cssi/SciSciGPT-SciSciNet huggingface dataset:
Quantum mechanics as a measurement theory on biconformal space

Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive standard quantum mechanics, and show how the need for probability amplitudes arises from the use of a standard of measurement. Additionally, we show that a postulate for unique, classical motion yields Hamiltonian dynamics with no measurable size changes, while a postulate for probabilistic evolution leads to physical dilatations manifested as measurable phase changes. Our results lead to the Feynman path integral formulation, from which follows the Schrodinger equation. We discuss the Heisenberg uncertainty relation and fundamental canonical commutation relations.
Sensitivity computation of statistically stationary quantities in turbulent flows

It is well-known that linearized perturbation methods for sensitivity analysis, such as tangent or adjoint equation-based, finite difference and automatic differentiation are not suitable for turbulent flows. The reason is that turbulent flows exhibit chaotic dynamics, leading to the norm of an infinitesimal perturbation to the state growing exponentially in time. As a result, these conventional methods cannot be used to compute the derivatives of long-time averaged quantities to control or design inputs. The ensemble-based approaches and shadowing-based approaches to circumvent the problems of the conventional methods in chaotic systems, also suffer from computational impracticality and lack of consistency guarantees, respectively. We introduce the space-split sensitivity, or the S3 algorithm, which is a Monte-Carlo approach to the chaotic sensitivity computation problem. In this work, we derive the S3 algorithm under simplifying assumptions on the dynamics and present a numerical validation on a low-dimensional example of chaos.
P(i-PrNCH2CH2)3N: an efficient catalyst for TMS-1,3-dithiane addition to aldehydes

Abstract Herein we report the use of commercially available P( i -PrNCH 2 CH 2 ) 3 N ( 1a ) as an efficient catalyst for 2-trimethylsilyl-1,3-dithiane (TMS–dithiane) addition to aldehydes at room temperature. The catalyst loading required for these reactions (5 mol %) is the lowest recorded in the literature, and the majority of the reaction times for this transformation are the shortest thus far reported. A variety of functional groups are tolerated on the aryl aldehyde substrates.
Optical Rotation Computation, Total Synthesis, and Stereochemistry Assignment of the Marine Natural Product Pitiamide A

We report the joint application of ab initio computations and total synthesis to assign the absolute configuration of a new natural product. The expected specific rotations of the (7S,10R)- and (7R,10R)-isomers of pitiamide A in a CHCl3 solvent continuum model were determined as +8 and −39, respectively, by CADPAC calculations of the electric-dipole−magnetic-dipole polarizability tensor. Total syntheses of these two stereoisomers of the marine metabolite were achieved by a convergent strategy that utilized Evans' oxazolidinone alkylation, a novel water-accelerated modification of Negishi's zirconocene-catalyzed asymmetric carbometalation as well as an unusual segment condensation via Mitsunobu alkylation of a nosyl-activated amide. The experimental optical rotation measurements confirmed the results of the computational optical rotation predictions. On the basis of NMR comparisons, the configuration of pitiamide A was assigned as (7R,10R). These studies highlight the considerable structural significance o...
1,5-Hydride transfer protocol for the synthesis of β-branched polyketide structural units

Abstract A novel method to induce 1,5-hydride transfer for the production of methyl substituted polyketide structural units was developed. A new avenue to the formation of a tertiary stereocenter was accomplished through the activation of benzyl protected homoallylic substrates with a variety of electrophilic activating conditions.
Understanding the contributions of visual stimuli to contextual fear conditioning: A proof-of-concept study using LCD screens

The precise contribution of visual information to contextual fear learning and discrimination has remained elusive. To better understand this contribution, we coupled the context pre-exposure facilitation effect (CPFE) fear conditioning paradigm with presentations of distinct visual scenes displayed on 4 LCD screens surrounding a conditioning chamber. Adult male Long-Evans rats received non-reinforced context pre-exposure on Day 1, an immediate 1.5mA foot shock on Day 2, and a non-reinforced context test on Day 3. Rats were pre-exposed to either digital Context (dCtx) A, dCtx B, a distinct Ctx C, or no context on Day 1. Digital context A and B were identical except for the visual image displayed on the LCD screens. Immediate shock and retention testing occurred in dCtx A. Rats pre-exposed dCtx A showed the CPFE with significantly higher levels of freezing compared to controls. Rats pre-exposed to Context B failed to show the CPFE, with freezing that did not highly differ from controls. These results suggest that visual information contributes to contextual fear learning and that visual components of the context can be manipulated via LCD screens. Our approach offers a simple modification to contextual fear conditioning paradigms whereby the visual features of a context can be manipulated to better understand the factors that contribute to contextual fear discrimination and generalization.
Photochemistry of 2-nitrobenzyl enol ethers: oxidative C=C bond scission.

