cssi/SciSciGPT-SciSciNet huggingface dataset:
Architecture and dynamics of overlapped RNA regulatory networks

A single protein can bind and regulate many mRNAs. Multiple proteins with similar specificities often bind and control overlapping sets of mRNAs. Yet little is known about the architecture or dynamics of overlapped networks. We focused on three proteins with similar structures and related RNA-binding specificities—Puf3p, Puf4p, and Puf5p of S. cerevisiae. Using RNA Tagging, we identified a “super-network” comprised of four subnetworks: Puf3p, Puf4p, and Puf5p subnetworks, and one controlled by both Puf4p and Puf5p. The architecture of individual subnetworks, and thus the super-network, is determined by competition among particular PUF proteins to bind mRNAs, their affinities for binding elements, and the abundances of the proteins. The super-network responds dramatically: The remaining network can either expand or contract. These strikingly opposite outcomes are determined by an interplay between the relative abundance of the RNAs and proteins, and their affinities for one another. The diverse interplay between overlapping RNA–protein networks provides versatile opportunities for regulation and evolution.
Hydrosilylation of alkynes catalyzed by ruthenium carbene complexes

Abstract Hydrosilylation of terminal alkynes with a variety of silanes catalyzed by Cl2(PCy3)2Ru CHPh ( 1 ) affords mainly the Z-isomer via trans addition in excellent yields. The presence of a hydroxyl group in close proximity to the triple bond was observed to exert a strong directing effect, resulting in the highly selective formation of the α-isomer. Intramolecular hydrosilylation of a homopropargylic silyl ether was demonstrated to give the cis addition product.
The Intramolecular, Stereoselective Addition of Sulfoximine Carbanions to α,β-Unsaturated Esters

ortho-Bromocinnamates can be coupled with methyl phenylsulfoximine to afford N-arylsulfoximines in excellent yield. Treatment of these products with an amide base results in a completely stereoselective cyclization to afford enantiomerically pure benzothiazines. This reaction is stereospecific.
Quartet Sampling distinguishes lack of support from conflicting support in the green plant tree of life.

PREMISE OF THE STUDY Phylogenetic support has been difficult to evaluate within the green plant tree of life partly due to a lack of specificity between conflicted versus poorly informed branches. As data sets continue to expand in both breadth and depth, new support measures are needed that are more efficient and informative. METHODS We describe the Quartet Sampling (QS) method, a quartet-based evaluation system that synthesizes several phylogenetic and genomic analytical approaches. QS characterizes discordance in large-sparse and genome-wide data sets, overcoming issues of alignment sparsity and distinguishing strong conflict from weak support. We tested QS with simulations and recent plant phylogenies inferred from variously sized data sets. KEY RESULTS QS scores demonstrated convergence with increasing replicates and were not strongly affected by branch depth. Patterns of QS support from different phylogenies led to a coherent understanding of ancestral branches defining key disagreements, including the relationships of Ginkgo to cycads, magnoliids to monocots and eudicots, and mosses to liverworts. The relationships of ANA-grade angiosperms (Amborella, Nymphaeales, Austrobaileyales), major monocot groups, bryophytes, and fern families are likely highly discordant in their evolutionary histories, rather than poorly informed. QS can also detect discordance due to introgression in phylogenomic data. CONCLUSIONS Quartet Sampling is an efficient synthesis of phylogenetic tests that offers more comprehensive and specific information on branch support than conventional measures. The QS method corroborates growing evidence that phylogenomic investigations that incorporate discordance testing are warranted when reconstructing complex evolutionary histories, in particular those surrounding ANA-grade, monocots, and nonvascular plants.
Integrative pipeline for profiling DNA copy number and inferring tumor phylogeny.

Summary Copy number variation is an important and abundant source of variation in the human genome, which has been associated with a number of diseases, especially cancer. Massively parallel next-generation sequencing allows copy number profiling with fine resolution. Such efforts, however, have met with mixed successes, with setbacks arising partly from the lack of reliable analytical methods to meet the diverse and unique challenges arising from the myriad experimental designs and study goals in genetic studies. In cancer genomics, detection of somatic copy number changes and profiling of allele-specific copy number (ASCN) are complicated by experimental biases and artifacts as well as normal cell contamination and cancer subclone admixture. Furthermore, careful statistical modeling is warranted to reconstruct tumor phylogeny by both somatic ASCN changes and single nucleotide variants. Here we describe a flexible computational pipeline, MARATHON, which integrates multiple related statistical software for copy number profiling and downstream analyses in disease genetic studies. Availability and implementation MARATHON is publicly available at https://github.com/yuchaojiang/MARATHON. Supplementary information Supplementary data are available at Bioinformatics online.
Asymmetric synthesis of trans-2,3-piperidinedicarboxylic acid and trans-3,4-piperidinedicarboxylic acid derivatives.

