cssi/SciSciGPT-SciSciNet huggingface dataset:
An efficient procedure for the preparation of 4-substituted 5-aminoimidazoles.

The preparation of O-methylimidates from α-aminonitriles and their subsequent co-cyclization with primary amines to afford 4-substituted 5-aminoimidazoles was studied. It was found that the mildly acidic pyridinium p-toluenesulfonate efficiently catalyzed each stage of the reaction sequence: (a) the formation of the O-methylimidates, (b) their co-cyclization with a variety of primary amines, and (c) certain derivatizations of the resultant heterocycles. The developed reaction conditions tolerate a wide variety of α-aminonitriles and primary amine co-reactants. Thus, it is possible to easily prepare a diverse array of substituted heterocyclic compounds in good yield. The requisite α-aminonitriles were synthesized either from amino acids or by phase-transfer alkylation of a glycine anion equivalent. The unstable free 5-aminoimidazoles were normally protected in situ to provide derivatives (methyl imidates or N,N-dimethylamidines) that were amenable to characterization.
THE ROLE OF OXYGEN IN RETROLENTAL FIBROPLASIA

The effects of oxygen on the immature or incompletely vascularized retina are conveniently divided into an initial vasoconstrictive and obliterative stage and a secondary vasoproliferative response that occurs after removal of the subject from an enriched oxygen environment. Vasoproliferation starts at the zone of perfused and nonperfused retina. The incompletely vascularized retina is uniquely responsive to these oxygen-induced changes. After vascularization is complete and the retinal vessels reach the ora, the susceptibility to hyperoxia disappears. The vessels in the temporal periphery of the retina have a peculiar susceptibility to the primary and secondary effects of hyperoxia on the immature retina. Ophthalmoscopic examination of the temporal periphery therefore should always be done carefully in the premature infant or in older individuals giving a history of prematurity. The indirect ophthalmoscope provides the most satisfactory instrument for examination.
More examples of non-rational adjoint groups

Abstract In this paper, we give a recursive construction to produce examples of quadratic forms q n in the n -th power of the fundamental ideal in the Witt ring whose corresponding adjoint groups PSO ( q n ) are not stably rational. Computations of the R-equivalence classes of adjoint classical groups by Merkurjev are used to show that these groups are not R-trivial. This extends earlier results of Merkurjev and Gille where the forms considered have non-trivial and trivial discriminants respectively.
Tight Bounds for Connectivity and Set Agreement in Byzantine Synchronous Systems

In this paper, we show that the protocol complex of a Byzantine synchronous system can remain (k −1)-connected for up to ⌈t/k⌉ rounds, where t is the maximum number of Byzantine processes, and t ≥ k ≥ 1. Protocol complex connectivity is important since a (k −1)-connected protocol complex does not admit solutions for the k-set agreement problem. In crash-failure systems, the connectivity upper bound is ⌊t/k⌋ rounds, therefore, in Byzantine systems, the ambiguity in the communication can potentially persist for one extra round, delaying the solution to k-set agreement and other related problems. Additionally, we show that our connectivity bound is tight, at least when n+1, the number of processes, is suitably large compared to t. We solve a formulation of k-set agreement appropriate for Byzantine systems in ⌈t/k⌉ + 1 rounds. Essentially, we see that Byzantine failures can potentially require us one extra round to handle ambiguity, and, in specific cases, at most that.
Phase retrieval from local measurements: Improved robustness via eigenvector-based angular synchronization

Abstract We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [30] . Our approach admits deterministic measurement constructions together with a robust, fast recovery algorithm that consists of solving a system of linear equations in a lifted space, followed by finding an eigenvector (e.g., via an inverse power iteration). Theoretical reconstruction error guarantees from [30] are improved as a result for the new and more robust reconstruction approach proposed herein. Numerical experiments demonstrate robustness and computational efficiency that compete with other approaches on large problems. Along the way, we show that this approach also trivially extends to phase retrieval problems based on windowed Fourier measurements.
Mixed multiplicities of filtrations

In this paper we define and explore properties of mixed multiplicities of (not necessarily Noetherian) filtrations of $m_R$-primary ideals in a Noetherian local ring $R$, generalizing the classical theory for $m_R$-primary ideals. We construct a real polynomial whose coefficients give the mixed multiplicities. This polynomial exists if and only if the dimension of the nilradical of the completion of $R$ is less than the dimension of $R$, which holds for instance if $R$ is excellent and reduced. We show that many of the classical theorems for mixed multiplicities of $m_R$-primary ideals hold for filtrations, including the famous Minkowski inequalities of Teissier, and Rees and Sharp.
A Note on the Boundedness of Riesz Transform for Some Subelliptic Operators

Let M be a smooth connected non-compact manifold endowed with a smooth measure μ and a smooth locally subelliptic diffusion operator L satisfying L1 = 0, and which is symmetric with respect to μ. We show that if L satisfies, with a non negative curvature parameter ρ1, the generalized curvature inequality in (2.9) below, then the Riesz transform is bounded in L(M) for every p > 1, that is
Toward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivity

We develop a general duality between neural networks and compositional kernel Hilbert spaces. We introduce the notion of a computation skeleton, an acyclic graph that succinctly describes both a family of neural networks and a kernel space. Random neural networks are generated from a skeleton through node replication followed by sampling from a normal distribution to assign weights. The kernel space consists of functions that arise by compositions, averaging, and non-linear transformations governed by the skeleton's graph topology and activation functions. We prove that random networks induce representations which approximate the kernel space. In particular, it follows that random weight initialization often yields a favorable starting point for optimization despite the worst-case intractability of training neural networks.
Permutation statistics and multiple pattern avoidance

For a set of permutation patterns $\Pi$, let $F^\text{st}_n(\Pi,q)$ be the st-polynomial of permutations avoiding all patterns in $\Pi$. Suppose $312\in\Pi$. For a class of permutation statistics which includes inversion and descent statistics, we give a formula that expresses $F^\text{st}_n(\Pi;q)$ in terms of these st-polynomials where we take some subblocks of the patterns in $\Pi$. Using this formula, we can construct many examples of nontrivial st-Wilf equivalences. In particular, this disproves a conjecture by Dokos, Dwyer, Johnson, Sagan, and Selsor that all $\text{inv}$-Wilf equivalences are trivial.
Practical Data-Dependent Metric Compression with Provable Guarantees

We introduce a new distance-preserving compact representation of multi-dimensional point-sets. Given n points in a d-dimensional space where each coordinate is represented using B bits (i.e., dB bits per point), it produces a representation of size O( d log(d B/epsilon) +log n) bits per point from which one can approximate the distances up to a factor of 1 + epsilon. Our algorithm almost matches the recent bound of Indyk et al, 2017} while being much simpler. We compare our algorithm to Product Quantization (PQ) (Jegou et al, 2011) a state of the art heuristic metric compression method. We evaluate both algorithms on several data sets: SIFT, MNIST, New York City taxi time series and a synthetic one-dimensional data set embedded in a high-dimensional space. Our algorithm produces representations that are comparable to or better than those produced by PQ, while having provable guarantees on its performance.
On mitigating the analytical limitations of finely stratified experiments

Although attractive from a theoretical perspective, finely stratified experiments such as paired designs suffer from certain analytical limitations that are not present in block‐randomized experiments with multiple treated and control individuals in each block. In short, when using a weighted difference in means to estimate the sample average treatment effect, the traditional variance estimator in a paired experiment is conservative unless the pairwise average treatment effects are constant across pairs; however, in more coarsely stratified experiments, the corresponding variance estimator is unbiased if treatment effects are constant within blocks, even if they vary across blocks. Using insights from classical least squares theory, we present an improved variance estimator that is appropriate in finely stratified experiments. The variance estimator remains conservative in expectation but is asymptotically no more conservative than the classical estimator and can be considerably less conservative. The magnitude of the improvement depends on the extent to which effect heterogeneity can be explained by observed covariates. Aided by this estimator, a new test for the null hypothesis of a constant treatment effect is proposed. These findings extend to some, but not all, superpopulation models, depending on whether the covariates are viewed as fixed across samples.
A Tutorial on Thompson Sampling

Thompson sampling is an algorithm for online decision problemswhere actions are taken sequentially in a manner thatmust balance between exploiting what is known to maximizeimmediate performance and investing to accumulatenew information that may improve future performance. Thealgorithm addresses a broad range of problems in a computationallyefficient manner and is therefore enjoying wideuse. This tutorial covers the algorithm and its application,illustrating concepts through a range of examples, includingBernoulli bandit problems, shortest path problems, productrecommendation, assortment, active learning with neuralnetworks, and reinforcement learning in Markov decisionprocesses. Most of these problems involve complex informationstructures, where information revealed by taking anaction informs beliefs about other actions. We will also discusswhen and why Thompson sampling is or is not effectiveand relations to alternative algorithms.
An exact solution of the 3-D Navier-Stokes equation

Abstract We continue our work (A. Muriel and M. Dresden, Physica D 101, 299, 1997) to calculate the time evolution of the one-particle distribution function. An improved operator formalism, heretofore unused, is applied for spatially uniform initial data. We then choose a Gaussian pair potential between particles. With these two conditions, the velocity fields, energy and pressure are calculated exactly. All stipulations of the Clay Mathematics Institute for proposed solutions of the 3-D Navier-Stokes Equation [ http://www.claymath.org/millennium/Navier-Stokes_Equations/navierstokes.pdf ] are satisfied by our time evolution equation. We then substitute our results for the velocity fields into the 3-D Navier-Stokes Equation and calculate the pressure. The results from our time evolution equation and the prescribed pressure from the Navier-Stokes Equation constitute an exact solution to the Navier-Stokes Equation. No turbulence is obtained from the solution.
Theoretical treatment of anharmonicity of vibrational modes of single-walled carbon nanotubes