2-Nitrobenzyl enol ethers, when photolyzed in the presence of air, result in an oxidative CC bond scission, forming a ketone as the major product (>60% yield). Enol release leads to the aldehyde as...
Dysregulation of EMT Drives the Progression to Clinically Aggressive Sarcomatoid Bladder Cancer

Sarcomatoid urothelial bladder cancer (SARC) displays a high propensity for distant metastasis and is associated with short survival. We report a comprehensive genomic analysis of 28 cases of SARC and 84 cases of conventional urothelial carcinoma (UC), with the TCGA cohort of 408 muscle-invasive bladder cancers serving as the reference. SARCs show a distinct mutational landscape, with enrichment of TP53, RB1, and PIK3CA mutations. They are related to the basal molecular subtype of conventional UCs and could be divided into epithelial-basal and more clinically aggressive mesenchymal subsets on the basis of TP63 and its target gene expression levels. Other analyses reveal that SARCs are driven by downregulation of homotypic adherence genes and dysregulation of the EMT network, and nearly half exhibit a heavily infiltrated immune phenotype. Our observations have important implications for prognostication and the development of more effective therapies for this highly lethal variant of bladder cancer.
Synthesis and Chemistry of Titanacyclopentane and Titanacyclopropane Rings Supported by Aryloxide Ligation

Treatment of the titanacyclopentadiene compound [Ti(OC6H3Ph2-2,6)2(C4Et4)] (3) (OC6H3Ph2-2,6 = 2,6-diphenylphenoxide) with olefins leads to the formation of a variety of stable titanacyclopentane derivatives along with one equivalent of substituted 1,3-cyclohexadiene. The structural and spectroscopic properties of the ethylene product [Ti(OC6H3Ph2-2,6)2(CH2)4] (4) show a ground state titanacyclopentane structure, but facile fragmentation on the NMR time scale to form a bis(ethylene) complex has been detected. The substituted products [Ti(OC6H3Ph2-2,6)2(C4H6R2)] (R = Me, 5; Et, 6; Ph, 7) formed from α-olefins RCHCH2 exist as a mixture of regio- and stereoisomers in hydrocarbon solution. Analysis of a crystal obtained from solutions of 7 showed a trans-2,5-diphenyl-titanacyclopentane ring to be present in the solid state. Alternative routes to the titanacyclopentane compounds involve treatment of the dichlorides [Ti(OC6H3Ph2-2,6)2Cl2] (1) or [Ti(OC6HPh4-2,3,5,6)2Cl2] (2) with either sodium amalgam (2 Na per...
One-Pot Synthesis of 2-Alkyl/Arylamino-4-oxo-4H-1-Benzopyran-3-Carboxaldehyde from 4-oxo-4H-1-Benzopyran-3-Carboxaldehyde:

Zn/NH4Cl–mediated reactions of aldehyde 1 with nitro compounds 2 afford 2-(N-alkyl/arylamino)-3-formylchromones 4, which on heating with 70% H2SO4 produces 9a-d and 11e-h from 4a-d and 4e-h, respec...
Dynamically Stable Matching

I introduce a stability notion, dynamic stability, for two-sided dynamic matching markets where (i) matching opportunities arrive over time, (ii) matching is one-to-one, and (iii) matching is irreversible. The definition addresses two conceptual issues. First, since not all agents are available to match at the same time, one must establish which agents are allowed to form blocking pairs. Second, dynamic matching markets exhibit a form of externality that is not present in static markets: an agent's payoff from remaining unmatched cannot be defined independently of what other contemporaneous agents' outcomes are. Dynamically stable matchings always exist. Dynamic stability is a necessary condition to ensure timely participation in the economy by ensuring that agents do not strategically delay the time at which they are available to match.
A preliminary analysis of the Shangri-La Bolide on 2017 Oct 4

At 12:07 UT (8:07 pm China Standard Time) on 2017 Oct 4, a bright bolide was widely observed in the Shangri-La region of the Province of Yunnan, China (Figure 1). The event was well observed by the general public as it took place on the night of the Mid Autumn Festival, which is associated with moon gazing. Sonic booms and ground shaking were reported in an area of about a thousand square kilometers northwest of Shangri-La City. Data from U.S. government sensors suggests that the impact energy of the event was approximately 0.54 kt TNT equivalent, with the terminus of the bolide positioned at 28.1°N, 99.4°E. This is the largest observed bolide event over land since the bolide event that took place in Mauritania on 2016 Jun 27 (1.2 kt).
The Politics of Routing: Investigating the Relationship between {AS} Connectivity and Internet Freedom

The Internet’s importance in promoting free and open communication has led to widespread crackdowns on its use in countries around the world. In this study, we investigate the relationship between national policies around freedom of speech and Internet topology in various countries. We combine techniques from network measurement and machine learning to identify features of Internet structure at the national level that are the best indicators of a country’s level of freedom. We find that IP density and path lengths to other countries are the best indicators of a country’s freedom. We also find that our methods predict the freedom category (Free/Partly Free/Not Free) of a country with 95% accuracy.
Modeling OWL with Rules: The ROWL Protege Plugin.