Asymmetric syntheses of (2S,3S)-3-(tert-butoxycarbonyl)-2-piperidinecarboxylic acid (1b), (3R,4S)-4-(tert-butoxycarbonyl)-3-piperidinecarboxylic acid (2b), and their corresponding N-Boc and N-Cbz protected analogues 8a,b and 17a,b are described. Enantiomerically pure 1b has been synthesized in five steps starting from l-aspartic acid β-tert-butyl ester. Tribenzylation of the starting material followed by alkylation with allyl iodide using KHMDS produces the key intermediate 5a in a 6:1 diastereomeric excess. Upon hydroboration, the alcohol 6a is oxidized, and the resulting aldehyde 7 is subjected to a ring closure via reductive amination, providing 1b in an overall yield of 38%. Optically pure 2b has been synthesized beginning with N-Cbz-β-alanine. The synthesis involves the induction of the first stereogenic center using Evans's chemistry and sequential LDA-promoted alkylations with tert-butyl bromoacetate and allyl iodide. Further elaboration by ozonolysis and reductive amination affords 2b in an overal...
A Biomimetic Approach to the Discorhabdin Alkaloids: Total Syntheses of Discorhabdins C and E and Dethiadiscorhabdin D.

The characteristic spirodienone structure of the discorhabdin alkaloids is readily formed by reaction of the tyramine-substituted indoloquinonimines 26, 35, and 36 with cupric chloride, triethylamine, and oxygen. This cyclization provides a possibly biomimetic route to discorhabdins C and E (41 and 42). The unbrominated spirodienone 40 reacts with hydrogen over Pd/C to give enone 46. Bromination at the α position gives a mixture of bromoenones that undergo smooth conversion to dethiadiscorhabdin D (4) upon treatment with basic alumina.
SYNTHESIS OF 1,9-DIAMIDINIUMACRIDINE AS A POTENTIAL RECEPTOR FOR PHOSPHATE ESTER RECOGNITION

(2000). SYNTHESIS OF 1,9-DIAMIDINIUMACRIDINE AS A POTENTIAL RECEPTOR FOR PHOSPHATE ESTER RECOGNITION. Organic Preparations and Procedures International: Vol. 32, No. 6, pp. 573-577.
The Toxoplasma Vacuolar H+-ATPase Regulates Intracellular pH and Impacts the Maturation of Essential Secretory Proteins

Summary Vacuolar-proton ATPases (V-ATPases) are conserved complexes that couple the hydrolysis of ATP to the pumping of protons across membranes. V-ATPases are known to play diverse roles in cellular physiology. We studied the Toxoplasma gondii V-ATPase complex and discovered a dual role of the pump in protecting parasites against ionic stress and in the maturation of secretory proteins in endosomal-like compartments. Toxoplasma V-ATPase subunits localize to the plasma membrane and to acidic vesicles, and characterization of conditional mutants of the a1 subunit highlighted the functionality of the complex at both locations. Microneme and rhoptry proteins are required for invasion and modulation of host cells, and they traffic via endosome-like compartments in which proteolytic maturation occurs. We show that the V-ATPase supports the maturation of rhoptry and microneme proteins, and their maturases, during their traffic to their corresponding organelles. This work underscores a role for V-ATPases in regulating virulence pathways.
Development of Catalytic Asymmetric Reactions Focussing on Fluoroorganic Compounds

Highly enantioselective catalyses for preparing α, α-difluoro-β-hydroxycarboxylates and secondary α-trifluoromethyl alcohols have been developed. Difluoroketene ethyl trimethylsilyl acetal reacts with aldehydes in the presence of chiral boron complexes to afford the aldol adducts with up to 98% ee. The hydrogenation of 1, 1, 1-trifluoroalkan-2-one enol acetates using chiral ruthenium catalysts provides the secondary α-trifluoromethyl alcohols of excellent enantiopurity. The trifluoromethylation of carbonyl compounds with TMSCF3catalyzed by chiral quaternary ammonium fluorides or triaminosulfonium salts was assessed for synthesizing optically active α-trifluoromethyl alcohols including the tertiary alcohols which, unfortunately, gave moderate enantioselection. Throughout the course of our search for asymmetric catalysts for the trifluoromethylation, two types of Lewis bases, chiral phosphoramides and formamides, have been newly synthesized, and their successful application to the allylation of aldehydes with allylic trichlorosilanes is also described, which provide the corresponding homoallylic alcohols with good-to-excellent enantioselectivity.
Highly selective synthesis of (E)-3-methyl-1-trialkylsilyl-3-en-1-ynes via trans-selective alkynylation catalyzed by Cl2Pd(DPEphos) and stereospecific methylation with methylzincs catalyzed by Pd(tBu3P)2.

trans-Selective (≥98%) monoalkynylation of 1,1-dibromo-1-alkenes and 1,1-dichloro-1-alkenes catalyzed by Cl2Pd(DPEphos) followed by stereospecific methylation with Me2Zn or MeZnX (X= Cl or Br) catalyzed by Pd(tBu3P)2 provides an efficient and stereoselective (≥98%) route to 5, convertible to a wide variety of enynes and conjugated dienes. In the cases of 1,1-dibromo-1-alkenes, the Sonogashira alkynylation may also be satisfactory, but it is distinctly less satisfactory than the alkynylzinc reaction in cases where 1,1-dichloro-1-alkenes are used.
EPR spectroscopy of fullerene adducts

