cssi/SciSciGPT-SciSciNet huggingface dataset:
New Quaternary Thiostannates and Thiogermanates A2Hg3M2S8 (A ) Cs, Rb; M ) Sn, Ge) through Molten A2Sx. Reversible Glass Formation in Cs2Hg3M2S8

Cs2Hg3M2S8 (M ) Ge, Sn) were synthesized in 70% and 65% yields by reacting HgS, and Sn or Ge, in molten Cs2Sx at 520 °C. Rb2Hg3Sn2S8 and Rb2Hg3Ge2S8 were synthesized in 42% and 73% yield by reacting the same reagents in molten Rb2Sx at 350 °C. Cs2Hg3M2S8 crystallize in the triclinic space group P1 h .C s 2Hg3Sn2S8: a ) 7.878(2) A, b ) 9.157(3) A, c ) 6.803(2) A, R) 92.96(2)°, ‚ ) 109.45(2)°, A ) 107.81(2)°, V ) 434.1(2) A 3 , and Dcalc ) 5.207 g/cm 3 . The unit cell of isostructural Cs2Hg3Ge2S8 is a ) 7.808(2) A, b ) 9.164(2) A, c ) 6.612(2) A, R) 92.02(2)°, ‚ ) 108.65(2)°g, A ) 108.10(2)°, and V ) 419.9(2) A 3 .R b 2Hg3M2S8 crystallize in the monoclinic space group P21/c ,R b2Hg3Sn2S8: a ) 10.132(2) A, b ) 6.540(2) A, c ) 13.434(2) A, ‚ ) 97.93(1)°, V ) 881.7(6) A 3 , and Dcalc ) 4.770 g/cm 3 . The unit cell of isostructural Rb2Hg3Ge2S8 is a ) 9.938 (3) A, b ) 6.352 (2) A, c ) 13.117 (3) A, ‚ ) 97.33 (2)°, and V ) 821.3 (4) A 3 . The structure of Cs2Hg3M2S8 consists of [Hg3M2S8] 2layers separated by Cs + cations. The layers contain tetrahedral Sn 4+ or Ge 4+ centers and two types of Hg 2+ , two coordinate linear and three-coordinate pseudotrigonal centers. The structure of Rb2Hg3M2S8consists of a 3-dimensional [Hg3M2S8] 2- framework with Rb + cations located within channels of the structure. This structure also contains tetrahedral Sn 4+ or Ge 4+ centers and two types of Hg 2+ , the two-coordinate linear type and a four-coordinate “seesaw” geometry. Optical band gaps, determined from single-crystal UV/vis spectroscopy, range from 2.52 eV in the tin-based compounds to 2.89 eV in the germanium-based analogues. Cs2Hg3M2S8 become glasses upon melting. Infrared and Raman spectroscopic characterization of the glasses are reported.
Diprotection of primary amines as N-substituted-2,5-bis[(triisopropylsilyl)oxy]pyrroles (BIPSOP)

Abstract Primary amines are diprotected as their 2,5-bis[(triisopropylsilyl)oxy]pyrrole derivatives (BIPSOP). This protecting group is stable to strong bases such as organolithiums and alkoxides at 0 °C and to temperatures up to about 150 °C. Removal may be accomplished by a mild two step sequence.
Dorsal anterior cingulate and ventromedial prefrontal cortex have inverse roles in both foraging and economic choice.