In our experience, some ontology users find it much easier to convey logical statements using rules rather than OWL (or description logic) axioms. Based on recent theoretical developments on transformations between rules and description logics, we develop ROWL, a Protege plugin that allows users to enter OWL axioms by way of rules; the plugin then automatically converts these rules into OWL DL axioms if possible, and prompts the user in case such a conversion is not possible without weakening the semantics of the rule.
Deterministic Sequencing of Exploration and Exploitation for Multi-Armed Bandit Problems

In the Multi-Armed Bandit (MAB) problem, there is a given set of arms with unknown reward models. At each time, a player selects one arm to play, aiming to maximize the total expected reward over a horizon of length T. An approach based on a Deterministic Sequencing of Exploration and Exploitation (DSEE) is developed for constructing sequential arm selection policies. It is shown that for all light-tailed reward distributions, DSEE achieves the optimal logarithmic order of the regret, where regret is defined as the total expected reward loss against the ideal case with known reward models. For heavy-tailed reward distributions, DSEE achieves O(T1/p) regret when the moments of the reward distributions exist up to the pth order for and O(T1/(1+p/2)) for p > 2. With the knowledge of an upper bound on a finite moment of the heavy-tailed reward distributions, DSEE offers the optimal logarithmic regret order. The proposed DSEE approach complements existing work on MAB by providing corresponding results for general reward distributions. Furthermore, with a clearly defined tunable parameter-the cardinality of the exploration sequence, the DSEE approach is easily extendable to variations of MAB, including MAB with various objectives, decentralized MAB with multiple players and incomplete reward observations under collisions, restless MAB with unknown dynamics, and combinatorial MAB with dependent arms that often arise in network optimization problems such as the shortest path, the minimum spanning tree, and the dominating set problems under unknown random weights.
Singular loci of cominuscule Schubert varieties

Let X=G/P be a cominuscule rational homogeneous variety. Equivalently, X admits the structure of a compact Hermitian symmetric space. I give a uniform description (that is, independent of type) of the irreducible components of the singular locus of a Schubert variety Y⊂X in terms of representation theoretic data. The result is based on a recent characterization of the Schubert varieties using an integer a≥0 and a marked Dynkin diagram. Corollaries include: (1) the variety is smooth if and only if a=0; (2) if G is of type ADE, then the singular locus occurs in codimension at least 3.
Analyzing Hidden Representations in End-to-End Automatic Speech Recognition Systems

Neural networks have become ubiquitous in automatic speech recognition systems. While neural networks are typically used as acoustic models in more complex systems, recent studies have explored end-to-end speech recognition systems based on neural networks, which can be trained to directly predict text from input acoustic features. Although such systems are conceptually elegant and simpler than traditional systems, it is less obvious how to interpret the trained models. In this work, we analyze the speech representations learned by a deep end-to-end model that is based on convolutional and recurrent layers, and trained with a connectionist temporal classification (CTC) loss. We use a pre-trained model to generate frame-level features which are given to a classifier that is trained on frame classification into phones. We evaluate representations from different layers of the deep model and compare their quality for predicting phone labels. Our experiments shed light on important aspects of the end-to-end model such as layer depth, model complexity, and other design choices.
Diffusion-based coarse graining in hybrid continuum–discrete solvers: Theoretical formulation and a priori tests

Abstract Coarse graining is an important ingredient in many multi-scale continuum–discrete solvers such as CFD–DEM (computational fluid dynamics–discrete element method) solvers for dense particle-laden flows. Although CFD–DEM solvers have become a mature technique that is widely used in multiphase flow research and industrial flow simulations, a flexible and easy-to-implement coarse graining algorithm that can work with CFD solvers of arbitrary meshes is still lacking. In this work, we proposed a new coarse graining algorithm for continuum–discrete solvers for dense particle-laden flows based on solving a transient diffusion equation. Via theoretical analysis we demonstrated that the proposed method is equivalent to the statistical kernel method with a Gaussian kernel, but the current method is much more straightforward to implement in CFD–DEM solvers. A priori numerical tests were performed to obtain the solid volume fraction fields based on given particle distributions, the results obtained by using the proposed algorithm were compared with those from other coarse graining methods in the literature (e.g., the particle centroid method, the divided particle volume method, and the two-grid formulation). The numerical tests demonstrated that the proposed coarse graining procedure based on solving diffusion equations is theoretically sound, easy to implement and parallelize in general CFD solvers, and has improved mesh-convergence characteristics compared with existing coarse graining methods. The diffusion-based coarse graining method has been implemented into a CFD–DEM solver, the results of which are presented in a separate work.
Video-rate large-scale imaging with Multi-Z confocal microscopy

Fast, volumetric imaging over large scales has been a long-standing challenge in biological microscopy. To address this challenge, we report an augmented variant of confocal microscopy that uses a series of reflecting pinholes axially distributed in the detection space, such that each pinhole probes a different depth within the sample. We thus obtain simultaneous multiplane imaging without the need for axial scanning. Our microscope technique is versatile and configured here to provide two-color fluorescence imaging with a field of view larger than a millimeter at video rate. Its general applicability is demonstrated with neuronal imaging of both Caenorhabditis elegans and mouse brains in vivo.
Equimultiplicity in Hilbert–Kunz theory