We report a computational study, using the "moments method" [Y. Gao and M. Daw, Modelling Simul. Mater. Sci. Eng. 23 045002 (2015)], of the anharmonicity of the vibrational modes of single-walled carbon nanotubes. We find that modes with displacements largely within the wall are more anharmonic than modes with dominantly radial character, except for a set of modes that are related to the radial breathing mode which are the most anharmonic of all. We also find that periodicity of the calculation along the tube length does not strongly affect the anharmonicity of the modes, but that the tubes with larger diameter show more anharmonicity. Comparison is made with available experiments and other calculations.
Resonance energy transfer and quantum entanglement mediated by epsilon-near-zero and other plasmonic waveguide systems

The resonance energy transfer and entanglement between two-level quantum emitters are typically limited to sub-wavelength distances due to the inherently short-range nature of the dipole–dipole interactions. Moreover, the entanglement of quantum systems is hard to preserve for a long time period due to decoherence and dephasing mainly caused by radiative and nonradiative losses. In this work, we outperform the aforementioned limitations by presenting efficient long-range inter-emitter entanglement and large enhancement of resonance energy transfer between two optical qubits mediated by epsilon-near-zero (ENZ) and other plasmonic waveguide types, such as V-shaped grooves and cylindrical nanorods. More importantly, we explicitly demonstrate that the ENZ waveguide resonant energy transfer and entanglement performance drastically outperforms the other waveguide systems. Only the excited ENZ mode has an infinite phase velocity combined with a strong and homogeneous electric field distribution, which leads to a giant energy transfer and efficient entanglement independent of the emitters’ separation distances and nanoscale positions in the ENZ nanowaveguide, an advantageous feature that can potentially accommodate multi-qubit entanglement. Moreover, the transient entanglement can be further improved and become almost independent of the detrimental decoherence effect when an optically active (gain) medium is embedded inside the ENZ waveguide. We also present that efficient steady-state entanglement can be achieved by using a coherent external pumping scheme. Finally, we report a practical way to detect the steady-state entanglement by computing the second-order correlation function. The presented findings stress the importance of plasmonic ENZ waveguides in the design of the envisioned on-chip quantum communication and information processing plasmonic nanodevices.
Deep learning for class-generic object detection

We investigate the use of deep neural networks for the novel task of class generic object detection. We show that neural networks originally designed for image recognition can be trained to detect objects within images, regardless of their class, including objects for which no bounding box labels have been provided. In addition, we show that bounding box labels yield a 1% performance increase on the ImageNet recognition challenge.
Constructing quantized enveloping algebras via inverse limits of finite dimensional algebras

Abstract It is known that a generalized q -Schur algebra may be constructed as a quotient of a quantized enveloping algebra U or its modified form U ˙ . On the other hand, we show here that both U and U ˙ may be constructed within an inverse limit of a certain inverse system of generalized q -Schur algebras. Working within the inverse limit U ˆ clarifies the relation between U ˙ and U . This inverse limit is a q -analogue of the linear dual R [ G ] ∗ of the coordinate algebra of a corresponding linear algebraic group G .
Blow-up rate of the mean curvature during the mean curvature flow and a gap theorem for self-shrinkers

In this paper, we prove that the mean curvature blows up at the same rate as the second fundamental form at the first singular time T of any compact, Type I mean curvature flow. For the mean curvature flow of surfaces, we obtain similar result provided that the Gaussian density is less than two. Our proofs are based on continuous rescaling and the classification of self-shrinkers. We show that all notions of singular sets defined in [19] coincide for any Type I mean curvature flow, thus generalizing the result of Stone who established that for any mean convex Type I Mean curvature flow. We also establish a gap theorem for self-shrinkers.
Degeneration of globally hyperbolic maximal anti-de Sitter structures along pinching sequences

Abstract Let S be a closed oriented surface of genus at least 2. Using the parameterisation of the deformation space of globally hyperbolic maximal anti-de Sitter structures on S × R by the cotangent bundle over the Teichmuller space of S, we study the behaviour of these geometric structures along pinching sequences. We show, in particular, that the regular globally hyperbolic anti-de Sitter structures introduced in [15] naturally appear as limiting points.
Towards attack tolerant networks: Concurrent multipath routing and the butterfly network.

