in which both a human and an autonomy protocol can issue commands to a robot towards performing a certain task. These commands are blended into a joint input to the robot. The autonomy protocol is synthesized using an abstraction of possible human commands accounting for randomness in decisions caused by factors such as fatigue or incomprehensibility of the problem at hand. The synthesis is designed to ensure that the resulting robot behavior satisfies given safety and performance specifications, e.g., in temporal logic. Our solution is based on nonlinear programming and we address the inherent scalability issue by presenting alternative methods. We assess the feasibility and the scalability of the approach by an experimental evaluation.
Natasha: Faster Non-Convex Stochastic Optimization via Strongly Non-Convex Parameter

Given a non-convex function f(x) that is an average of n smooth functions, we design stochastic first-order methods to find its approximate stationary points. The performance of our new methods depend on the smallest (negative) eigenvalue −σ of the Hessian. This parameter σ captures how strongly non-convex f(x) is, and is analogous to the strong convexity parameter for convex optimization. Our methods outperform the best known results for a wide range of σ, and can also be used to find approximate local minima. In particular, we find an interesting dichotomy: there exists a threshold σ0 so that the fastest methods for σ>σ0 and for σ0 have drastically different behaviors: the former scales with n2/3 and the latter scales with n3/4.
High resolution muon computed tomography at neutrino beam facilities

X-ray computed tomography (CT) has an indispensable role in constructing 3D images of objects made from light materials. However, limited by absorption coefficients, X-rays cannot deeply penetrate materials such as copper and lead. Here we show via simulation that muon beams can provide high resolution tomographic images of dense objects and of structures within the interior of dense objects. The effects of resolution broadening from multiple scattering diminish with increasing muon momentum. As the momentum of the muon increases, the contrast of the image goes down and therefore requires higher resolution in the muon spectrometer to resolve the image. The variance of the measured muon momentum reaches a minimum and then increases with increasing muon momentum. The impact of the increase in variance is to require a higher integrated muon flux to reduce fluctuations. The flux requirements and level of contrast needed for high resolution muon computed tomography are well matched to the muons produced in the pion decay pipe at a neutrino beam facility and what can be achieved for momentum resolution in a muon spectrometer. Such an imaging system can be applied in archaeology, art history, engineering, material identification and whenever there is a need to image inside a transportable object constructed of dense materials.
The generalized dock problem

We show existence and uniqueness for a linearized water wave problem in a two dimensional domain G with corner, formed by two semi-axes Γ1 and Γ2 which intersect under an angle α ∈ (0, π]. The existence and uniqueness of the solution is proved by considering an auxiliary mixed problem with Dirichlet and Neumann boundary conditions. The latter guarantees the existence of the Dirichlet to Neumann map. The water wave boundary value problem is then shown to be equivalent to an equation like vtt + gΛv = Pt with initial conditions, where t stands for time, g is the gravitational constant, P means pressure and Λ is the Dirichlet to Neumann map. We then prove that Λ is a positive self-adjoint operator.
Asymptotic expansion of the difference of two Mahler measures

Abstract Text We show that for almost every polynomial P ( x , y ) with complex coefficients, the difference of the logarithmic Mahler measures of P ( x , y ) and P ( x , x n ) can be expanded in a type of formal series similar to an asymptotic power series expansion in powers of 1 / n . This generalizes a result of Boyd. We also show that such an expansion is unique and provide a formula for its coefficients. When P has algebraic coefficients, the coefficients in the expansion are linear combinations of polylogarithms of algebraic numbers, with algebraic coefficients. Video For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=8VB7gxgPqdc .
Evidence for Tadpole Cancellation in the Topological String

We study the topological string on compact Calabi-Yau threefolds in the presence of orientifolds and D-branes. In examples, we find that the total topological string amplitude admits a BPS expansion only if the topological charge of the D-brane is equal to that of the orientifold plane. We interpret this as a manifestation of a general tadpole cancellation condition in the topological string that is necessary for decoupling of A- and B-model in loop amplitudes. Our calculations in the A-model involve an adapted version of existing localization techniques, and give predictions for the real enumerative geometry of higher genus curves in Calabi-Yau manifolds. In the B-model, we introduce an extension of the holomorphic anomaly equation to unoriented strings.
Nonlocal transformations for accelerated observers