EPR spectroscopy has been used to identify and characterize the paramagnetic adducts of small free radicals with C60 through measurements of the hyperfine interactions of protons and13C nuclei. The initially formed mono-radical adducts (RC60) have unpaired spin density localized near the point of attachment of the radical. Generally, they are in thermal equilibrium with their diamagnetic dimer, and have a surprisingly large barrier to internal rotation about the new bond. The tri- and penta-radical adducts have electronic structures similar to those of allyl and cyclopentadienyl radicals, respectively.
Further studies on the synthesis of quinazolines from 2-fluorobenzonitriles

Recently, we reported that appropriately substituted 2-fluorobenzonitriles undergo cyclization with guanidine carbonate to afford 2,4-diaminoquinazolines usually in good to excellent yield. This paper describes the preparation of a variety of new 2,4-diaminoquinazolines substituted at positions five or seven. In addition, the reactions of selected 2-fluorobenzonitriles with formamidine acetate or acetamidine acetate were examined. The results obtained demonstrate that the analogous 4-amino- and 2-methyl-4-aminoquinazolines can be prepared by this approach but that the yields are considerably lower than when guanidine carbonate is employed as the cyclization reagent.
Structure/Property Relationships of Polystannanes

Publisher Summary This chapter focuses on the structure or property relationships of polystannanes. Distannane, which can be considered a heavy-atom analog of ethane, is the simplest chemical structure that falls under the preceding definition for the class of compounds known as polystannanes. It has long been known that the electronic spectrum of hexaphenyldistannane exhibits a strong absorption maximum, which has been attributed to the presence of the Sn–Sn bond in this compound. Sulfur and selenium can similarly be inserted into the Sn–Sn bond, and while peralkyl distannanes are typically more reactive than peraryl ones, bulky substituents can retard these reactions by raising energy barriers for bimolecular processes. The use of sterically demanding substituents is, in fact, the basis for a strategy known as kinetic stabilization, which has been successfully employed for the synthesis of polystannane frameworks that would normally have highly reactive Sn–Sn bond. Propellanes are a class of nonclassical structures, since they possess bridgehead atoms having formally inverted tetrahedral geometries that force the four bonds from each of the bridgehead atoms to lie within the same hemisphere. Given this configuration, theoretical investigations have long sought to determine the stability and reactivity of these molecular frameworks prior to the availability of representative synthetic derivatives.
Uncured PDMS inhibits myosin in vitro motility in a microfluidic flow cell

The myosin motor powers cardiac contraction and is frequently implicated in hereditary heart disease by its mutation. Principal motor function characteristics include myosin unitary step size, duty cycle, and force-velocity relationship for translating actin under load. These characteristics are sometimes measured in vitro with a motility assay detecting fluorescent labeled actin filament gliding velocity over a planar array of surface immobilized myosin. Assay miniaturization in a polydimethylsiloxane/glass (PDMS/glass) hybrid microfluidic flow channel is an essential component to a small sample volume assay applicable to costly protein samples however the PDMS substrate dramatically inhibits myosin motility. Myosin in vitro motility in a PDMS/glass hybrid microfluidic flow cell was tested under a variety of conditions to identify and mitigate the effect of PDMS on myosin. Substantial contamination by unpolymerized species in the PDMS flow cells is shown to be the cause of myosin motility inhibition. Normal myosin motility recovers by either extended cell aging (~20 days) to allow more complete polymerization or by direct chemical extraction of the unpolymerized species from the polymer substrate. PDMS flow cell aging is the low cost alternative compatible with the other PDMS and glass modifications needed for in vitro myosin motility assaying.
Modulating CRISPR gene drive activity through nucleocytoplasmic localization of Cas9 in S. cerevisiae

The bacterial CRISPR/Cas genome editing system has provided a major breakthrough in molecular biology. One use of this technology is within a nuclease-based gene drive. This type of system can install a genetic element within a population at unnatural rates. Combatting of vector-borne diseases carried by metazoans could benefit from a delivery system that bypasses traditional Mendelian laws of segregation. Recently, laboratory studies in fungi, insects, and even mice, have demonstrated successful propagation of CRISPR gene drives and the potential utility of this type of mechanism. However, current gene drives still face challenges including evolved resistance, containment, and the consequences of application in wild populations. Additional research into molecular mechanisms that would allow for control, titration, and inhibition of drive systems is needed. In this study, we use artificial gene drives in budding yeast to explore mechanisms to modulate nuclease activity of Cas9 through its nucleocytoplasmic localization. We examine non-native nuclear localization sequences (both NLS and NES) on Cas9 fusion proteins in vivo through fluorescence microscopy and genomic editing. Our results demonstrate that mutational substitutions to nuclear signals and combinatorial fusions can both modulate the level of gene drive activity within a population of cells. These findings have implications for control of traditional nuclease-dependent editing and use of gene drive systems within other organisms. For instance, initiation of a nuclear export mechanism to Cas9 could serve as a molecular safeguard within an active gene drive to reduce or eliminate editing.
Stereodefined Cyclopentanes by Hydroarylation–Ring Opening