It is crucial for large-scale communication networks such as the internet to be resilient against attacks such as censorship and surveillance, which pose a threat to free expression and free association. Self-organized networks such as the internet’s router network typically have heavy-tailed degree distributions, making them highly vulnerable to targeted attacks against central nodes. While cryptographic solutions exist, they fail to address the underlying topological problem, and remain vulnerable to man-in-the-middle attacks and coercion. Coercion-resistant, topological approaches to attack tolerance are needed to address the current vulnerability of communications infrastructure to censorship and surveillance. We present a novel concurrent multipath routing (CMR) algorithm for the wraparound butterfly network topology, as well as a highly attack-tolerant Structured Multipath Fault Tolerance (SMFT) architecture which incorporates the butterfly CMR algorithm. We also identify a previously unexplored relationship between network topology, trust transitivity, and attack-tolerance, and provide a framework for further exploration of this relationship. Our work is the first theoretical demonstration of a point-to-point communication network architecture that can resist coercion and other non-technical attacks, without requiring infinitely transitive trust. To address cases where the network structure cannot be fully controlled, we demonstrate how a snapshot of the internet’s router network can be partially rewired for greater attack-tolerance. More broadly, we hope that this work will serve as a starting point for the evelopment of additional topology-based attack-tolerant communication architectures to guard against the dangers of censorship and surveillance.
Chernoff bounds for analysis of rate-compatible sphere-packing with numerous transmissions

Recent results by Chen et al. and Polyanskiy et al. explore using feedback to approach capacity with short blocklengths. This paper explores Chernoff bounding techniques to extend the rate-compatible sphere-packing (RCSP) analysis proposed by Chen et al. to scenarios involving numerous retransmissions and different step sizes in each incremental retransmission. Williamson et al. employ exact RCSP computations for up to six transmissions. However, exact RCSP computation with more than six retransmissions becomes unwieldy because of joint error probabilities involving numerous chi-squared distributions. This paper explores Chernoff approaches for upper and lower bounds on the error probability to provide support for computations involving more than six transmissions. We present two versions of upper and lower bounds on the error probability for the two-transmission case. One of the versions is extended to the general case of m transmissions where m ≥ 1. Computing the bounds for general m requires minimization of exponential functions with the auxiliary parameters. The numerical results, however, show that weakening the bounds by considering marginal probabilities and the case of two transmissions is already tight. These bounds also provide good estimates of the expected throughput and expected latency, which are useful for optimization purposes.
Visual Tracking with Similarity Matching Ratio

This paper presents a novel approach to visual tracking: Similarity Matching Ratio (SMR). The traditional approach of tracking is minimizing some measures of the difference between the template and a patch from the frame. This approach is vulnerable to outliers and drastic appearance changes and an extensive study is focusing on making the approach more tolerant to them. However, this often results in longer, corrective algorithms which do not solve the original problem. This paper proposes a novel approach to the definition of the tracking problems, SMR, which turns the differences into probability measures. Only pixel differences below a threshold count towards deciding the match, the rest are ignored. This approach makes the SMR tracker robust to outliers and points that dramatically change appearance. The SMR tracker is tested on challenging video sequences and achieves state-of-the-art performance.
Skein algebras of surfaces

We show that the Kauffman bracket skein algebra of any oriented surface F (possibly with marked points in its boundary) has no zero divisors and that its center is generated by knots parallel to the unmarked components of the boundary of F. Furthermore, we show that skein algebras are Noetherian and Ore. Our proofs rely on certain filtrations of skein algebras induced by pants decompositions of surfaces. We prove some basic algebraic properties of the associated graded algebras along the way.
Blockchain-Assisted Crowdsourced Energy Systems

Crowdsourcing relies on people’s contributions to meet product- or system-level objectives. Crowdsourcing-based methods have been implemented in various cyber-physical systems and realtime markets. This paper explores a framework for Crowdsourced Energy Systems (CES), where small-scale energy generation or energy trading is crowdsourced from distributed energy resources, electric vehicles, and shapable loads. The merits/pillars of energy crowdsourcing are discussed. Then, an operational model for CESs in distribution networks with different types of crowdsourcees is proposed. The model yields a market equilibrium depicting traditional and distributed generator and load setpoints. Given these setpoints, crowdsourcing incentives are designed to steer crowdsourcees to the equilibrium. As the number of crowdsourcees and energy trading transactions scales up, a secure energy trading platform is required. To that end, the presented framework is integrated with a lightweight Blockchain implementation and smart contracts. Numerical tests are provided to showcase the overall implementation.
Minimizing area and energy of deep learning hardware design using collective low precision and structured compression

Deep learning algorithms have shown tremendous success in many recognition tasks; however, these algorithms typically include a deep neural network (DNN) structure and a large number of parameters, which makes it challenging to implement them on power/area-constrained embedded platforms. To reduce the network size, several studies investigated compression by introducing element-wise or row-/column-/block-wise sparsity via pruning and regularization. In addition, many recent works have focused on reducing precision of activations and weights with some reducing down to a single bit. However, combining various sparsity structures with binarized or very-low-precision (2–3 bit) neural networks have not been comprehensively explored. In this work, we present design techniques for minimum-area/-energy DNN hardware with minimal degradation in accuracy. During training, both binarization/low-precision and structured sparsity are applied as constraints to find the smallest memory footprint for a given deep learning algorithm. The DNN model for CIFAR-10 dataset with weight memory reduction of 50X exhibits accuracy comparable to that of the floating-point counterpart. Area, performance and energy results of DNN hardware in 40nm CMOS are reported for the MNIST dataset. The optimized DNN that combines 8X structured compression and 3-bit weight precision showed 98.4% accuracy at 20nJ per classification.
A note on probably certifiably correct algorithms