According to the locality postulate of special relativity, the measurements of physical fields by accelerated observers at a given event in Minkowski spacetime are related to each other by the representations of the Lorentz group. Nonlocal extensions of these representations are necessary, however, once acceleration-induced nonlocality is taken into account. The particular case of Dirac spinors is treated in detail and the corresponding nonlocal transformation group is studied.
Entropic Causal Inference

We consider the problem of identifying the causal direction between two discrete random variables using observational data. Unlike previous work, we keep the most general functional model but make an assumption on the unobserved exogenous variable: Inspired by Occam's razor, we assume that the exogenous variable is simple in the true causal direction. We quantify simplicity using Renyi entropy. Our main result is that, under natural assumptions, if the exogenous variable has low H0 entropy (cardinality) in the true direction, it must have high H0 entropy in the wrong direction. We establish several algorithmic hardness results about estimating the minimum entropy exogenous variable. We show that the problem of finding the exogenous variable with minimum H1 entropy (Shannon Entropy) is equivalent to the problem of finding minimum joint entropy given n marginal distributions, also known as minimum entropy coupling problem. We propose an efficient greedy algorithm for the minimum entropy coupling problem, that for n=2 provably finds a local optimum. This gives a greedy algorithm for finding the exogenous variable with minimum Shannon entropy. Our greedy entropy-based causal inference algorithm has similar performance to the state of the art additive noise models in real datasets. One advantage of our approach is that we make no use of the values of random variables but only their distributions. Our method can therefore be used for causal inference for both ordinal and also categorical data, unlike additive noise models.
Uniqueness of asymptotic cones of complete noncompact shrinking gradient Ricci solitons with Ricci curvature decay

Abstract We show that any complete noncompact shrinking gradient Ricci soliton with (1) | Rc | → 0 at infinity or (2) R → 0 at infinity, | Rm | bounded, and κ-noncollapsed has a unique asymptotic cone.
Combined heat and power unit commitment with smart parking lots of plug-in electric vehicles

Vehicle-to-grid (V2G) technology has drawn great interest in the recent years and its efficiency depends on scheduling of charging process of plug-in electric vehicles (PEVs) as small portable power plants in smart parking lots. On the other hand, active shift from centralized to decentralized power generation and environmental concerns have caused an increase in the utilization of combined heat and power (CHP) units in power systems. The goal of this study is to develop and simulate a novel approach for combined heat and power unit commitment with PEVs for cost reduction in electric power system. A schedule for charging and discharging processes of PEVs with respect to load curve variations is proposed in this paper. A modified test system consisting of conventional TG (thermal power generating) units, CHP units, and PEVs is employed to investigate the impacts of PEVs on generation scheduling. For the modified test system, results obtained are encouraging and indicate both the feasibility of the proposed technique and its effectiveness on generation scheduling.
On Haar meager sets

Abstract The notion of Haar null set was introduced by J.P.R. Christensen in 1973 and reintroduced in 1992 in the context of dynamical systems by Hunt, Sauer and Yorke. During the last twenty years this notion has been useful in studying exceptional sets in diverse areas. These include analysis, dynamical systems, group theory, and descriptive set theory. Inspired by these various results, we introduce the topological analogue of the notion of Haar null set. We call it Haar meager set. We prove some basic properties of this notion, state some open problems and suggest a possible line of investigation which may lead to the unification of these two notions in certain context.
UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ARISING FROM HILBERT MODULAR SURFACES

Let p be a prime number and F a totally real number eld. For each prime p of F above p we construct a Hecke operator Tp acting on (modp m ) Katz Hilbert modular classes which agrees with the classical Hecke operator at p for global sections that lift to characteristic zero. Using these operators and the techniques of patching complexes of F. Calegari and D. Geraghty we prove that the Galois representations arising from torsion Hilbert modular classes of parallel weight 1 are unramied at p when (F : Q) = 2. Some partial and some conjectural results are obtained when (F : Q) > 2.
A periodic model for the dynamics of cell volume