Abstract The hydroarylation of 2-azabicyclo[2.2.1]hept-5-en-3-one followed by nucleophilic ring opening was employed as an operationally simple route to stereodefined trisubstituted cyclopentane analogs. This synthetic sequence was successfully executed using a variety of nucleophiles including hydroxide, alkoxide, hydride, Grignard reagents, and amines. This methodology facilitated the preparation of a constrained version of dipeptidyl peptidase 4 inhibitor sitagliptin.
Rearrangements of Linear Triquinanes to the Angular Isomers

Warming substituted linear triquinanes in t-BuOK/t-BuOH resulted in their isomerization to the corresponding angularly fused isomers in good yield (59−84%). An alternate route employs a base-catalyzed intramolecular Michael addition of bicyclo[6.3.0]undecenediones, a class of compounds found to be readily available from 1-alkenylbicyclo[3.2.0]hepten-7-ones via a “one-pot” sequence of reactions. This method is complementary to the isomerization reaction since it provides access to angular triquinanes not readily available from their linear isomers.
5,6-Diaminocytidine, a Versatile Synthon for Pyrimidine-Based Bicyclic Nucleosides†

This communication describes a convenient, facile, and high-yield synthesis of 3-(β-d-ribofuranosyl)isoguanine and its 8-methyl derivative, as well as nucleoside analogues of pteridines, from a common precursor, 5,6-diaminocytidine. 5,6-Diamino-2‘,3‘,5‘-tri-O-benzoylcytidine was synthesized from 4,6-diamino-2-oxopyrimidine in three steps.
Synthesis of α,α-dialkylated amino acids with adenine or thymine residues a new mild and facile hydrolysis of hydantoins

Abstract The synthesis of α,α-dialkylated amino acids which contain two adenine or thymine residues in their side chains is presented. In this context, a mild method for the cleavage of hydantoins is introduced.
A resurrection experiment finds evidence of both reduced genetic diversity and potential adaptive evolution in the agricultural weed Ipomoea purpurea

Despite the negative economic and ecological impact of weeds, relatively little is known about the evolutionary mechanisms that influence their persistence in agricultural fields. Here, we use a resurrection approach to examine the potential for genotypic and phenotypic evolution in Ipomoea purpurea, an agricultural weed that is resistant to glyphosate, the most widely used herbicide in current-day agriculture. We found striking reductions in allelic diversity between cohorts sampled nine years apart (2003 vs. 2012), suggesting that populations of this species sampled from agricultural fields have experienced genetic bottleneck events that have led to lower neutral genetic diversity. Heterozygosity excess tests indicate that these bottlenecks may have occurred prior to 2003. A greenhouse assay of individuals sampled from the field as seed found that populations of this species, on average, exhibited modest increases in herbicide resistance over time. However, populations differed significantly between sampling years for resistance: some populations maintained high resistance between the sampling years whereas others exhibited increased or decreased resistance. Our results show that populations of this noxious weed, capable of adapting to strong selection imparted by herbicide application, may lose genetic variation as a result of this or other environmental factors. We probably uncovered only modest increases in resistance on average between sampling cohorts due to a strong and previously identified fitness cost of resistance in this species, along with the potential that nonresistant migrants germinate from the seed bank.
Sparse Infomax Based on Hoyer Projection and its Application to Simulated Structural MRI and SNP Data

Independent component analysis has been widely applied to brain imaging and genetic data analyses for its ability to identify interpretable latent sources. Nevertheless, leveraging source sparsity in a more granular way may further improve its ability to optimize the solution for certain data types. For this purpose, we propose a sparse infomax algorithm based on nonlinear Hoyer projection, leveraging both sparsity and statistical independence of latent sources. The proposed algorithm iteratively updates the unmixing matrix by infomax (for independence) and the sources by Hoyer projection (for sparsity), feeding the sparse sources back as input data for the next iteration. Consequently, sparseness propagates effectively through infomax iterations, producing sources with more desirable properties. Simulation results on both brain imaging and genetic data demonstrate that the proposed algorithm yields improved pattern recovery, particularly under low signal-to-noise ratio conditions, as well as improved sparseness compared to traditional infomax.
A Linear-algebraic Proof of Hilbert’s Ternary Quartic Theorem

Hilbert’s ternary quartic theorem states that every nonnegative degree 4 homogeneous polynomial in three variables can be written as a sum of three squares of homogeneous quadratic polynomials. We ...
FAST ALGORITHM FOR PERIODIC DENSITY FITTING FOR BLOCH WAVES

We propose an efficient algorithm for density fitting of Bloch waves for Hamiltonian operators with periodic potential. The algorithm is based on column selection and random Fourier projection of the orbital functions. The computational cost of the algorithm scales as O i NgridN 2 ¯ NgridN K log(N K ) ¢ , where Ngrid is number of spatial grid points, K is the number of sampling k- points in first Brillouin zone, and N is the number of bands under consideration. We validate the algorithm by numerical examples in both two and three dimensions.
The PPW conjecture in curved spaces

Abstract In Euclidean ( [1] ) and Hyperbolic ( [5] ) space, and the round hemisphere ( [2] ), geodesic balls maximize the gap λ 2 − λ 1 of Dirichlet eigenvalues, among domains with fixed λ 1 . We prove an upper bound on λ 2 − λ 1 for domains in manifolds with certain curvature bounds. The inequality is sharp on geodesic balls in spaceforms.
Deep Multitask Learning for Semantic Dependency Parsing