Abstract Many optimization problems of interest are known to be intractable, and while there are often heuristics that are known to work on typical instances, it is usually not easy to determine a posteriori whether the optimal solution was found. In this short note, we discuss algorithms that not only solve the problem on typical instances, but also provide a posteriori certificates of optimality, probably certifiably correct (PCC) algorithms. As an illustrative example, we present a fast PCC algorithm for minimum bisection under the stochastic block model and briefly discuss other examples.
Neuron Segmentation Using Deep Complete Bipartite Networks

In this paper, we consider the problem of automatically segmenting neuronal cells in dual-color confocal microscopy images. This problem is a key task in various quantitative analysis applications in neuroscience, such as tracing cell genesis in Danio rerio (zebrafish) brains. Deep learning, especially using fully convolutional networks (FCN), has profoundly changed segmentation research in biomedical imaging. We face two major challenges in this problem. First, neuronal cells may form dense clusters, making it difficult to correctly identify all individual cells (even to human experts). Consequently, segmentation results of the known FCN-type models are not accurate enough. Second, pixel-wise ground truth is difficult to obtain. Only a limited amount of approximate instance-wise annotation can be collected, which makes the training of FCN models quite cumbersome. We propose a new FCN-type deep learning model, called deep complete bipartite networks (CB-Net), and a new scheme for leveraging approximate instance-wise annotation to train our pixel-wise prediction model. Evaluated using seven real datasets, our proposed new CB-Net model outperforms the state-of-the-art FCN models and produces neuron segmentation results of remarkable quality.
Ensemble Properties of RVQ-Based Limited-Feedback Beamforming Codebooks

The ensemble properties of random vector quantization (RVQ) codebooks for limited-feedback beamforming in multiinput multioutput (MIMO) systems are studied with the metrics of interest being the received \ssr SNR loss and mutual information loss, both relative to a perfect channel state information (CSI) benchmark. The simplest case of unskewed codebooks is first studied in the correlated MIMO setting and these loss metrics are computed as a function of the number of bits of feedback ( B), transmit antenna dimension ( Nt), and spatial correlation. In particular, it is established that: 1) the loss metrics are a product of two components-a quantization component and a channel-dependent component; 2) the quantization component, which is also common to analysis of channels with i.i.d. fading, decays as B increases at the rate 2-B/(Nt-1); 3) the channel-dependent component reflects the condition number of the channel. Further, the precise connection between the received \ssr SNR loss and the squared singular values of the channel is shown to be a Schur-convex majorization relationship. Finally, the ensemble properties of skewed codebooks that are generated by skewing RVQ codebooks with an appropriately designed fixed skewing matrix are studied. Based on an estimate of the loss expression for skewed codebooks, it is established that the structure of a good skewing matrix is critically dependent on the condition numbers of the effective channel (product of the true channel and the skewing matrix) and the skewing matrix.
On the local structure of quantizations in characteristic p

Let $A$ be a central quantization of an affine Poisson variety $X$ over a field of characteristic $p>0.$ We show that the completion of $A$ with respect to a closed point $y\in X$ is isomorphic to the tensor product of the Weyl algebra with a local Poisson algebra. This result can be thought of as a positive characteristic analogue of results of Losev and Kaledin about slice algebras of quantizations in characteristic 0.
Task-centric optimization of configurations for assistive robots

Robots can provide assistance to a human by moving objects to locations around the person’s body. With a well-chosen initial configuration, a robot can better reach locations important to an assistive task despite model error, pose uncertainty, and other sources of variation. However, finding effective configurations can be challenging due to complex geometry, a large number of degrees of freedom, task complexity, and other factors. We present task-centric optimization of robot configurations (TOC), which is an algorithm that finds configurations from which the robot can better reach task-relevant locations and handle task variation. Notably, TOC can return one or two configurations to be used sequentially while assisting with a task. TOC performs computationally demanding optimizations offline to generate a function that rapidly outputs the configurations online based on the robot’s observations. TOC explicitly models the task, environment, and user, and implicitly handles error using representations of robot dexterity. We evaluated TOC with a software simulation of a mobile manipulator (a PR2) providing assistance with 9 activities of daily living to a user in a wheelchair and a robotic bed. TOC had an overall average success rate of 90.6% compared to 50.4%, 43.5%, and 58.9% for three baseline algorithms based on state-of-the-art methods from the literature. We additionally demonstrate how TOC can find configurations for more than one robot and can help with the optimization of environments for assistance.
Asymptotic linearity of regularity and $a^*$-invariant of powers of ideals

Let X = ProjR be a projective scheme over a field k, and let IR be an ideal generated by forms of the same degree d. Let � : e X ! X be the blowing up of X along the subscheme defined by I, and let � : e X ! ¯ X be the projection given by the divisor dE0 −E, where E is the exceptional divisor ofand E0 is the pullback of a general hyperplane in X. We investigate how the asymptotic linearity of the regularity and the a � -invariant of I q (for q � 0) is related to invariants of fibers of �.
Efficient Accelerated Coordinate Descent Methods and Faster Algorithms for Solving Linear Systems

