cssi/SciSciGPT-SciSciNet huggingface dataset:
Synthesis of a polymerizable metal-ion-chelating lipid for fluid bilayers.

Hydrated lipid structures, such as liposomes, that display tethered metal-ion-chelating groups have proven useful in peptide and protein binding, as well as 2D protein crystallization through molecular recognition of accessible histidine sites in proteins and peptides. Polymerizable metal-ion-chelating lipids bearing a reactive diacetylene group have been described. These interesting compounds can be polymerized in the solid-analogous phase. Here we describe the design of the first polymerizable metal-ion-chelating lipid that can be used in the fluid, i.e., liquid analogous, phase of lipid bilayers. The synthesis of 1-palmitoyl-2-[8-[(E,E)-2‘,4‘-hexadienoyloxy]octanoyl]-sn-glycero-3-N-[11-[N‘,N‘-bis[carboxymethyl]imino]-3,6,9-trioxaundecanoyl] phosphatidylethanolamine (1) is described. The chelator moiety, iminodiacetate (IDA), was linked to the polymerizable phosphatidylethanolamine (PE) with a terminal 2,4-hexadienoyl (sorbyl) group through an oligo(ethylene glycol)-based spacer. Lipid 1−Cu complex is d...
Complexity-aware simple modeling.

Mathematical models continue to be essential for deepening our understanding of biology. On one extreme, simple or small-scale models help delineate general biological principles. However, the parsimony of detail in these models as well as their assumption of modularity and insulation make them inaccurate for describing quantitative features. On the other extreme, large-scale and detailed models can quantitatively recapitulate a phenotype of interest, but have to rely on many unknown parameters, making them often difficult to parse mechanistically and to use for extracting general principles. We discuss some examples of a new approach — complexity-aware simple modeling — that can bridge the gap between the small-scale and large-scale approaches.
Accordion porphyrins: Hybrid models for heme and binuclear monooxygenases

Abstract The synthesis, characterization, and examination of the monooxygenase activity of tetrapyrrolic macrocyclic complexes with an accordion porphyrin-like ligand framework are described. Cyanovinyl protection techniques were used to obtain a diformyl dipyrromethane, which was condensed with 1,3-diaminopropane in the presence of metal acetate template to achieve manganese(II), nickel(II), and copper(II) complexes. The macrocycle was found to be in the dipyrromethene form for both the manganese(II) and copper(II) complexes, and in the dipyrromethane form for the nickel(II) complex. The crystal structure of the acetate salt of the manganese(II) complex was obtained. The manganese(II) complex was found to catalyze the epoxidation of cyclohexene, yielding primarily the epoxide (40%) with only minor side products, while the nickel(II) and copper(II) complexes showed little catalytic activity. A lack of stereoselectivity was observed in the epoxidation of cis - and trans -stilbene by the manganese(II) complex, which yielded only trans -epoxide in the reaction with trans -stilbene, but both cis and trans products in the reaction with cis -stilbene.
Zinc(II) promoted conversion of aryltriazenes to aryl iodides and aryl nitriles

Abstract Aryltriazenes react with zinc perchlorate/zinc cyanide to produces arylnitriles and react with zinc iodide to produce aryliodides. The reaction mechanism involves aryl radicals that have been trapped by addition to propenenitriles in a good preparative Meerwein arylation process.
Diastereoselective, Titanium-Mediated Cyclization of ω-Vinyl Tethered Imides

Diastereoselective reductive coupling reactions of ω-vinyl tethered cyclic imides are achieved by a preexisting stereocenter at an allylic position. Particularly noteworthy is the effective use of a 1:2 mixture of Ti(O-i-Pr)4 and n-BuLi to afford the N-acylhemiaminal products in good yields.
Solid State Synthesis and Characterization of Tin-Based Low-Dimensional Materials

We report the synthetic conditions, physical properties and potential applications of late group 14 metal (Sn) 0D, 1D, 2D and 3D extended materials. The structures are primarily neutral chain and anionic layered compounds. The latter are charge-balanced by ammonium cations, as in and BING-7 [Sn(C 2 O 4 )F - ] [NH 4 + ] and BING-8 [Sn(PO 4 H)F - ] [NH 4 + ]. The neutral layered compound and chain compounds BING-1 [Na 4 Sn 4 (C 2 O 4 )F 6 ], BING-2 [KSn(C 2 O 4 )F] and BING-4 [Sn(C 2 O 4 )(C 5 H 5 N)] have also been synthesized solvothermally. Thermogravimetric analysis (TGA) under nitrogen and in-situ variable temperature X-ray diffraction show that the materials decompose in the 200°C to 300°C range to more stable phases. Nuclear magnetic resonance (NMR) was used to monitor the ion-exchange properties of some of the materials. The intercalation properties of these materials are still being investigated.
Synthesis of Higher Oxidized Metabolites of Dibenz[a,j]anthracene Implicated in the Mechanism of Carcinogenesis