We present a deep neural architecture that parses sentences into three semantic dependency graph formalisms. By using efficient, nearly arc-factored inference and a bidirectional-LSTM composed with a multi-layer perceptron, our base system is able to significantly improve the state of the art for semantic dependency parsing, without using hand-engineered features or syntax. We then explore two multitask learning approaches—one that shares parameters across formalisms, and one that uses higher-order structures to predict the graphs jointly. We find that both approaches improve performance across formalisms on average, achieving a new state of the art. Our code is open-source and available at https://github.com/Noahs-ARK/NeurboParser.
Balanced Policy Evaluation and Learning

We present a new approach to the problems of evaluating and learning personalized decision policies from observational data of past contexts, decisions, and outcomes. Only the outcome of the enacted decision is available and the historical policy is unknown. These problems arise in personalized medicine using electronic health records and in internet advertising. Existing approaches use inverse propensity weighting (or, doubly robust versions) to make historical outcome (or, residual) data look like it were generated by a new policy being evaluated or learned. But this relies on a plug-in approach that rejects data points with a decision that disagrees with the new policy, leading to high variance estimates and ineffective learning. We propose a new, balance-based approach that too makes the data look like the new policy but does so directly by finding weights that optimize for balance between the weighted data and the target policy in the given, finite sample, which is equivalent to minimizing worst-case or posterior conditional mean square error. Our policy learner proceeds as a two-level optimization problem over policies and weights. We demonstrate that this approach markedly outperforms existing ones both in evaluation and learning, which is unsurprising given the wider support of balance-based weights. We establish extensive theoretical consistency guarantees and regret bounds that support this empirical success.
Equi-Coverage Contours in Cellular Networks

In this letter, we introduce a general cellular network model, where: 1) users and base stations (BSs) are distributed as two general point processes that may be coupled; 2) pathloss is assumed to follow a multi-slope power-law pathloss model; and 3) fading (power) is assumed to be independent across all wireless links. For this setup, we first obtain a set of contours representing the same meta distribution of signal-to-interference ratio , which is the distribution of the conditional coverage probability given the point process, for different values of the parameters of the pathloss function and BS and user point processes. This general result is then specialized to 3GPP-inspired user and BS configurations obtained by combining Poisson point process and Poisson cluster process.
Generation of synthetic spatially embedded power grid networks

The development of algorithms for enhancing the resilience and efficiency of the power grid requires evaluation with topologies of real transmission networks. However, due to security reasons, such topologies and particularly the locations of the substations and lines are usually not publicly available. Therefore, we study the structural properties of the North American grids and present an algorithm for generating synthetic spatially embedded networks with similar properties to a given grid. The algorithm has several tunable parameters that allow generating grids similar to any given grid. We apply it to the Western Interconnection (WI) and to grids that operate under the SERC Reliability Corporation (SERC) and the Florida Reliability Coordinating Council (FRCC), and show that the generated grids have similar structural and spatial properties to these grids. To the best of our knowledge, this is the first attempt to consider the spatial distribution of the nodes and lines and its importance in generating synthetic grids.
Limited feedback in multiple-antenna systems with one-bit quantization

Communication systems with low-resolution analog- to-digital-converters (ADCs) can exploit channel state information at the transmitter (CSIT) and receiver. This paper presents initial results on codebook design and performance analysis for limited feedback systems with one-bit ADCs. Different from the high-resolution case, the absolute phase at the receiver is important to align the phase of the received signals when the received signal is sliced by one-bit ADCs. A new codebook design for the beamforming case is proposed that separately quantizes the channel direction and the residual phase.
Gaussian elements of a semicontent algebra

Abstract The connection between a univariate polynomial having locally principal content and the content function acting like a homomorphism (the so-called Gaussian property) has been explored by many authors. In this work, we extend several such results to the contexts of multivariate polynomials, power series over a Noetherian ring, and base change of affine K-algebras by separable algebraically closed field extensions. We do so by using the framework of the Ohm–Rush content function. The correspondence is particularly strong in cases where the base ring is approximately Gorenstein or the element of the target ring is regular.
A bound on the cohomology of quasiregularly elliptic manifolds

We show that a closed, connected and orientable Riemannian manifold of dimension $d$ that admits a quasiregular mapping from $\mathbb R^d$ must have bounded cohomological dimension independent of the distortion of the map. The dimension of the degree $l$ de Rham cohomology of $M$ is bounded above by $\binom{d}{l}$. This is a sharp upper bound that proves the Bonk-Heinonen conjecture. A corollary of this theorem answers an open problem posed by Gromov in 1981. He asked whether there exists a $d$-dimensional, simply connected manifold that does not admit a quasiregular map from $\mathbb R^d$. Our result gives an affirmative answer to this question.
Incoherent Tensor Norms and Their Applications in Higher Order Tensor Completion