In this paper we show how to accelerate randomized coordinate descent methods and achieve faster convergence rates without paying per-iteration costs in asymptotic running time. In particular, we show how to generalize and efficiently implement a method proposed by Nesterov, giving faster asymptotic running times for various algorithms that use standard coordinate descent as a black box. In addition to providing a proof of convergence for this new general method, we show that it is numerically stable, efficiently implementable, and in certain regimes, asymptotically optimal. To highlight the power of this algorithm, we show how it can used to create faster linear system solvers in several regimes: - We show how this method achieves a faster asymptotic runtime than conjugate gradient for solving a broad class of symmetric positive definite systems of equations. - We improve the convergence guarantees for Kaczmarz methods, a popular technique for image reconstruction and solving over determined systems of equations, by accelerating an algorithm of Strohmer and Vershynin. - We achieve the best known running time for solving Symmetric Diagonally Dominant (SDD) system of equations in the unit-cost RAM model, obtaining a running time of O(m log3/2n (log log n)1/2 log((log n)/eps)) by accelerating a recent solver by Kelner et al. Beyond the independent interest of these solvers, we believe they highlight the versatility of the approach of this paper and we hope that they will open the door for further algorithmic improvements in the future.
Localized solar power prediction based on weather data from local history and global forecasts

With the recent interest in net-zero sustainability for commercial buildings, integration of photovoltaic (PV) assets becomes even more important. This integration remains a challenge due to high solar variability and uncertainty in the prediction of PV output. Most existing methods predict PV output using either local power/weather history or global weather forecasts, thereby ignoring either the impending global phenomena or the relevant local characteristics, respectively. This work proposes to leverage weather data from both local weather history and global forecasts based on time series modeling with exogenous inputs. The proposed model results in eighteen hour ahead forecasts with a mean accuracy of ≈ 80 % and uses data from the National Ocean and Atmospheric Administration’s (NOAA) High-Resolution Rapid Refresh (HRRR) model.
Automatic Pulmonary Lobe Segmentation Using Deep Learning

Pulmonary lobe segmentation is an important task for pulmonary disease related Computer Aided Diagnosis systems (CADs). Classical methods for lobe segmentation rely on successful detection of fissures and other anatomical information such as the location of blood vessels and airways. With the success of deep learning in recent years, Deep Convolutional Neural Network (DCNN) has been widely applied to analyze medical images like Computed Tomography (CT) and Magnetic Resonance Imaging (MRI), which, however, requires a large number of ground truth annotations. In this work, we release our manually labeled 50 CT scans which are randomly chosen from the LUNA16 dataset and explore the use of deep learning on this task. We propose pre-processing CT image by cropping region that is covered by the convex hull of the lungs in order to mitigate the influence of noise from outside the lungs. Moreover, we use a hybrid loss function with dice loss to tackle extreme class imbalance issue and focal loss to force model to focus on voxels that are hard to be discriminated. To validate the robustness and performance of our proposed framework trained with a small number of training examples, we further tested our model on CT scans from an independent dataset. Experimental results show the robustness of the proposed approach, which consistently improves performance across different datasets by a maximum of 5.87% as compared to a baseline model. The annotations are public available https://github.com/deep-voxel/automatic_pulmonary_lobe_segmentation_using_deep_learning/ and are for non-commercial use only.
Astrometry with Hubble Space Telescope Fine Guidance Sensors—A Review*

Over the last 20 years Hubble Space Telescope Fine Guidance Sensor interferometric astrometry has produced precise and accurate parallaxes of astrophysical interesting stars and mass estimates for stellar companions. We review parallax results, and binary star and exoplanet mass determinations, and compare a subset of these parallaxes with preliminary Gaia results. The approach to single-field relative astrometry described herein may continue to have value for targets fainter than the Gaia limit in the coming era of 20-30m telescopes.
Flexible and approximate computation through state-space reduction

In the real world, insufficient information, limited computation resources, and complex problem structures often force an autonomous agent to make a decision in time less than that required to solve the problem at hand completely. Flexible and approximate computation are two approaches to decision making under limited computation resources. Flexible computation helps an agent to flexibly allocate limited computation resources so that the overall system utility is maximized. Approximate computation enables an agent to find the best satisfactory solution within a deadline. In this paper, we present two state-space reduction methods for flexible and approximate computation: quantitative reduction to deal with inaccurate heuristic information, and structural reduction to handle complex problem structures. These two methods can be applied successively to continuously improve solution quality if more computation is available. Our results show that these reduction methods are effective and efficient, finding better solutions with less computation than some existing well-known methods.
The planar algebra of group-type subfactors☆