Higher oxidized metabolites are implicated as active carcinogenic forms of polycyclic aromatic hydrocarbons which have two or more bay or fjord molecular regions, such as dibenz[a,j]anthracene. These include the bis(dihydrodiols) and phenolic dihydrodiols which may potentially undergo further metabolism to the corresponding diol epoxides. The latter react with DNA resulting in mutations that lead to tumorigenesis. Prior characterization of these metabolites has been based largely on HPLC and spectroscopic evidence. This paper reports efficient syntheses of the trans-trans-3,4,8,9-dihydrodiol (1) and the 10- and 11-phenolic trans-3,4-dihydrodiols of dibenz[a,j]anthracene (3a,b). The synthetic route to 1 entails as the key steps asymmetric dihydroxylation of an appropriately substituted stilbene precursor employing a Sharpless catalyst followed by intramolecular cyclodehydrobromination catalyzed by Pd(PPh3)2Cl2. The syntheses of 3a,b proceed via sequences involving a Wittig reaction of anisaldehyde with a p...
Inverse electron demand hetero -Diels–Alder reaction in preparing 1,4-benzodioxin from o -quinone and enamine

Abstract A process for synthesizing 1,4-benzodioxin, through oxidation of a phenol to an o-quinone followed by treatment with an enamine, has been developed. Adduct stereochemistry is found to be retained via this one-pot reaction. The method uses hypervalent iodine reagent under mild conditions and is compatible with a wide scope of phenols and enamines.
Chiral styrene oxides from α-haloacetophenones using NaBH4 and TarB-NO2, a chiral Lewis acid

Abstract High enantioselectivities are obtained for the preparation of chiral styrene oxides through reduction of α-haloacetophenones using TarB-NO2 reagent and the inexpensive and mild reducing agent NaBH4. The epoxides are easily obtained in up to 95% ee through routine acid–base workup of the product alcohols. Either the (R) or (S) epoxide can be obtained by using the appropriate l - or d -tartaric acid starting material in the TarB-NO2 reagent.
Regioselective synthesis of 9‐substituted‐8‐azaguanines (5‐amino‐3‐substituted‐3,6‐dihydro‐7H‐1,2,3‐triazolo[4,5‐d]pyrimidin‐7‐one)

By modifying previously described methods for the synthesis of 9-substituted-guanines from imidazoles, we have developed a new procedure for the regioselective synthesis of 9-substituted-8-azaguanines (5-amino-3-substituted-3,6-dihydro-7H-1,2,3-triazolo[4,5-d]pyrimidin-7-one) from triazoles in high yields. The method seems suitable for the introduction of a variety of substituents including sugars, carbocyclic, acyclic and carboacyclic chains.
Galerkin approximation of dynamical quantities using trajectory data

Understanding chemical mechanisms requires estimating dynamical statistics such as expected hitting times, reaction rates, and committors. Here, we present a general framework for calculating these dynamical quantities by approximating boundary value problems using dynamical operators with a Galerkin expansion. A specific choice of basis set in the expansion corresponds to the estimation of dynamical quantities using a Markov state model. More generally, the boundary conditions impose restrictions on the choice of basis sets. We demonstrate how an alternative basis can be constructed using ideas from diffusion maps. In our numerical experiments, this basis gives results of comparable or better accuracy to Markov state models. Additionally, we show that delay embedding can reduce the information lost when projecting the system’s dynamics for model construction; this improves estimates of dynamical statistics considerably over the standard practice of increasing the lag time.Understanding chemical mechanisms requires estimating dynamical statistics such as expected hitting times, reaction rates, and committors. Here, we present a general framework for calculating these dynamical quantities by approximating boundary value problems using dynamical operators with a Galerkin expansion. A specific choice of basis set in the expansion corresponds to the estimation of dynamical quantities using a Markov state model. More generally, the boundary conditions impose restrictions on the choice of basis sets. We demonstrate how an alternative basis can be constructed using ideas from diffusion maps. In our numerical experiments, this basis gives results of comparable or better accuracy to Markov state models. Additionally, we show that delay embedding can reduce the information lost when projecting the system’s dynamics for model construction; this improves estimates of dynamical statistics considerably over the standard practice of increasing the lag time.
Estimating mutual information by local Gaussian approximation

Estimating mutual information (MI) from samples is a fundamental problem in statistics, machine learning, and data analysis. Recently it was shown that a popular class of non-parametric MI estimators perform very poorly for strongly dependent variables and have sample complexity that scales exponentially with the true MI. This undesired behavior was attributed to the reliance of those estimators on local uniformity of the underlying (and unknown) probability density function. Here we present a novel semi-parametric estimator of mutual information, where at each sample point, densities are locally approximated by a Gaussians distribution. We demonstrate that the estimator is asymptotically unbiased. We also show that the proposed estimator has a superior performance compared to several baselines, and is able to accurately measure relationship strengths over many orders of magnitude.
Bennett-type generalization bounds: large-deviation case and faster rate of convergence