In this paper, we investigate the sample size requirement for a general class of nuclear norm minimization methods for higher order tensor completion. We introduce a class of tensor norms by allowing for different levels of coherence, which allows us to leverage the incoherence of a tensor. In particular, we show that a $k$ th-order tensor of multilinear rank $r$ and dimension $d \times \cdots \times d$ can be recovered perfectly from as few as $O((r^{(k-1)/2}d^{3/2}+r^{k-1}d)(\log (d))^{2})$ uniformly sampled entries through an appropriate incoherent nuclear norm minimization. Our results demonstrate some key differences between completing a matrix and a higher order tensor: they not only point to potential room for improvement over the usual nuclear norm minimization but also highlight the importance of explicitly accounting for incoherence, when dealing with higher order tensors. Although our focus is primarily on the theoretical guarantees for nuclear norm minimization, such insights may prove useful for understanding performance of other related methods and developing improved practical algorithms.
An analytic theory of generalization dynamics and transfer learning in deep linear networks.

Much attention has been devoted recently to the generalization puzzle in deep learning: large, deep networks can generalize well, but existing theories bounding generalization error are exceedingly loose, and thus cannot explain this striking performance. Furthermore, a major hope is that knowledge may transfer across tasks, so that multi-task learning can improve generalization on individual tasks. However we lack analytic theories that can quantitatively predict how the degree of knowledge transfer depends on the relationship between the tasks. We develop an analytic theory of the nonlinear dynamics of generalization in deep linear networks, both within and across tasks. In particular, our theory provides analytic solutions to the training and testing error of deep networks as a function of training time, number of examples, network size and initialization, and the task structure and SNR. Our theory reveals that deep networks progressively learn the most important task structure first, so that generalization error at the early stopping time primarily depends on task structure and is independent of network size. This suggests any tight bound on generalization error must take into account task structure, and explains observations about real data being learned faster than random data. Intriguingly our theory also reveals the existence of a learning algorithm that proveably out-performs neural network training through gradient descent. Finally, for transfer learning, our theory reveals that knowledge transfer depends sensitively, but computably, on the SNRs and input feature alignments of pairs of tasks.
FINITENESS PROPERTIES OF SOME GROUPS OF LOCAL SIMILARITIES

Hughes has defined a class of groups, which we call FSS (finite similarity structure) groups. Each FSS group acts on a compact ultrametric space by local similarities. The best-known example is Thompson's group V. Guided by previous work on Thompson's group V , we establish a number of new results about FSS groups. Our main result is that a class of FSS groups are of type F1. This generalizes work of Ken Brown from the 1980s. Next, we develop methods for distinguishing between isomorphism types of some of the Nekrashevych-Rover groups Vd(H), where H is a finite group, and show that all such groups Vd(H) have simple subgroups of finite index. Lastly, we show that FSS groups defined by small Sim-structures are braided diagram groups over tree-like semigroup presentations. This generalizes a result of Guba and Sapir, who first showed that Thompson's group V is a braided diagram group.
FATE: fast and accurate timing error prediction framework for low power DNN accelerator design

Deep neural networks (DNN) are increasingly being accelerated on application-specific hardware such as the Google TPU designed especially for deep learning. Timing speculation is a promising approach to further increase the energy efficiency of DNN accelerators. Architectural exploration for timing speculation requires detailed gate-level timing simulations that can be time-consuming for large DNNs which execute millions of multiply-and-accumulate (MAC) operations. In this paper we propose FATE, a new methodology for fast and accurate timing simulations of DNN accelerators like the Google TPU. FATE proposes two novel ideas: (i) DelayNet, a DNN based timing model for MAC units; and (ii) a statistical sampling methodology that reduces the number of MAC operations for which timing simulations are performed. We show that FATE results in between 8 × −58× speed-up in timing simulations, while introducing less than 2% error in classification accuracy estimates. We demonstrate the use of FATE by comparing a conventional DNN accelerator that uses 2's complement (2C) arithmetic with one that uses signed magnitude representation (SMR). We show that that the SMR implementation provides 18% more energy savings for the same classification accuracy than 2C, a result that might be of independent interest.
The rational and computational scope of probabilistic rule-based expert systems

Belief consolidation schemes in AI can be viewed as three dimensional languages, consisting of a syntax (e.g. probabilities or certainty Factors), a calculus (e.g. Bayesian rules or CF combination rules), and a semantics (i.e. cognitive interpretations of competing formalisms). This paper studies the underlying rationality of those languages on the syntax and calculus grounds. In particular, the paper presents the CF-Bayesian Endomorphism Theorem, which explicitly defines the class of real-life problems of expertise that have a rational CF interpretation. Some implications of the theorem to the relationship between the CF and the Bayesian languages and the Dempster-Shafer Theory of Evidence are presented. Finally, the paper discusses the implications of the theorem on the science and practice of rule-based knowledge engineering.
Scalable digital hardware for a trapped ion quantum computer