If G is a countable, discrete group generated by two finite subgroups H and K and P is a II1 factor with an outer G-action, one can construct the group-type subfactor PH⊂P⋊K introduced by Haagerup and the first author to obtain numerous examples of infinite depth subfactors whose standard invariant has exotic growth properties. We compute the planar algebra of this subfactor and prove that any subfactor with an abstract planar algebra of “group type” arises from such a subfactor. The action of Jones' planar operad is determined explicitly.
A BCMP Network Approach to Modeling and Controlling Autonomous Mobility-on-Demand Systems

In this paper we present a queuing network approach to the problem of routing and rebalancing a fleet of self-driving vehicles providing on-demand mobility within a capacitated road network. We refer to such systems as autonomous mobility-on-demand systems, or AMoD. We first cast an AMoD system into a closed, multi-class BCMP queuing network model. Second, we present analysis tools that allow the characterization of performance metrics for a given routing policy, in terms, e.g., of vehicle availabilities, and first and second order moments of vehicle throughput. Third, we propose a scalable method for the synthesis of routing policies, with performance guarantees in the limit of large fleet sizes. Finally, we validate the theoretical results on a case study of New York City. Collectively, this paper provides a unifying framework for the analysis and control of AMoD systems, which subsumes earlier Jackson and network flow models, provides a quite large set of modeling options (e.g., the inclusion of road capacities and general travel time distributions), and allows the analysis of second and higher-order moments for the performance metrics.
Boundary Value Problems for Mixed Type Equations and Applications

Abstract In this paper we outline a general method for finding well-posed boundary value problems for linear equations of mixed elliptic and hyperbolic type, which extends previous techniques of Berezanskii, Didenko, and Friedrichs. This method is then used to study a particular class of fully nonlinear mixed type equations which arise in applications to differential geometry.
Signal Classification in Quotient Spaces via Globally Optimal Variational Calculus

A ubiquitous problem in pattern recognition is that of matching an observed time-evolving pattern (or signal) to a gold standard in order to recognize or characterize the meaning of a dynamic phenomenon. Examples include matching sequences of images in two videos, matching audio signals in speech recognition, or matching framed trajectories in robot action recognition. This paper shows that all of these problems can be aided by reparameterizing the temporal dependence of each signal individually to a universal standard timescale that allows pointwise comparison at each instance of time. Given two sequences, each with N timesteps, the complexity of the algorithm has a cost of O(N), which is an improvement on the most common method for matching two signals, i.e., dynamic time warping. The core of the approach presented here is that the universal standard timescale is found by solving a variational calculus problem related to differential geometry.
A Hidden Signal in the Ulam Sequence

AbstractThe Ulam sequence is defined as a1 = 1, a2 = 2, and an being the smallest integer that can be written as the sum of two distinct earlier elements in a unique way. This gives Ulam remarked that understanding the sequence, which has been described as “quite erratic,” seems difficult and indeed nothing is known. We report the empirical discovery of a surprising global rigidity phenomenon: there seems to exist a real α ∼ 2.5714474995… such that supported on a subset of . Indeed, for the first 107 elements of Ulam’s sequence, The same phenomenon arises for some other initial conditions a1, a2: the distribution functions look very different from each other and have curious shapes. A similar but more subtle phenomenon seems to arise in Lagarias’ variant of MacMahon’s “primes of measurement” sequence.
Almost all circle polyhedra are rigid

We verify the infinitesimal inversive rigidity of almost all triangulated circle polyhedra in the Euclidean plane $${\mathbb {E}}^{2}$$ , as well as the infinitesimal inversive rigidity of tangency circle packings on the 2-sphere $${\mathbb {S}}^{2}$$ . From this the rigidity of almost all triangulated circle polyhedra follows. The proof adapts Gluck’s proof (Geometric Topology, volume 238 of Lecture Notes in Mathematics, pp 225–239, 1975) of the rigidity of almost all Euclidean polyhedra to the setting of circle polyhedra, where inversive distances replace Euclidean distances and Mobius transformations replace rigid Euclidean motions.
Maass forms and the mock theta function f(q)

Let $$f(q):=1+\sum _{n=1}^{\infty } \alpha (n)q^n$$ be the well-known third order mock theta of Ramanujan. In 1964, George Andrews proved an asymptotic formula of the form $$\begin{aligned} \alpha (n)= \sum _{c\le \sqrt{n}} \psi (n)+O_\epsilon \left( n^\epsilon \right) , \end{aligned}$$ where $$\psi (n)$$ is an expression involving generalized Kloosterman sums and the I-Bessel function. Andrews conjectured that the series converges to $$\alpha (n)$$ when extended to infinity, and that it does not converge absolutely. Bringmann and Ono proved the first of these conjectures. Here we obtain a power savings bound for the error in Andrews’ formula, and we also prove the second of these conjectures. Our methods depend on the spectral theory of Maass forms of half-integral weight, and in particular on an average estimate for the Fourier coefficients of such forms which gives a power savings in the spectral parameter. As a further application of this result, we derive a formula which expresses $$\alpha (n)$$ with small error as a sum of exponential terms over imaginary quadratic points (this is similar in spirit to a recent result of Masri). We also obtain a bound for the size of the error term incurred by truncating Rademacher’s analytic formula for the ordinary partition function which improves a result of the first author and Andersen when $$24n-23$$ is squarefree.
Spine-local Type Inference