We study further the properties of Hilbert–Kunz multiplicity as a measure of singularity. This paper develops a theory of equimultiplicity for Hilbert–Kunz multiplicity and applies it to study the behavior of Hilbert–Kunz multiplicity on the Brenner–Monsky hypersurface. A number of applications follows, in particular we show that Hilbert–Kunz multiplicity attains infinitely many values and that equimultiple strata may not be locally closed.
Speech Enhancement In Multiple-Noise Conditions using Deep Neural Networks

In this paper we consider the problem of speech enhancement in real-world like conditions where multiple noises can simultaneously corrupt speech. Most of the current literature on speech enhancement focus primarily on presence of single noise in corrupted speech which is far from real-world environments. Specifically, we deal with improving speech quality in office environment where multiple stationary as well as non-stationary noises can be simultaneously present in speech. We propose several strategies based on Deep Neural Networks (DNN) for speech enhancement in these scenarios. We also investigate a DNN training strategy based on psychoacoustic models from speech coding for enhancement of noisy speech
Homology and closure properties of autostackable groups

Abstract Autostackability for finitely presented groups is a topological property of the Cayley graph combined with formal language theoretic restrictions, that implies solvability of the word problem. The class of autostackable groups is known to include all asynchronously automatic groups with respect to a prefix-closed normal form set, and all groups admitting finite complete rewriting systems. Although groups in the latter two classes all satisfy the homological finiteness condition F P ∞ , we show that the class of autostackable groups includes a group that is not of type F P 3 . We also show that the class of autostackable groups is closed under graph products and extensions.
Fundamental limits of distributed caching in D2D wireless networks

We consider a wireless Device-to-Device (D2D) network where communication is restricted to be single-hop, users make arbitrary requests from a finite library of possible files and user devices cache information in the form of carefully designed sets of packets from all files in the library. We consider the combined effect of coding in the delivery phase, achieving “coded multicast gain”, and of spatial reuse due to local short-range D2D communication. Somewhat counterintuitively, we show that the coded multicast gain and the spatial reuse gain do not cumulate, in terms of the throughput scaling laws. In particular, the spatial reuse gain shown in our previous work on uncoded random caching and the coded multicast gain shown in this paper yield the same scaling laws behavior, but no further scaling law gain can be achieved by using both coded caching and D2D spatial reuse.
Image De-Raining Using a Conditional Generative Adversarial Network

Severe weather conditions, such as rain and snow, adversely affect the visual quality of images captured under such conditions, thus rendering them useless for further usage and sharing. In addition, such degraded images drastically affect the performance of vision systems. Hence, it is important to address the problem of single image de-raining. However, the inherent ill-posed nature of the problem presents several challenges. We attempt to leverage powerful generative modeling capabilities of the recently introduced conditional generative adversarial networks (CGAN) by enforcing an additional constraint that the de-rained image must be indistinguishable from its corresponding ground truth clean image. The adversarial loss from GAN provides additional regularization and helps to achieve superior results. In addition to presenting a new approach to de-rain images, we introduce a new refined loss function and architectural novelties in the generator–discriminator pair for achieving improved results. The loss function is aimed at reducing artifacts introduced by GANs and ensure better visual quality. The generator sub-network is constructed using the recently introduced densely connected networks, whereas the discriminator is designed to leverage global and local information to decide if an image is real/fake. Based on this, we propose a novel single image de-raining method called image de-raining conditional generative adversarial network (ID-CGAN) that considers quantitative, visual, and also discriminative performance into the objective function. The experiments evaluated on synthetic and real images show that the proposed method outperforms many recent state-of-the-art single image de-raining methods in terms of quantitative and visual performances. Furthermore, the experimental results evaluated on object detection datasets using the Faster-RCNN also demonstrate the effectiveness of proposed method in improving the detection performance on images degraded by rain.
Thermal corrections to Rényi entropies for conformal field theories

We compute thermal corrections to Renyi entropies of d dimensional conformal field theories on spheres. Consider the nth Renyi entropy for a cap of opening angle 2θ on S d−1. From a Boltzmann sum decomposition and the operator-state correspondence, the leading correction is related to a certain two-point correlation function of the operator (not equal to the identity) with smallest scaling dimension. More specifically, via a conformal map, the correction can be expressed in terms of the two-point function on a certain conical space with opening angle 2πn. In the case of free conformal field theories, this two-point function can be computed explicitly using the method of images. We perform the computation for the conformally coupled scalar. From the n → 1 limit of our results, we extract the leading thermal correction to the entanglement entropy, reproducing results of arXiv:1407.1358.
Principal component analysis with tensor train subspace

Abstract Tensor train is a hierarchical tensor network structure that helps alleviate the curse of dimensionality by parameterizing large-scale multidimensional data via a set of network of low-rank tensors. Associated with such a construction is a notion of Tensor Train subspace and in this paper we propose a TT-PCA algorithm for estimating this structured subspace from the given data. By maintaining low rank tensor structure, TT-PCA is empirically more robust to noise as compared to PCA or Tucker-PCA. This is borne out numerically by testing the proposed approach on the Extended YaleFace Dataset B, MINIST Dataset, CIFAR-10 dataset. This paper shows that the TT-PCA methods achieve less storage requirements, and have computationally faster online implementation with improved classification performance.
Studying Very Low Resolution Recognition Using Deep Networks