Recent research has highlighted a distinction between sequential foraging choices and traditional economic choices between simultaneously presented options. This was partly motivated by observations in Kolling, Behrens, Mars, and Rushworth, Science, 336(6077), 95–98 (2012) (hereafter, KBMR) that these choice types are subserved by different circuits, with dorsal anterior cingulate (dACC) preferentially involved in foraging and ventromedial prefrontal cortex (vmPFC) preferentially involved in economic choice. To support this account, KBMR used fMRI to scan human subjects making either a foraging choice (between exploiting a current offer or swapping for potentially better rewards) or an economic choice (between two reward-probability pairs). This study found that dACC better tracked values pertaining to foraging, whereas vmPFC better tracked values pertaining to economic choice. We recently showed that dACC’s role in these foraging choices is better described by the difficulty of choosing than by foraging value, when correcting for choice biases and testing a sufficiently broad set of foraging values (Shenhav, Straccia, Cohen, & Botvinick Nature Neuroscience, 17(9), 1249–1254, 2014). Here, we extend these findings in 3 ways. First, we replicate our original finding with a larger sample and a task modified to address remaining methodological gaps between our previous experiments and that of KBMR. Second, we show that dACC activity is best accounted for by choice difficulty alone (rather than in combination with foraging value) during both foraging and economic choices. Third, we show that patterns of vmPFC activity, inverted relative to dACC, also suggest a common function across both choice types. Overall, we conclude that both regions are similarly engaged by foraging-like and economic choice.
Synthesis of [n]- and [n.n]cyclophanes by using Suzuki-Miyaura coupling.

Reaction of the bis-9-BBN adduct of several dienes with 1,3-dibromobenzene via Suzuki coupling leads to a series of [n]metacyclophanes ranging in size from 10 to 17 atom members. In each case, two carbon-carbon bonds are formed in one reaction vessel. However, when the bis-9-BBN adduct of 1,5-hexadiene is coupled with a variety of aryl dihalides, larger [n.n]cyclophanes were formed in preference to the [n]cyclophanes. Four carbon-carbon bonds are formed in this instance. Single-crystal X-ray analyses of these [n.n]cyclophanes reveal interestingly shaped molecules with large cavities.
NOVEL AND FACILE SYNTHESES OF ALKENYL, ALKYNYL, AND ARYL 1,2-DIKETONES

Novel and facile routes to alkenyl, alkynyl, and aryl 1,2-diketones utilize treatment of benzotriazole derivatives 1, 7a,b, and 15a−d with butyllithium and subsequent reaction with esters or acid chlorides to yield the substituted intermediates 2a−d, 8a,b, and 16a−g. Reactions of the deprotonated 1 and 7 with α,β-unsaturated aldehydes followed by oxidation also produces similar intermediates 5 and 11a,b. Subsequent hydrolyses of the intermediates of type 2, 5, 8, 11, and 16 afford diverse 1,2-diketones in good yields.
Caterpillars Count! A Citizen Science Project for Monitoring Foliage Arthropod Abundance and Phenology

Caterpillars Count! is a citizen science project that allows participants to collect data on the seasonal timing, or phenology, of foliage arthropods that are important food resources for forest birds. This project has the potential to address questions about the impacts of climate change on birds over biogeographic scales. Here, we provide a description of the project’s two survey protocols, evaluate the impact of survey methodology on results, compare findings made by citizen scientist participants versus trained scientists, and identify the minimum levels of sampling frequency and intensity needed to accurately capture phenological dynamics. We find that beat sheet surveys and visual surveys yield similar relative and absolute density estimates of different arthropod groups, with beat sheet surveys recording a higher frequency of beetles and visual surveys recording a higher frequency of flies. Citizen scientists generated density estimates within 6% of estimates obtained by trained scientists regardless of survey method. However, patterns of phenology were more consistent between citizen scientists and trained scientists when using beat sheet surveys than visual surveys. By subsampling our survey data, we found that conducting 30 foliage surveys on a weekly basis led to 95% of peak caterpillar date estimates to fall within one week of the “true” peak. We demonstrate the utility of Caterpillars Count! for generating a valuable dataset for ecological research, and call for future studies to evaluate how training and resource materials impact data quality and participant learning gains.
Ordered nanowell arrays

Ordered arrays of micrometer- and nanometer-sized wells were fabricated by chemically etching an optical imaging fiber's distal face. Well depth was controlled by the etch reaction time. Well packi...
Predicting property damage from tornadoes with zero-inflated neural networks