In this paper, we present the Bennett-type generalization bounds of the learning process for i.i.d. samples, and then show that the generalization bounds have a faster rate of convergence than the traditional results. In particular, we first develop two types of Bennett-type deviation inequality for the i.i.d. learning process: one provides the generalization bounds based on the uniform entropy number; the other leads to the bounds based on the Rademacher complexity. We then adopt a new method to obtain the alternative expressions of the Bennett-type generalization bounds, which imply that the bounds have a faster rate o(N-½) of convergence than the traditional results O(N-½). Additionally, we find that the rate of the bounds will become faster in the large-deviation case, which refers to a situation where the empirical risk is far away from (at least not close to) the expected risk. Finally, we analyze the asymptotical convergence of the learning process and compare our analysis with the existing results.
Quantum measurable cardinals

Abstract We investigate states on von Neumann algebras which are not normal but enjoy various forms of infinite additivity, and show that these exist on B ( H ) if and only if the cardinality of an orthonormal basis of H satisfies various large cardinal conditions. For instance, there is a singular countably additive pure state on B ( l 2 ( κ ) ) if and only if κ is Ulam measurable, and there is a singular κ -additive pure state on B ( l 2 ( κ ) ) if and only if κ is measurable. The proofs make use of Farah and Weaver's theory of quantum filters [12] . We can generalize some of these characterizations to arbitrary von Neumann algebras. Applications to Ueda's peak set theorem for von Neumann algebras are discussed in the final section.
Learning an Optimization Algorithm Through Human Design Iterations

Solving optimal design problems through crowdsourcing faces a dilemma: On one hand, human beings have been shown to be more effective than algorithms at searching for good solutions of certain real-world problems with high-dimensional or discrete solution spaces; on the other hand, the cost of setting up crowdsourcing environments, the uncertainty in the crowd's domain-specific competence, and the lack of commitment of the crowd, all contribute to the lack of real-world application of design crowdsourcing. We are thus motivated to investigate a solution-searching mechanism where an optimization algorithm is tuned based on human demonstrations on solution searching, so that the search can be continued after human participants abandon the problem. To do so, we model the iterative search process as a Bayesian Optimization (BO) algorithm, and propose an inverse BO (IBO) algorithm to find the maximum likelihood estimators of the BO parameters based on human solutions. We show through a vehicle design and control problem that the search performance of BO can be improved by recovering its parameters based on an effective human search. Thus, IBO has the potential to improve the success rate of design crowdsourcing activities, by requiring only good search strategies instead of good solutions from the crowd.
Learning Implicit Sampling Distributions for Motion Planning

Sampling-based motion planners have experienced much success due to their ability to efficiently and evenly explore the state space. However, for many tasks, it may be more efficient to not uniformly explore the state space, especially when there is prior information about its structure. Previous methods have attempted to modify the sampling distribution using hand selected heuristics that can work well for specific environments but not universally. In this paper, a policy-search based method is presented as an adaptive way to learn implicit sampling distributions for different environments. It utilizes information from past searches in similar environments to generate better distributions in novel environments, thus reducing overall computational cost. Our method can be incorporated with a variety of sampling-based planners to improve performance. Our approach is validated on a number of tasks, including a 7DOF robot arm, showing marked improvement in number of collision checks as well as number of nodes expanded compared with baseline methods.
Virtual Specht stability for FI-modules in positive characteristic

Abstract We define a notion of virtual Specht stability which is a relaxation of the Church–Farb notion of representation stability for sequences of symmetric group representations. Using a structural result of Nagpal, we show that FI -modules over fields of positive characteristic exhibit virtual Specht stability. As a corollary we answer a question posed by Farb in his 2014 ICM address.
Approximate Supermodularity Bounds for Experimental Design

This work provides performance guarantees for the greedy solution of experimental design problems. In particular, it focuses on A- and E-optimal designs, for which typical guarantees do not apply since the mean-square error and the maximum eigenvalue of the estimation error covariance matrix are not supermodular. To do so, it leverages the concept of approximate supermodularity to derive non-asymptotic worst-case suboptimality bounds for these greedy solutions. These bounds reveal that as the SNR of the experiments decreases, these cost functions behave increasingly as supermodular functions. As such, greedy A- and E-optimal designs approach (1-1/e)-optimality. These results reconcile the empirical success of greedy experimental design with the non-supermodularity of the A- and E-optimality criteria.
GENERALIZED GRAMIANS: CREATING FRAME VECTORS IN MAXIMAL SUBSPACES

A frame is a system of vectors S in Hilbert space ℋ with properties which allow one to write algorithms for the two operations, analysis and synthesis, relative to S, for all vectors in ℋ; expressed in norm-convergent series. Traditionally, frame properties are expressed in terms of an S-Gramian, GS (an infinite matrix with entries equal to the inner product of pairs of vectors in S); but still with strong restrictions on the given system of vectors in S, in order to guarantee frame-bounds. In this paper, we remove these restrictions on GS, and we obtain instead direct-integral analysis/synthesis formulas. Applications are given to reproducing kernel Hilbert spaces, and to random fields.
Distribution system voltage control under uncertainties