Visual recognition research often assumes a sufficient resolution of the region of interest (ROI). That is usually violated in practice, inspiring us to explore the Very Low Resolution Recognition (VLRR) problem. Typically, the ROI in a VLRR problem can be smaller than 16 16 pixels, and is challenging to be recognized even by human experts. We attempt to solve the VLRR problem using deep learning methods. Taking advantage of techniques primarily in super resolution, domain adaptation and robust regression, we formulate a dedicated deep learning method and demonstrate how these techniques are incorporated step by step. Any extra complexity, when introduced, is fully justified by both analysis and simulation results. The resulting Robust Partially Coupled Networks achieves feature enhancement and recognition simultaneously. It allows for both the flexibility to combat the LR-HR domain mismatch, and the robustness to outliers. Finally, the effectiveness of the proposed models is evaluated on three different VLRR tasks, including face identification, digit recognition and font recognition, all of which obtain very impressive performances.
Evaluation of the utility of localized adjuvant radiation for node-negative primary cutaneous squamous cell carcinoma with clear histologic margins.

Background Though the National Comprehensive Cancer Network recommends consideration of localized adjuvant radiation after clear-margin surgery for cutaneous squamous cell carcinoma (cSCC) with large-caliber (≥0.1-mm) nerve invasion (LCNI) and other high-risk features, only a single small study has compared surgery plus adjuvant radiation therapy (S+ART) to surgical monotherapy (SM) for cSCC. Objective Compare S+ART to SM for primary cSCCs with LCNI and other risk factors. Methods Matched retrospective cohort study of primary cSCCs (matched on sex, age, immune status, type of surgery, diameter, differentiation, depth, and LCNI) treated with S+ART versus SM. A subgroup analysis of cSCCs with LCNI was performed. Results In total, 62 cSCCs were included in matched analysis (31 S+ART and 31 SM) and 33 cSCCs in the LCNI analysis (16 S+ART and 17 SM). There were no significant differences in local recurrence, metastasis, or death from disease in either analysis. Risk of local recurrence was low (8%, 7/89), with 3 of the local recurrences being effectively treated upon recurrence. Limitations Single academic center and nonrandomized design. Conclusion Adjuvant radiation did not improve outcomes compared with SM due to a low baseline risk of recurrence, although adjuvant radiation for named nerve invasion and LCNI of ≥3 nerves has been shown to improve outcomes in a prior study. Randomized studies are needed to define the subset of cSCC for whom adjuvant radiation has utility.
Mirror symmetry for closed, open, and unoriented Gromov–Witten invariants

Abstract In the first part of this paper, we obtain mirror formulas for twisted genus 0 two-point Gromov–Witten (GW) invariants of projective spaces and for the genus 0 two-point GW-invariants of Fano and Calabi–Yau complete intersections. This extends previous results for projective hypersurfaces, following the same approach, but we also completely describe the structure coefficients in both cases and obtain relations between these coefficients that are vital to the applications to mirror symmetry in the rest of this paper. In the second and third parts of this paper, we confirm Walcher's mirror symmetry conjectures for the annulus and Klein bottle GW-invariants of Calabi–Yau complete intersection threefolds; these applications are the main results of this paper. In a separate paper, the genus 0 two-point formulas are used to obtain mirror formulas for the genus 1 GW-invariants of all Calabi–Yau complete intersections.
Fast Convergence Rates for Distributed Non-Bayesian Learning

We consider the problem of distributed learning , where a network of agents collectively aim to agree on a hypothesis that best explains a set of distributed observations of conditionally independent random processes. We propose a distributed algorithm and establish consistency, as well as a nonasymptotic, explicit, and geometric convergence rate for the concentration of the beliefs around the set of optimal hypotheses. Additionally, if the agents interact over static networks, we provide an improved learning protocol with better scalability with respect to the number of nodes in the network.
Return to the Kuiper Belt: Launch Opportunities from 2025 to 2040

Preliminary spacecraft trajectories for 45 Kuiper Belt objects (KBOs) and Pluto suitable for launch between 2025 and 2040 are presented. These 46 objects comprise all objects with H magnitude <4.0 ...
A weak Zassenhaus Lemma for discrete subgroups of Diff(I)

We prove a weaker version of the Zassenhaus Lemma for subgroups of Diff.I/. We also show that a group with commutator subgroup containing a non-Abelian free subsemigroup does not admit a C0 ‐discrete faithful representation in Diff.I/. 37C05; 20F65
Stability of 2nd Hilbert Points of Canonical Curves

We establish GIT semistability of the 2nd Hilbert point of every Gieseker-Petri general canonical curve by a simple geometric argument. As a consequence, we obtain an upper bound on slopes of general families of Gorenstein curves. We also explore the question of what replaces hyperelliptic curves in the GIT quotients of the Hilbert scheme of canonical curves.
Iterative Proportional Scaling Revisited: A Modern Optimization Perspective