Many of the challenges of scaling quantum computer hardware lie at the interface between the qubits and the classical control signals used to manipulate them. Modular ion trap quantum computer architectures address scalability by constructing individual quantum processors interconnected via a network of quantum communication channels. Successful operation of such quantum hardware requires a fully programmable classical control system capable of frequency stabilizing the continuous wave lasers necessary for loading, cooling, initialization, and detection of the ion qubits, stabilizing the optical frequency combs used to drive logic gate operations on the ion qubits, providing a large number of analog voltage sources to drive the trap electrodes, and a scheme for maintaining phase coherence among all the controllers that manipulate the qubits. In this work, we describe scalable solutions to these hardware development challenges.
Which subsets of an infinite random graph look random

Given a countable graph, we say a set $A$ of its vertices is \emph{universal} if it contains every countable graph as an induced subgraph, and $A$ is \emph{weakly universal} if it contains every finite graph as an induced subgraph. We show that, for almost every graph on $\mathbb N$, $(1)$ every set of positive upper density is universal, and $(2)$ every set with divergent reciprocal sums is weakly universal. We show that the second result is sharp (i.e., a random graph on $\mathbb N$ will almost surely contain non-universal sets with divergent reciprocal sums) and, more generally, that neither of these two results holds for a large class of partition regular families.
THE NEXT SIMPLEST HYPERBOLIC KNOTS

We complete the project begun by Callahan, Dean and Weeks to identify all knots whose complements are in the SnapPea census of hyperbolic manifolds with seven or fewer tetrahedra. Many of these "simple" hyperbolic knots have high crossing number. We also compute their Jones polynomials.
Solving dynamic programming with supremum terms in the objective and application to optimal battery scheduling for electricity consumers subject to demand charges

In this paper, we consider the problem of dynamic programming when supremum terms appear in the objective function. Such terms can represent overhead costs associated with the underlying state variables. Specifically, this form of optimization problem can be used to represent optimal scheduling of batteries such as the Tesla Powerwall for electrical consumers subject to demand charges — a charge based on the maximum rate of electricity consumption. These demand charges reflect the cost to the utility of building and maintaining generating capacity. Unfortunately, we show that dynamic programming problems with supremum terms do not satisfy the principle of optimality. However, we also show that the supremum is a special case of the class of forward separable objective functions. To solve the dynamic programming problem, we propose a general class of optimization problems with forward separable objectives. We then show that for any problem in this class, there exists an augmented-state dynamic programming problem which satisfies the principle of optimality and the solutions to which yield solutions to the original forward separable problem. We further generalize this approach to stochastic dynamic programming problems and apply the results to the problem of optimal battery scheduling with demand charges using a data-based stochastic model for electricity usage and solar generation by the consumer.
Distributed Saddle-Point Subgradient Algorithms With Laplacian Averaging

We present distributed subgradient methods for min-max problems with agreement constraints on a subset of the arguments of both the convex and concave parts. Applications include constrained minimization problems where each constraint is a sum of convex functions in the local variables of the agents. In the latter case, the proposed algorithm reduces to primal-dual updates using local subgradients and Laplacian averaging on local copies of the multipliers associated to the global constraints. For the case of general convex-concave saddle-point problems, our analysis establishes the convergence of the running time-averages of the local estimates to a saddle point under periodic connectivity of the communication digraphs. Specifically, choosing the gradient step-sizes in a suitable way, we show that the evaluation error is proportional to $1/\sqrt{t}$ , where $t$ is the iteration step. We illustrate our results in simulation for an optimization scenario with nonlinear constraints coupling the decisions of agents that cannot communicate directly.
Information Propagation in Clustered Multilayer Networks

In today's world, individuals interact with each other in more complicated patterns than ever. Some individuals engage through online social networks (e.g., Facebook, Twitter), while some communicate only through conventional ways (e.g., face-to-face). Therefore, understanding the dynamics of information propagation among humans calls for a multi-layer network model where an online social network is conjoined with a physical network. In this work, we initiate a study of information diffusion in a clustered multi-layer network model, where all constituent layers are random networks with high clustering. We assume that information propagates according to the SIR model and with different information transmissibility across the networks. We give results for the conditions, probability, and size of information epidemics, i.e., cases where information starts from a single individual and reaches a positive fraction of the population. We show that increasing the level of clustering in either one of the layers increases the epidemic threshold and decreases the final epidemic size in the whole system. An interesting finding is that information with low transmissibility spreads more effectively with a small but densely connected social network, whereas highly transmissible information spreads better with the help of a large but loosely connected social network.
How Frequently is a System of $2$-Linear Boolean Equations Solvable?