Voltage control plays an important role in the operation of electricity distribution networks, especially with high penetration of distributed energy resources. These resources introduces significant and fast varying uncertainties. In this paper, we focus on reactive power compensation to control voltage in the presence of uncertainties. We adopt a probabilistic approach that accounts for arbitrary correlations between renewable resources at each of the buses and we use the linearized DistFlow equations to model the distribution network. We then show that this optimization problem is convex for a wide variety of probabilistic distributions. Compared to conventional per-bus chance constraints, our formulation is more robust to uncertainty and more computationally tractable. We illustrate the results using standard IEEE distribution test feeders.
Integrality estimates in orbits over function fields

Abstract We prove a version of Silverman's dynamical integral point theorem for a large class of rational functions defined over global function fields.
Mean Curvature Flow of Arbitrary Co-Dimensional Reifenberg Sets

We study the existence and uniqueness of smooth mean curvature flow, in arbitrary dimension and co-dimension, emanating from so called k-dimensional $$(\varepsilon ,R)$$ Reifenberg flat sets in $$\mathbb {R}^n$$ . The Reifenberg condition, roughly speaking, says that the set has a weak metric notion of a k-dimensional tangent plane at every point and scale, but those tangents are allowed to tilt as the scales vary. We show that if the Reifenberg parameter $$\varepsilon $$ is small enough, the (arbitrary co-dimensional) level set flow (in the sense of Ambrosio and Soner in J Differ Geom 43(4):694–737, 1996) is non fattening, smooth and attains the initial value in the Hausdorff sense. Our results generalize the ones from Hershkovits (Geom Topol 21(1):441–484, 2017), in which the co-dimension one case was studied. We also prove a general (short time) smooth uniqueness result, generalizing the one for evolution of smooth submanifolds, which may be of independent interest, even in co-dimension one.
New Variable Compliance Method for Estimating In-Situ Stress and Leak-Off from DFIT Data

Over the past two decades, Diagnostic Fracture Injection Tests (DFIT), which have also been referred to as Injection-Falloff Tests, Fracture Calibration Tests, Mini-Frac Tests in the literature, have evolved into a commonly used and reliable technique to evaluate reservoir properties, fracturing parameters and obtain in-situ stresses. Since the introduction of DFIT analysis based on G-function and its derivative, this method has become standard practice for quantifying minimum in-situ stress and leak-off coefficient. However, the pressure decline model that underlies the G-function plot makes two distinct and important assumptions: (1) leak-off is not pressure-dependent and, (2) fracture stiffness (or compliance) is assumed to be constant during fracture closure. In this study, we first review Nolte's original G-function model and examine the assumptions inherent in the model. We then present a new global pressure transient model for pressure decline after shut-in which not only preserves the physics of unsteady-state reservoir flow behavior, elastic fracture mechanics and material balance, but also incorporates the gradual changes of fracture stiffness (or compliance) due to the contact of rough fracture walls during closure. Analysis of synthetic cases, along with field data are presented to demonstrate how the coupled effects of fracture geometry, fracture surface asperities, formation properties, pore pressure and wellbore storage can impact fracturing pressure decline and the estimation of minimum in-situ stress. It is shown that using Carter's leak-off is an oversimplification that leads to significant errors in the interpretation of DFIT data. Most importantly, this article reveals that previous methods of estimating minimum in-situ stress often lead to significant over or underestimates. Based on our modeling and simulation results, we propose a much more accurate and reliable method to estimate the minimum in-situ stress and fracture pressure dependent leak-off rate.
Composable Core-sets for Determinant Maximization: A Simple Near-Optimal Algorithm

``Composable core-sets'' are an efficient framework for solving optimization problems in massive data models. In this work, we consider efficient construction of composable core-sets for the determinant maximization problem. This can also be cast as the MAP inference task for determinantal point processes, that have recently gained a lot of interest for modeling diversity and fairness. The problem was recently studied in [IMOR'18], where they designed composable core-sets with the optimal approximation bound of $\tilde O(k)^k$. On the other hand, the more practical Greedy algorithm has been previously used in similar contexts. In this work, first we provide a theoretical approximation guarantee of $O(C^{k^2})$ for the Greedy algorithm in the context of composable core-sets; Further, we propose to use a Local Search based algorithm that while being still practical, achieves a nearly optimal approximation bound of $O(k)^{2k}$; Finally, we implement all three algorithms and show the effectiveness of our proposed algorithm on standard data sets.
Shampoo: Preconditioned Stochastic Tensor Optimization

Preconditioned gradient methods are among the most general and powerful tools in optimization. However, preconditioning requires storing and manipulating prohibitively large matrices. We describe and analyze a new structure-aware preconditioning algorithm, called Shampoo, for stochastic optimization over tensor spaces. Shampoo maintains a set of preconditioning matrices, each of which operates on a single dimension, contracting over the remaining dimensions. We establish convergence guarantees in the stochastic convex setting, the proof of which builds upon matrix trace inequalities. Our experiments with state-of-the-art deep learning models show that Shampoo is capable of converging considerably faster than commonly used optimizers. Although it involves a more complex update rule, Shampoo's runtime per step is comparable to that of simple gradient methods such as SGD, AdaGrad, and Adam.
More than a million ways to be pushed. A high-fidelity experimental dataset of planar pushing