ABSTRACTThis article revisits the classic iterative proportional scaling (IPS) from a modern optimization perspective. In contrast to the criticisms made in the literature, we show that based on a ...
Post-regularization inference for time-varying nonparanormal graphical models

We propose a novel class of time-varying nonparanormal graphical models, which allows us to model high dimensional heavy-tailed systems and the evolution of their latent network structures. Under this model we develop statistical tests for presence of edges both locally at a fixed index value and globally over a range of values. The tests are developed for a high-dimensional regime, are robust to model selection mistakes and do not require commonly assumed minimum signal strength. The testing procedures are based on a high dimensional, debiasing-free moment estimator, which uses a novel kernel smoothed Kendall's tau correlation matrix as an input statistic. The estimator consistently estimates the latent inverse Pearson correlation matrix uniformly in both the index variable and kernel bandwidth. Its rate of convergence is shown to be minimax optimal. Our method is supported by thorough numerical simulations and an application to a neural imaging data set.
Architecture for communication with a fidelity criterion in unknown networks

Abstract We prove that in order to communicate independent sources between various users over an unknown medium to within various distortion levels, it is sufficient to consider source-channel separation based architectures: architectures which first compress the sources to within the corresponding distortion levels followed by reliable communication over the unknown medium.
A Bochner formula for harmonic maps into non-positively curved metric spaces

We study harmonic maps from Riemannian manifolds into arbitrary non-positively curved and CAT( $$-\,1$$ ) metric spaces. First we discuss the domain variation formula with special emphasis on the error terms. Expanding higher order terms of this and other formulas in terms of curvature, we prove an analogue of the Eells–Sampson Bochner formula in this more general setting. In particular, we show that harmonic maps from spaces of non-negative Ricci curvature into non-positively curved spaces have subharmonic energy density. When the domain is compact the energy density is constant, and if the domain has a point of positive Ricci curvature every harmonic map into an NPC space must be constant.
Dynamic Tensor Clustering

Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-o...
Matrix Inequality for the Laplace Equation

Since Li and Yau obtained the gradient estimate for the heat equation, related estimates have been extensively studied. With additional curvature assumptions, matrix estimates that generalize such estimates have been discovered for various time-dependent settings, including the heat equation on a Kahler manifold, Ricci flow, Kahler-Ricci flow, and mean curvature flow, to name a few. As an elliptic analogue, Colding proved a sharp gradient estimate for the Green function on a manifold with nonnegative Ricci curvature. In this paper we prove a related matrix inequality on manifolds with suitable curvature and volume growth assumptions.
On the predictive risk in misspecified quantile regression

Abstract In the present paper we investigate the predictive risk of possibly misspecified quantile regression functions. The in-sample risk is well-known to be an overly optimistic estimate of the predictive risk and we provide two relatively simple (asymptotic) characterizations of the associated bias, also called expected optimism. We propose estimates for the expected optimism and the predictive risk, and establish their uniform consistency under mild conditions. Our results hold for models of moderately growing size and allow the quantile function to be incorrectly specified. Empirical evidence from our estimates is encouraging as it compares favorably with cross-validation.
Solving 1D Conservation Laws Using Pontryagin's Minimum Principle

This paper discusses a connection between scalar convex conservation laws and Pontryagin's minimum principle. For flux functions for which an associated optimal control problem can be found, a minimum value solution of the conservation law is proposed. For scalar space-independent convex conservation laws such a control problem exists and the minimum value solution of the conservation law is equivalent to the entropy solution. This can be seen as a generalization of the Lax---Oleinik formula to convex (not necessarily uniformly convex) flux functions. Using Pontryagin's minimum principle, an algorithm for finding the minimum value solution pointwise of scalar convex conservation laws is given. Numerical examples of approximating the solution of both space-dependent and space-independent conservation laws are provided to demonstrate the accuracy and applicability of the proposed algorithm. Furthermore, a MATLAB routine using Chebfun is provided (along with demonstration code on how to use it) to approximately solve scalar convex conservation laws with space-independent flux functions.
The traveling salesman problem in the Heisenberg group: Upper bounding curvature

We show that if a subset $K$ in the Heisenberg group (endowed with the Carnot-Caratheodory metric) is contained in a rectifiable curve, then it satisfies a modified analogue of Peter Jones's geometric lemma. This is a quantitative version of the statement that a finite length curve has a tangent at almost every point. This condition complements that of \cite{FFP} except a power 2 is changed to a power 4. Two key tools that we use in the proof are a geometric martingale argument like that of \cite{Schul-TSP} as well as a new curvature inequality in the Heisenberg group.
Modeling Naive Psychology of Characters in Simple Commonsense Stories

Understanding a narrative requires reading between the lines and reasoning about the unspoken but obvious implications about events and people’s mental states — a capability that is trivial for humans but remarkably hard for machines. To facilitate research addressing this challenge, we introduce a new annotation framework to explain naive psychology of story characters as fully-specified chains of mental states with respect to motivations and emotional reactions. Our work presents a new large-scale dataset with rich low-level annotations and establishes baseline performance on several new tasks, suggesting avenues for future research.
Categorical pairs and the indicative shift