We prove the existence and uniqueness of positive periodic solution for a model describing the dynamics of cell volume flux, introduced in Julio A. Hernandez \cite{H}. We also show that the periodic solution is a global attractor. Our results confirm the conjectures made in an interesting recent book of P.J. Torres \cite{T}.
Error estimates of Runge–Kutta discontinuous galerkin methods for the Vlasov–Maxwell system

In this paper, error analysis is established for Runge–Kutta discontinuous Galerkin (RKDG) methods to solve the Vlasov–Maxwell system. This nonlinear hyperbolic system describes the time evolution of collisionless plasma particles of a single species under the self-consistent electromagnetic field, and it models many phenomena in both laboratory and astrophysical plasmas. The methods involve a third order TVD Runge–Kutta discretization in time and upwind discontinuous Galerkin discretizations of arbitrary order in phase domain. With the assumption that the exact solutions have sufficient regularity, the L 2 errors of the particle number density function as well as electric and magnetic fields at any given time T are bounded by C h k + 1 / 2 + C τ 3 under a CFL condition τ / h ≤ γ . Here k is the polynomial degree used in phase space discretization, satisfying (with d x being the dimension of spatial domain), τ is the time step, and h is the maximum mesh size in phase space. Both C and γ are positive constants independent of h and τ , and they may depend on the polynomial degree k , time T , the size of the phase domain, certain mesh parameters, and some Sobolev norms of the exact solution. The analysis can be extended to RKDG methods with other numerical fluxes and to RKDG methods solving relativistic Vlasov–Maxwell equations.
Two Layer 3D Floor Planning

A 3D floorplan is a non-overlapping arrangement of blocks within a large box. Floor planning is a central notion in chip-design, and with recent advances in 3D integrated circuits, understanding 3D floorplans has become important. In this paper, we study so called mosaic 3D floorplans where the interior blocks partition the host box under a topological equivalence. We give representations which give an upper bound on the number of general 3D floorplans, and further consider the number of two layer mosaic floorplans. We prove that the number of two layer mosaic floorplans is $n^{(1+o(1))n/3}$. This contrasts with previous work which has studied 'corner free' mosaic floorplans, where the number is just exponential. The upper bound is by giving a representation, while the lower bound is a randomized construction.
A STAR-FORMING SHOCK FRONT IN RADIO GALAXY 4C+41.17 RESOLVED WITH LASER-ASSISTED ADAPTIVE OPTICS SPECTROSCOPY

Near-infrared integral-field spectroscopy of redshifted [O III], H?, and optical continuum emission from the z = 3.8 radio galaxy 4C+41.17 is presented, obtained with the laser-guide-star adaptive optics facility on the Gemini North telescope. Employing a specialized dithering technique, a spatial resolution of 0.''10, or 0.7?kpc, is achieved in each spectral element, with a velocity resolution of ~70 km s?1. Spectra similar to local starbursts are found for bright knots coincident in archival Hubble Space Telescope ( HST) rest-frame ultraviolet images, which also allows a key line diagnostic to be mapped together with new kinematic information. There emerges a clearer picture of the nebular emission associated with the jet in 8.3?GHz and 15?GHz Very Large Array maps, closely tied to a Ly?-bright shell-shaped structure seen with HST. This supports a previous interpretation of that arc tracing a bow shock, inducing ~1010 ? 11 M ? star formation regions that comprise the clumpy broadband optical/ultraviolet morphology near the core.
Dedekind sums with even denominators

Abstract Let S ( a , b ) denote the normalized Dedekind sum. We study the range of possible values for S ( a , b ) = k q with gcd ⁡ ( k , q ) = 1 . Girstmair proved local restrictions on k depending on q ( mod 12 ) and whether q is a square and conjectured that these are the only restrictions possible. We verify the conjecture in the cases q even, q a square divisible by 3 or 5, and 2 ≤ q ≤ 200 (the latter by computer), and provide progress towards a general approach.
On the regularity of orientable matroids

Abstract We present two characterizations of regular matroids among orientable matroids and use them to give a measure of “how far” an orientable matroid is from being regular.