Pushing is a motion primitive useful to handle objects that are too large, too heavy, or too cluttered to be grasped. It is at the core of much of robotic manipulation, in particular when physical interaction is involved. It seems reasonable then to wish for robots to understand how pushed objects move.
A construction for difference sets with local properties

Abstract We construct finite sets of real numbers that have a small difference set and strong local properties. In particular, we construct a set A of n real numbers such that | A − A | = n log 2 3 and that every subset A ′ ⊆ A of size k satisfies | A ′ − A ′ | ≥ k log 2 3 . This construction leads to the first non-trivial upper bound for the problem of distinct distances with local properties.
Higher-Order Coreference Resolution with Coarse-to-Fine Inference

We introduce a fully-differentiable approximation to higher-order inference for coreference resolution. Our approach uses the antecedent distribution from a span-ranking architecture as an attention mechanism to iteratively refine span representations. This enables the model to softly consider multiple hops in the predicted clusters. To alleviate the computational cost of this iterative process, we introduce a coarse-to-fine approach that incorporates a less accurate but more efficient bilinear factor, enabling more aggressive pruning without hurting accuracy. Compared to the existing state-of-the-art span-ranking approach, our model significantly improves accuracy on the English OntoNotes benchmark, while being far more computationally efficient.
Shallow water models with constant vorticity

Abstract We modify the nonlinear shallow water equations, the Korteweg–de Vries equation, and the Whitham equation, to permit constant vorticity, and examine wave breaking, or the lack thereof. By wave breaking, we mean that the solution remains bounded but its slope becomes unbounded in finite time. We show that a solution of the vorticity-modified shallow water equations breaks if it carries an increase of elevation; the breaking time decreases to zero as the size of vorticity increases. We propose a full-dispersion shallow water model, which combines the dispersion relation of water waves and the nonlinear shallow water equations in the constant vorticity setting, and which extends the Whitham equation to permit bidirectional propagation. We show that its small amplitude and periodic traveling wave is unstable to long wavelength perturbations if the wave number is greater than a critical value, and stable otherwise, similarly to the Benjamin–Feir instability in the irrotational setting; the critical wave number grows unboundedly large with the size of vorticity. The result agrees with that from a multiple scale expansion of the physical problem. We show that vorticity considerably alters the modulational stability and instability in the presence of the effects of surface tension.
Placing Marangoni instabilities under arrest

Soap bubbles occupy the rare position of delighting and fascinating both young children and scientific minds alike. Sir Isaac Newton, Joseph Plateau, Carlo Marangoni, and Pierre-Gilles de Gennes, not to mention countless others, have discovered remarkable results in optics, molecular forces and fluid dynamics from investigating this seemingly simple system. We present here a compilation of curiosity-driven experiments that systematically investigate the surface flows on a rising soap bubble. From childhood experience, we are familiar with the vibrant colors and mesmerizing display of chaotic flows on the surface of a soap bubble. These flows arise due to surface tension gradients, also known as Marangoni flows or instabilities. In Figure 1, we show the surprising effect of layering multiple instabilities on top of each other, highlighting that unexpected new phenomena are still waiting to be discovered, even in the simple soap bubble.
Indirect Gaussian Graph Learning Beyond Gaussianity

This paper studies how to capture dependency graph structures from real data that may not be multivariate Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive over-parametrization with shrinkage to incorporate variable dependencies into the criterion. An iterative Gaussian graph learning algorithm is proposed with ease in implementation. Statistical analysis shows that the estimators achieve satisfactory accuracy with the error measured in terms of a proper Bregman divergence. Real-life examples in different settings are given to demonstrate the efficacy of the proposed methodology.
Information Constraints on Auto-Encoding Variational Bayes

Parameterizing the approximate posterior of a generative model with neural networks has become a common theme in recent machine learning research. While providing appealing flexibility, this approach makes it difficult to impose or assess structural constraints such as conditional independence. We propose a framework for learning representations that relies on Auto-Encoding Variational Bayes and whose search space is constrained via kernel-based measures of independence. In particular, our method employs the $d$-variable Hilbert-Schmidt Independence Criterion (dHSIC) to enforce independence between the latent representations and arbitrary nuisance factors. We show how to apply this method to a range of problems, including the problems of learning invariant representations and the learning of interpretable representations. We also present a full-fledged application to single-cell RNA sequencing (scRNA-seq). In this setting the biological signal in mixed in complex ways with sequencing errors and sampling effects. We show that our method out-performs the state-of-the-art in this domain.
Submodular maximization with nearly-optimal approximation and adaptivity in nearly-linear time

In this paper, we study the tradeoff between the approximation guarantee and adaptivity for the problem of maximizing a monotone submodular function subject to a cardinality constraint. The adaptivity of an algorithm is the number of sequential rounds of queries it makes to the evaluation oracle of the function, where in every round the algorithm is allowed to make polynomially-many parallel queries. Adaptivity is an important consideration in settings where the objective function is estimated using samples and in applications where adaptivity is the main running time bottleneck. Previous algorithms achieving a nearly-optimal 1 − 1/e − e approximation require Ω(n) rounds of adaptivity. In this work, we give the first algorithm that achieves a 1 − 1/e − e approximation using O(In n/e2) rounds of adaptivity. The number of function evaluations and additional running time of the algorithm are O(n poly(logn, 1/e)).
Coulomb Blockade in Superconducting Quantum Point Contacts