Abstract The paper introduces the notion of a categorical pair , a pair of categories ( C , C ′) such that every morphism in C is an object in C ′. Arrows in C ′ can express relationships between the morphisms of C . In particular we show that by using a model of the linguistic process of naming, we can ensure that morphisms F in C can have an indirect self-reference of the form a → Fa where this arrow occurs in the category C ′. This result is shown to complement and clarify known fixed point theorems in logic and categories, and is applied to Godel’s Incompleteness Theorem, the Cantor Diagonal Process and the Lawvere Fixed Point Theorem.
Online Learning with Graph-Structured Feedback against Adaptive Adversaries

We derive upper and lower bounds for the policy regret of $T$ -round online learning problems with graph-structured feedback, where the adversary is nonoblivious but assumed to have a bounded memory. We obtain upper bounds of $\mathcal{O}(T^{2/3})$ and $\tilde{\mathrm{O}}(T^{3/4})$ for strongly-observable and weakly-observable graphs, respectively, based on analyzing a variant of the Exp3 algorithm. When the adversary is allowed a bounded memory of size 1, we show that a matching lower bound of $\tilde{\Omega}(T^{2/3})$ is achieved in the case of full-information feedback. We also study the particular loss structure of an oblivious adversary with switching costs, and show that in such a setting, nonrevealing strongly-observable feedback graphs achieve a lower bound of $\tilde{\Omega}(T^{2/3})$ , as well.
Downlink Power Allocation for Stored Variable-Bit-Rate Videos

In this paper, we study the problem of power allocation for streaming multiple variable-bit-rate (VBR) videos in the downlink of a cellular network. We consider a deterministic model for VBR video traffic and finite playout buffer at the mobile users. The objective is to derive the optimal downlink power allocation for the VBR video sessions, such that the video data can be delivered in a timely fashion without causing playout buffer overflow and underflow. The formulated problem is a nonlinear nonconvex optimization problem. We analyze the convexity conditions for the formulated problem and propose a two-step greedy approach to solve the problem. We also develop a distributed algorithm based on the dual decomposition technique. The performance of the proposed algorithms are validated with simulations using VBR video traces under realistic scenarios.
Uniform Ergodicity for Brownian Motion in a Bounded Convex Set

We consider an n-dimensional Brownian motion trapped inside a bounded convex set by normally reflecting boundaries. It is well known that this process is uniformly ergodic. However, the rates of this ergodicity are not well understood, especially in the regime of very high-dimensional sets. Here we present new bounds on these rates for convex sets with a given diameter. Our bounds do not depend upon the smoothness of the boundary nor the value of the ambient dimension, n.
Model completeness of o-minimal fields with convex valuations

We let R be an o-minimal expansion of a field, V a convex subring, and (R0,V0) an elementary substructure of (R,V ). Our main result is that (R,V ) considered as a structure in a language containing constants for all elements of R0 is model complete relative to quantifier elimination in R, provided that kR (the residue field with structure induced from R) is o-minimal. Along the way we show that o-minimality of kR implies that the sets definable in kR are the same as the sets definable in k with structure induced from (R,V ). We also give a criterion for a superstructure of (R,V ) being an elementary extension of (R,V ).
Acceleration of tensor-product operations for high-order finite element methods

This article is devoted to graphics processing unit (GPU) kernel optimization and performance analysis of three tensor-product operations arising in finite element methods. We provide a mathematica...
Making Name-Based Content Routing More Efficient than Link-State Routing

The Diffusive Name-based Routing Protocol (DNRP) is introduced for efficient name-based routing in information-centric networks (ICN). DNRP establishes and maintains multiple loop-free routes to the nearest instances of a name prefix using only distance information. DNRP eliminates the need for periodic updates, maintaining topology information, storing complete paths to content replicas, or knowing about all the sites storing replicas of named content. DNRP is suitable for large ICNs with large numbers of prefixes stored at multiple sites. It is shown that DNRP provides loop-free routes to content independently of the state of the topology, and that it converges within a finite time to correct routes to name prefixes after arbitrary changes in the network topology or the placement of prefix instances. The result of simulation experiments illustrate that DNRP is more efficient than link-state routing approaches.
JUMPING CHAMPIONS AND GAPS BETWEEN CONSECUTIVE PRIMES

The most common difference that occurs among the consecutive primes less than or equal to x is called a jumping champion. Occasionally there are ties. Therefore there can be more than one jumping champion for a given x. In 1999 Odlyzko, Rubinstein and Wolf provided heuristic and empirical evidence in support of the conjecture that the numbers greater than 1 that are jumping champions are 4 and the primorials 2, 6, 30, 210, 2310,…. As a step toward proving this conjecture they introduced a second weaker conjecture that any fixed prime p divides all sufficiently large jumping champions. In this paper we extend a method of Erdős and Straus from 1980 to prove that the second conjecture follows directly from the prime pair conjecture of Hardy and Littlewood.
Finite element approximation of the Isaacs equation