We consider a random system of equations $x_i+x_j=b_{(i,j)} ({\rm mod }2)$, $(x_u\in \{0,1\},\, b_{(u,v)}=b_{(v,u)}\in\{0,1\})$, with the pairs $(i,j)$ from $E$, a symmetric subset of $[n]\times [n]$. $E$ is chosen uniformly at random among all such subsets of a given cardinality $m$; alternatively $(i,j)\in E$ with a given probability $p$, independently of all other pairs. Also, given $E$, ${\rm Pr}\{b_{e}=0\}={\rm Pr}\{b_e=1\}$ for each $e\in E$, independently of all other $b_{e\prime}$. It is well known that, as $m$ passes through $n/2$ ($p$ passes through $1/n$, resp.), the underlying random graph $G(n,\#{\rm edges}=m)$, ($G(n,{\rm Pr}({\rm edge})=p)$, resp.) undergoes a rapid transition, from essentially a forest of many small trees to a graph with one large, multicyclic, component in a sea of small tree components. We should expect then that the solvability probability decreases precipitously in the vicinity of $m\sim n/2$ ($p\sim 1/n$), and indeed this probability is of order $(1-2m/n)^{1/4}$, for $m 0$. Mike Molloy noticed that the Boolean system with $b_e\equiv 1$ is solvable iff the underlying graph is $2$-colorable, and asked whether this connection might be used to determine an order of probability of $2$-colorability in the near-critical case. We answer Molloy's question affirmatively and show that, for $\lambda=o(n^{1/12})$, the probability of $2$-colorability is ${}\lesssim 2^{-1/4}e^{1/8}c(\lambda)n^{-1/12}$, and asymptotic to $2^{-1/4}e^{1/8}c(\lambda)n^{-1/12}$ at a critical phase $\lambda=O(1)$, and for $\lambda\to -\infty$.
Optimal Power Control for Fading Channels With Arbitrary Input Distributions and Delay-Sensitive Traffic

This paper presents the optimal power control policies maximizing the effective capacity achieved with arbitrary input distributions subject to an average power constraint and quality of service (QoS) requirements. The analysis leads to simplified expressions for the optimal power control strategies in the low power regime and two limiting cases, i.e., extremely stringent QoS constraints and vanishing QoS constraints. In the low power regime, the energy efficiency (EE) performance with the constant-power scheme is also determined by characterizing both the minimum energy per bit and wideband slope for arbitrary input signaling and general fading distributions. Subsequently, the results are specialized to Nakagami- $m$ and Rician fading channels. Also, tradeoff between the effective capacity and EE is studied by determining the optimal power control scheme that maximizes the effective capacity subject to constraints on the minimum required EE and average transmission power. Circuit power consumption is explicitly considered in the EE formulation. Through numerical results, the performance comparison between constant-power and optimal power control schemes for different signal constellations and Gaussian signals is carried out. The impact of QoS constraints, input distributions, fading severity, and average transmit power level on the proposed power control schemes, maximum achievable effective capacity and EE is evaluated.
The Lusztig automorphism of the q-Onsager algebra

Abstract Pascal Baseilhac and Stefan Kolb recently introduced the Lusztig automorphism L of the q-Onsager algebra O q . In this paper, we express each of L , L − 1 as a formal sum involving some quantum adjoints. In addition, (i) we give a computer-free proof that L exists; (ii) we establish the higher order q-Dolan/Grady relations previously conjectured by Baseilhac and Thao Vu; (iii) we obtain a Lusztig automorphism for the current algebra A q associated with O q ; (iv) we describe what happens when a finite-dimensional irreducible O q -module is twisted via L.
Detecting and preventing multiple-account cheating in massive open online courses

We describe a cheating strategy enabled by the features of massive open online courses (MOOCs) and detectable by virtue of the sophisticated data systems that MOOCs provide. The strategy, Copying Answers using Multiple Existences Online (CAMEO), involves a user who gathers solutions to assessment questions using a "harvester" account and then submits correct answers using a separate "master" account. We use a small-scale experiment to verify CAMEO and estimate a "lower bound" for its prevalence among 1.9 million course participants in 115 MOOCs from two universities. Using conservative thresholds, we estimate CAMEO prevalence at 1237 certificates, accounting for 1.3% of the certificates in the 69 MOOCs with CAMEO users. Among earners of 20 or more certificates, 25% have used the CAMEO strategy. CAMEO users are more likely to be young, male, and international than other MOOC certificate earners. We identify preventive strategies that can decrease CAMEO rates and show evidence of their effectiveness in science courses. We detect a cheating strategy used in Massive Open Online Courses (MOOCs).We call this strategy, "Copying Answers using Multiple Existences Online" (CAMEO).We estimate conservatively that at least 1.3% of certificates were earned by CAMEO.Among earners of 20 or more certificates, 25% have used the CAMEO strategy.CAMEO represents one of many threats to the validity of MOOC certifications.
Efficient algorithms for cur and interpolative matrix decompositions

The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized library codes can be utilized for implementation. For certain applications, further acceleration can be attained by incorporating techniques based on randomized projections. Numerical experiments demonstrate advantageous performance compared to existing techniques for computing CUR factorizations.
NUMERICAL ANALYSIS OF PARALLEL REPLICA DYNAMICS

Parallel replica dynamics is a method for accelerating the computation of processes charac- terized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of their time about the minima of the underlying poten- tial, occasionally transitioning into different basins of attraction. The essential idea of parallel replica dynamics is that the exit distribution from a given well for a single process can be approximated by the distribution of the first exit of N independent identical processes, each run for only 1/N -th the amount of time. While promising, this leads to a series of numerical analysis questions about the accuracy of the exit distributions. Building upon the recent work in (C. Le Bris, T. Lelievre, M. Luskin and D. Perez, Monte Carlo Methods Appl. 18 (2012) 119-146), we prove a unified error estimate on the exit distributions of the algorithm against an unaccelerated process. Furthermore, we study a dephasing mechanism, and prove that it will successfully complete.