The amplitude of the Coulomb blockade oscillations is calculated for a single-mode Josephson junction with arbitrary electron transparency $D$. It is shown that a mechanism related to chiral anomaly completely suppresses the Coulomb blockade in ballistic junctions with $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$. At finite reflection probability, the suppression process is described quantitatively in terms of the Landau-Zener transition.
Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs

The eigenvalues of graphs are related to many of its combinatorial properties. In his fundamental work, Fiedler showed the close connections between the Laplacian eigenvalues and eigenvectors of a graph and its vertex-connectivity and edge-connectivity. We present some new results describing the connections between the spectrum of a regular graph and other combinatorial parameters such as its generalized connectivity, toughness, and the existence of spanning trees with bounded degree.
Existence of weighted pseudo-almost periodic solutions to some classes of nonautonomous partial evolution equations

Abstract In this paper, under Acquistapace–Terreni conditions, we make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of weighted pseudo-almost periodic solutions to some classes of nonautonomous partial evolution equations. Applications include the existence of weighted pseudo-almost periodic solutions to a nonautonomous heat equation with gradient coefficients.
DERIVATIONS AND PROJECTIONS ON JORDAN TRIPLES An introduction to nonassociative algebra, continuous cohomology, and quantum functional analysis

This paper is an elaborated version of the material presented by the author in a three hour minicourse at V International Course of Mathematical Analysis in Andalusia, at Almeria, Spain September 12-16, 2011. The author wishes to thank the scientific committee for the opportunity to present the course and to the organizing committee for their hospitality. The author also personally thanks Antonio Peralta for his collegiality and encouragement.
REGULARITY OF THE MINIMIZERS IN THE COMPOSITE MEMBRANE PROBLEM IN R 2

We study the regularity of the minimizers to the problem: λ(α,A)=infu∈H01(Ω),‖u‖2=1,|D|=A∫Ω|Du|2+α∫Du2. We prove that in the physical case α c} is analytic where c is the constant such that D={u<c} (up to a zero measure set).
Price of anarchy for Mean Field Games

The price of anarchy, originally introduced to quantify the inefficiency of selfish behavior in routing games, is extended to mean field games. The price of anarchy is defined as the ratio of a worst case social cost computed for a mean field game equilibrium to the optimal social cost as computed by a central planner. We illustrate properties of such a price of anarchy on linear quadratic extended mean field games, for which explicit computations are possible. A sufficient and necessary condition to have no price of anarchy is presented. Various asymptotic behaviors of the price of anarchy are proved for limiting behaviors of the coefficients in the model and numerics are presented.
Asynchronous Adaptation and Learning Over Networks—Part I: Modeling and Stability Analysis

In this work and the supporting Parts II and III of this paper, also in the current issue, we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We examine asynchronous networks that are subject to fairly general sources of uncertainties, such as changing topologies, random link failures, random data arrival times, and agents turning on and off randomly. Under this model, agents in the network may stop updating their solutions or may stop sending or receiving information in a random manner and without coordination with other agents. We establish in Part I conditions on the first and second-order moments of the relevant parameter distributions to ensure mean-square stable behavior. We derive in Part II expressions that reveal how the various parameters of the asynchronous behavior influence network performance. We compare in Part III the performance of asynchronous networks to the performance of both centralized solutions and synchronous networks. One notable conclusion is that the mean-square-error performance of asynchronous networks shows a degradation only in the order of O(ν), where ν is a small step-size parameter, while the convergence rate remains largely unaltered. The results provide a solid justification for the remarkable resilience of cooperative networks in the face of random failures at multiple levels: agents, links, data arrivals, and topology.
Landscaping the strong CP problem

One often hears that the strong CP problem is the one problem which cannot be solved by anthropic reasoning. We argue that this is not so. Due to nonperturbative dynamics, states with a different CP violating paramenter θ acquire different vacuum energies after the QCD phase transition. These add to the total variation of the cosmological constant in the putative landscape of Universes. An interesting possibility arises when the cosmological constant is mostly cancelled by the membrane nucleation mechanism. If the step size in the resulting discretuum of cosmological constants, ΔΛ, is in the interval (meV)4< ΔΛ < (100 MeV)4, the cancellation of vacuum energy can be assisted by the scanning of θ. For (meV)4< ΔΛ < (keV)4 this may yield θ < 10−10, meeting the observational limits. This scenario opens up 24 orders of magnitude of acceptable parameter space for ΔΛ compared to membrane nucleation acting alone. In such a Universe one may not need a light axion to solve the strong CP problem.
A variational perspective on accelerated methods in optimization