We propose and analyze a two-scale finite element method for the Isaacs equation. The fine scale is given by the mesh size h whereas the coarse scale e is dictated by an integro-differential approximation of the partial differential equation. We show that the method satisfies the discrete maximum principle provided that the mesh is weakly acute. This, in conjunction with weak operator consistency of the finite element method, allows us to establish convergence of the numerical solution to the viscosity solution as e , h → 0, and e ≳ (h |log h |)1/2 . In addition, using a discrete Alexandrov Bakelman Pucci estimate we deduce rates of convergence, under suitable smoothness assumptions on the exact solution.
Maximum Likelihood Estimation of Functionals of Discrete Distributions

We consider the problem of estimating functionals of discrete distributions, and focus on a tight (up to universal multiplicative constants for each specific functional) nonasymptotic analysis of the worst case squared error risk of widely used estimators. We apply concentration inequalities to analyze the random fluctuation of these estimators around their expectations and the theory of approximation using positive linear operators to analyze the deviation of their expectations from the true functional, namely their bias . We explicitly characterize the worst case squared error risk incurred by the maximum likelihood estimator (MLE) in estimating the Shannon entropy $H(P) = \sum _{i = 1}^{S} -p_{i} \ln p_{i}$ , and the power sum $F_\alpha (P) = \sum _{i = 1}^{S} p_{i}^\alpha ,\alpha >0$ , up to universal multiplicative constants for each fixed functional, for any alphabet size $S\leq \infty $ and sample size $n$ for which the risk may vanish. As a corollary, for Shannon entropy estimation, we show that it is necessary and sufficient to have $n \gg S$ observations for the MLE to be consistent. In addition, we establish that it is necessary and sufficient to consider $n \gg S^{1/\alpha }$ samples for the MLE to consistently estimate $F_\alpha (P), 0 . The minimax rate-optimal estimators for both problems require $S/\ln S$ and $S^{1/\alpha }/\ln S$ samples, which implies that the MLE has a strictly sub-optimal sample complexity. When $1 , we show that the worst case squared error rate of convergence for the MLE is $n^{-2(\alpha -1)}$ for infinite alphabet size, while the minimax squared error rate is $(n\ln n)^{-2(\alpha -1)}$ . When $\alpha \geq 3/2$ , the MLE achieves the minimax optimal rate $n^{-1}$ regardless of the alphabet size. As an application of the general theory, we analyze the Dirichlet prior smoothing techniques for Shannon entropy estimation. In this context, one approach is to plug-in the Dirichlet prior smoothed distribution into the entropy functional, while the other one is to calculate the Bayes estimator for entropy under the Dirichlet prior for squared error, which is the conditional expectation. We show that in general such estimators do not improve over the maximum likelihood estimator. No matter how we tune the parameters in the Dirichlet prior, this approach cannot achieve the minimax rates in entropy estimation. The performance of the minimax rate-optimal estimator with $n$ samples is essentially at least as good as that of Dirichlet smoothed entropy estimators with $n\ln n$ samples.
Subprime Solutions of the Classical Yang-Baxter Equation

Abstract We introduce a new family of classical r-matrices for the Lie algebra sl n that lies in the Zariski boundary of the Belavin–Drinfeld space M of quasi-triangular solutions to the classical Yang–Baxter equation. In this setting M is a finite disjoint union of components; exactly ϕ ( n ) of these components are S L n -orbits of single points. These points are the generalized Cremmer–Gervais r-matrices r i , n which are naturally indexed by pairs of positive coprime integers, i and n, with i n . A conjecture of Gerstenhaber and Giaquinto states that the boundaries of the Cremmer–Gervais components contain r-matrices having maximal parabolic subalgebras p i , n ⊆ sl n as carriers. We prove this conjecture in the cases when n ≡ ± 1 (mod i). The subprime linear functionals f ∈ p i , n ⁎ and the corresponding principal elements H ∈ p i , n play important roles in our proof. Since the subprime functionals are Frobenius precisely in the cases when n ≡ ± 1 (mod i), this partly explains our need to require these conditions on i and n. We conclude with a proof of the GG boundary conjecture in an unrelated case, namely when ( i , n ) = ( 5 , 12 ) , where the subprime functional is no longer a Frobenius functional.
DEEP BACK PROJECTION FOR SPARSE-VIEW CT RECONSTRUCTION

Filtered back projection (FBP) is a classical method for image reconstruction from sinogram CT data. FBP is computationally efficient but produces lower quality reconstructions than more sophisticated iterative methods, particularly when the number of views is lower than the number required by the Nyquist rate. In this paper, we use a deep convolutional neural network (CNN) to produce high-quality reconstructions directly from sinogram data. A primary novelty of our approach is that we first back project each view separately to form a stack of back projections and then feed this stack as input into the convolutional neural network. These single-view back projections convert the encoding of sinogram data into the appropriate spatial location, which can then be leveraged by the spatial invariance of the CNN to learn the reconstruction effectively. We demonstrate the benefit of our CNN based back projection on simulated sparse-view CT data over classical FBP.