We present spine-local type inference, a method of partially inferring omitted type annotations for System F based on local type inference. Local type inference relies on bidirectional rules to propagate type information into and out of adjacent nodes of the AST and restricts type-argument inference to a single node. Spine-local inference relaxes this restriction, allowing it to occur only within an application spine, and improves upon it by using contextual type-argument inference. As our goal is to explore the design space of local type inference, we show that, relative to other variants, spine-local type inference better supports desirable features such as first-class curried applications and partial type applications, and it has the ability to infer types for some terms not otherwise possible. Our approach enjoys usual properties of a bidirectional system of having a specification for our inference algorithm and predictable requirements for typing annotations, and in particular maintains some advantages of local type inference such as a relatively simple implementation and a tendency to produce good-quality error messages when type inference fails.
On the Dual Geometry of Laplacian Eigenfunctions

AbstractWe discuss the geometry of Laplacian eigenfunctions −Δϕ=λϕ on compact manifolds (M, g) and combinatorial graphs G=(V,E). The “dual” geometry of Laplacian eigenfunctions is well understood o...
Heegaard Floer invariants in codimension one

Using Heegaard Floer homology, we construct a numerical invariant for any smooth, oriented $4$-manifold $X$ with the homology of $S^1 \times S^3$. Specifically, we show that for any smoothly embedded $3$-manifold $Y$ representing a generator of $H_3(X)$, a suitable version of the Heegaard Floer $d$ invariant of $Y$, defined using twisted coefficients, is a diffeomorphism invariant of $X$. We show how this invariant can be used to obstruct embeddings of certain types of $3$-manifolds, including those obtained as a connected sum of a rational homology $3$-sphere and any number of copies of $S^1 \times S^2$. We also give similar obstructions to embeddings in certain open $4$-manifolds, including exotic $\mathbb{R}^4$s.
Minimizing risk of load shedding and renewable energy curtailment in a microgrid with energy storage

We consider a microgrid with random load realization, stochastic renewable energy production, and an energy storage unit. The grid controller provides the total net load trajectory that the microgrid should present to the main grid and the microgrid must impose load shedding and renewable energy curtailment if necessary to meet that net load trajectory. The microgrid controller seeks to operate the local energy storage unit to minimize the risk of load shedding, and renewable energy curtailment over a finite time horizon. We formulate the problem of optimizing the operation of the storage unit as a finite stage dynamic programming problem. We prove that the multi-stage objective function of the energy storage is strictly convex in the state of charge of the battery at each stage. The uniqueness of the optimal decision is proven under some additional assumptions. The optimal strategy is then obtained. The effectiveness of the energy storage in decreasing load shedding and renewable energy (RE) curtailment is illustrated in simulations.
A Newton-CG algorithm with complexity guarantees for smooth unconstrained optimization

We consider minimization of a smooth nonconvex objective function using an iterative algorithm based on Newton’s method and the linear conjugate gradient algorithm, with explicit detection and use of negative curvature directions for the Hessian of the objective function. The algorithm tracks Newton-conjugate gradient procedures developed in the 1980s closely, but includes enhancements that allow worst-case complexity results to be proved for convergence to points that satisfy approximate first-order and second-order optimality conditions. The complexity results match the best known results in the literature for second-order methods.
Lipschitz extensions into Jet space Carnot groups

The aim of this article is to prove a Lipschitz extension theorem for partially defined Lipschitz maps to jet spaces endowed with a left-invariant sub-Riemannian Carnot-Carath\'eodory distance. The jet spaces give a model for a certain class of Carnot groups, including in particular all Heisenberg groups. The proofs or our theorems are rather elementary, they are inspired by ideas in papers of Gromov, Young, and Lang-Schlichenmaier.
Random Laplacian Matrices and Convex Relaxations

The largest eigenvalue of a matrix is always larger or equal than its largest diagonal entry. We show that for a class of random Laplacian matrices with independent off-diagonal entries, this bound is essentially tight: the largest eigenvalue is, up to lower order terms, often the size of the largest diagonal. entry. Besides being a simple tool to obtain precise estimates on the largest eigenvalue of a class of random Laplacian matrices, our main result settles a number of open problems related to the tightness of certain convex relaxation-based algorithms. It easily implies the optimality of the semidefinite relaxation approaches to problems such as \({{\mathbb {Z}}}_2\) Synchronization and stochastic block model recovery. Interestingly, this result readily implies the connectivity threshold for Erdős–Renyi graphs and suggests that these three phenomena are manifestations of the same underlying principle. The main tool is a recent estimate on the spectral norm of matrices with independent entries by van Handel and the author.