Accelerated gradient methods play a central role in optimization, achieving optimal rates in many settings. Although many generalizations and extensions of Nesterov’s original acceleration method have been proposed, it is not yet clear what is the natural scope of the acceleration concept. In this paper, we study accelerated methods from a continuous-time perspective. We show that there is a Lagrangian functional that we call the Bregman Lagrangian, which generates a large class of accelerated methods in continuous time, including (but not limited to) accelerated gradient descent, its non-Euclidean extension, and accelerated higher-order gradient methods. We show that the continuous-time limit of all of these methods corresponds to traveling the same curve in spacetime at different speeds. From this perspective, Nesterov’s technique and many of its generalizations can be viewed as a systematic way to go from the continuous-time curves generated by the Bregman Lagrangian to a family of discrete-time accelerated algorithms.
Detecting infinitely many semisimple representations in a fixed finite dimension

Let n be a positive integer, and let k be a field (of arbitrary characteristic) accessible to symbolic computation. We describe an algorithmic test for determining whether or not a finitely presented k-algebra R has infinitely many equivalence classes of semisimple representations R→Mn(k′), where k′ is the algebraic closure of k. The test reduces the problem to computational commutative algebra over k, via famous results of Artin, Procesi, and Shirshov. The test is illustrated by explicit examples, with n=3.
Multi-view Factorization AutoEncoder with Network Constraints for Multi-omic Integrative Analysis

Multi-omic data provides multiple views of the same patients. Integrative analysis of multi-omic data is crucial to elucidate the molecular underpinning of disease etiology. However, multi-omic data has the “big p, small N” problem (the number of features is large, but the number of samples is small), it is challenging to train a complicated machine learning model from the multi-omic data alone and make it generalize well. Here we propose a framework termed Multi-view Factorization AutoEncoder with network constraints to integrate multi-omic data with domain knowledge (biological interaction networks). Our framework employs deep representation learning to learn feature embeddings and patient embeddings simultaneously, enabling us to integrate feature interaction network and patient view similarity network constraints into the training objective. The whole framework is end-to-end differentiable. We applied our approach to two TCGA datasets and achieved satisfactory results on predicting disease Progression-Free Interval (PFI) event.
Design of First-Order Optimization Algorithms via Sum-of-Squares Programming

In this paper, we propose a framework based on sum-of-squares programming to design iterative first-order optimization algorithms for smooth and strongly convex problems. Our starting point is to develop a polynomial matrix inequality as a sufficient condition for exponential convergence of the algorithm. The entries of this matrix are polynomial functions of the unknown parameters (exponential decay rate, stepsize, momentum coefficient, etc.). We then formulate a polynomial optimization, in which the objective is to optimize the exponential decay rate over the parameters of the algorithm. Finally, we use sum-of-squares programming as a tractable relaxation of the proposed polynomial optimization problem. We illustrate the utility of the proposed framework by designing a first-order algorithm that shares the same structure as Nesterov's accelerated gradient method.
High-Energy Neutrino Astronomy: From AMANDA to IceCube

Kilometer-scale neutrino detectors such as IceCube are discovery instruments covering nuclear and particle physics, cosmology and astronomy. Examples of their multidisciplinary missions include the search for the particle nature of dark matter and for additional small dimensions of space. In the end, their conceptual design is very much anchored to the observational fact that Nature accelerates protons and photons to energies in excess of 10^{20} and 10^{13} eV, respectively. The cosmic ray connection sets the scale of cosmic neutrino fluxes. In this context, we discuss the first results of the completed AMANDA detector and the reach of its extension, IceCube.
A model for collective dynamics in ant raids

Ant raiding, the process of identifying and returning food to the nest or bivouac, is a fascinating example of collective motion in nature. During such raids ants lay pheromones to form trails for others to find a food source. In this work a coupled PDE/ODE model is introduced to study ant dynamics and pheromone concentration. The key idea is the introduction of two forms of ant dynamics: foraging and returning, each governed by different environmental and social cues. The model accounts for all aspects of the raiding cycle including local collisional interactions, the laying of pheromone along a trail, and the transition from one class of ants to another. Through analysis of an order parameter measuring the orientational order in the system, the model shows self-organization into a collective state consisting of lanes of ants moving in opposite directions as well as the transition back to the individual state once the food source is depleted matching prior experimental results. This indicates that in the absence of direct communication ants naturally form an efficient method for transporting food to the nest/bivouac. The model exhibits a continuous kinetic phase transition in the order parameter as a function of certain system parameters. The associated critical exponents are found, shedding light on the behavior of the system near the transition.
A stability result using the matrix norm to bound the permanent

We prove a stability version of a general result that bounds the permanent of a matrix in terms of its operator norm. More specifically, suppose A is an n × n matrix over C (resp. R), and let P denote the set of n × n matrices over C (resp. R) that can be written as a permutation matrix times a unitary diagonal matrix. Then it is known that the permanent of A satisfies |per(A)| ≤ ||A|| n 2 with equality iff A/||A||2 ∈ P (where ||A||2 is the operator 2-norm of A). We show a stability version of this result asserting that unless A is very close (in a particular sense) to one of these extremal matrices, its permanent is exponentially smaller (as a function of n) than ||A|| n 2. In particular, for any fixed α, β > 0, we show that |per(A)| is exponentially smaller than ||A|| n 2 unless all but at most αn rows contain entries of modulus at least ||A||2(1−β).
Polynomials meeting Ax's bound

Let $f\in\Bbb F_q[X_1,\dots,X_n]$ with $°f=d>0$ and let $Z(f)=\{(x_1,\dots,x_n)\in \Bbb F_q^n: f(x_1,\dots,x_n)=0\}$. Ax's theorem states that $|Z(f)|\equiv 0\pmod {q^{\lceil n/d\rceil-1}}$, that is, $\nu_p(|Z(f)|)\ge m(\lceil n/d\rceil-1)$, where $p=\text{char}\,\Bbb F_q$, $q=p^m$, and $\nu_p$ is the $p$-adic valuation. In this paper, we determine a condition on the coefficients of $f$ that is necessary and sufficient for $f$ to meet Ax's bound, that is, $\nu_p(|Z(f)|)=m(\lceil n/d\rceil-1)$. Let $R_q(d,n)$ denote the $q$-ary Reed-Muller code $\{f\in\Bbb F_q[X_1,\dots,X_n]: °f\le d,\ °_{X_j}f\le q-1,\ 1\le j\le n\}$, and let $N_q(d,n;t)$ be the number of codewords of $R_q(d,n)$ with weight divisible by $p^t$. As applications of the aforementioned result, we find explicit formulas for $N_q(d,n;t)$ in the following cases: (i) $q=2^m$, $n$ even, $d=n/2$, $t=m+1$; (ii) $q=2$, $n/2\le d\le n-2$, $t=2$; (iii) $q=3^m$, $d=n$, $t=1$; (iv) $q=3$, $n\le d\le 2n$, $t=1$.
Simulating Vehicle Movement and Multi-Hop Connectivity from Basic Safety Messages

The Basic Safety Message (BSM) is a standardized communication packet that is sent every tenth of a second between connected vehicles using Dedicated Short Range Communication (DSRC). BSMs contain data about the sending vehicle's state, such as speed, location, and the status of the turn signal [1]. Presently, many BSM datasets from various United States locations are available through the connected vehicle testbeds of U.S. Department of Transportation. However, without a proper visualization tool, it is not possible to analyze or obtain a visual overview of the spatio-temporal distribution of the data. For this purpose, a web application has been developed which can ingest a raw BSM dataset and display a time-based simulation of vehicle movement. The simulation also displays multi-hop vehicular network connectivity for DSRC. This paper gives details about the application, including an explanation of the multi-hop partitioning algorithm used to classify the vehicles into separate network partitions. A performance analysis for the simulation is included, in which it is suggested that calculating a connectivity matrix with the multi-hop partitioning algorithm is computationally expensive for a large number of vehicles.
Knotting probability of equilateral hexagons

For a positive integer n ≥ 3, the collection of n-sided polygons embedded in 3-space defines the space of geometric knots. We will consider the subspace of equilateral knots, consisting of embedded...
WRPN: Wide Reduced-Precision Networks

For computer vision applications, prior works have shown the efficacy of reducing numeric precision of model parameters (network weights) in deep neural networks. Activation maps, however, occupy a large memory footprint during both the training and inference step when using mini-batches of inputs. One way to reduce this large memory footprint is to reduce the precision of activations. However, past works have shown that reducing the precision of activations hurts model accuracy. We study schemes to train networks from scratch using reduced-precision activations without hurting accuracy. We reduce the precision of activation maps (along with model parameters) and increase the number of filter maps in a layer, and find that this scheme matches or surpasses the accuracy of the baseline full-precision network. As a result, one can significantly improve the execution efficiency (e.g. reduce dynamic memory footprint, memory bandwidth and computational energy) and speed up the training and inference process with appropriate hardware support. We call our scheme WRPN - wide reduced-precision networks. We report results and show that WRPN scheme is better than previously reported accuracies on ILSVRC-12 dataset while being computationally less expensive compared to previously reported reduced-precision networks.
The capacity of cache aided private information retrieval

The problem of cache enabled private information retrieval (PIR) is considered in which a user wishes to privately retrieve one out of K messages, each of size L bits from N distributed databases. The user has a local cache of storage SL bits which can be used to store any function of the K messages. The main contribution of this work is the exact characterization of the capacity of cache enabled PIR as a function of the storage parameter S. In particular, for a given cache storage parameter S, the information-theoretically optimal download cost D∗(S)/L (or the inverse of capacity) is shown to be equal to (1 − S/K)(1 + 1/N + … + 1/NK−1). Special cases of this result correspond to the settings when S = 0, for which the optimal download cost was shown by Sun and Jafar to be (1 + 1/N + … + 1/NK−1), and the case when S = K, i.e., cache size is large enough to store all messages locally, for which the optimal download cost is 0. The intermediate points S ∊ (0, K) can be readily achieved through a simple memory-sharing based PIR scheme. The key technical contribution of this work is the converse, i.e., a lower bound on the download cost as a function of storage S which shows that memory sharing is information-theoretically optimal.