Abstract Tornadoes are the most violent of all atmospheric storms. In a typical year, the United States experiences hundreds of tornadoes with associated damages on the order of one billion dollars. Community preparation and resilience would benefit from accurate predictions of these economic losses, particularly as populations in tornado-prone areas increase in density and extent. Here, we use a zero-inflated modeling approach and artificial neural networks to predict tornado-induced property damage using publicly available data. We developed a neural network that predicts whether a tornado will cause property damage (out-of-sample accuracy = 0.821 and area under the receiver operating characteristic curve, AUROC, = 0.872). Conditional on a tornado causing damage, another neural network predicts the amount of damage (out-of-sample mean squared error = 0.0918 and R 2 = 0.432). When used together, these two models function as a zero-inflated log-normal regression with hidden layers. From the best-performing models, we provide static and interactive gridded maps of monthly predicted probabilities of damage and property damages for the year 2019. Two primary weaknesses include (1) model fitting requires log-scale data which leads to large natural-scale residuals and (2) beginning tornado coordinates were utilized rather than tornado paths. Ultimately, this is the first known study to directly model tornado-induced property damages, and all data, code, and tools are publicly available. The predictive capacity of this model along with an interactive interface may provide an opportunity for science-informed tornado disaster planning.
How do insurance firms respond to financial risk sharing regulations? Evidence from the Affordable Care Act

Many insurance markets have reinstated premium stabilization programs to ensure financial protection from market volatility. In this paper, we focus on one such regulation-risk corridors (RCs)-in the context of the Health Insurance Marketplaces established under the Affordable Care Act. We develop a model to show how the program provided incentives for some insurers to lower their premiums. The RCs program was defunded unexpectedly for coverage year 2016, before its legislated end in 2016. Consistent with the model, we find that making a RCs claim before the program ended is associated with higher premium growth after the program's demise. The model and empirical evidence are consistent with the view that the end of the RCs program contributed to premium growth in the Marketplaces.
Regularized EM algorithms: a unified framework and statistical guarantees

Latent models are a fundamental modeling tool in machine learning applications, but they present significant computational and analytical challenges. The popular EM algorithm and its variants, is a much used algorithmic tool; yet our rigorous understanding of its performance is highly incomplete. Recently, work in [1] has demonstrated that for an important class of problems, EM exhibits linear local convergence. In the high-dimensional setting, however, the M-step may not be well defined. We address precisely this setting through a unified treatment using regularization. While regularization for high-dimensional problems is by now well understood, the iterative EM algorithm requires a careful balancing of making progress towards the solution while identifying the right structure (e.g., sparsity or low-rank). In particular, regularizing the M-step using the state-of-the-art high-dimensional prescriptions (e.g., a la [19]) is not guaranteed to provide this balance. Our algorithm and analysis are linked in a way that reveals the balance between optimization and statistical errors. We specialize our general framework to sparse gaussian mixture models, high-dimensional mixed regression, and regression with missing variables, obtaining statistical guarantees for each of these examples.
Conforming Restricted Delaunay Mesh Generation for Piecewise Smooth Complexes

Abstract A Frontal-Delaunay refinement algorithm for mesh generation in piecewise smooth domains is described. Built using a restricted Delaunay framework, this new algorithm combines a number of novel features, including: (i) an unweighted, conforming restricted Delaunay representation for domains specified as a (non-manifold) collection of piecewise smooth surface patches and curve segments, (ii) a protection strategy for domains containing curve segments that subtend sharply acute angles, and (iii) a new class of off-centre refinement rules designed to achieve high-quality point-placement along embedded curve features. Experimental comparisons show that the new Frontal-Delaunay algorithm outperforms a classical (statically weighted) restricted Delaunay- refinement technique for a number of three-dimensional benchmark problems.
On Representation Zeta Functions for Special Linear Groups

We prove that the numbers of irreducible n-dimensional complex continuous representations of the special linear groups over p-adic integers grow slower than the square of n. We deduce that the abscissas of convergence of the representation zeta functions of the special linear groups over the ring of integers are bounded above by 2. In order to show these results we prove also that if G is a connected, simply connected, semi-simple algebraic group defined over the field of rational numbers, then the G-representation variety of the fundamental group of a compact Riemann surface of genus n has rational singularities if and only if the G-character variety has rational singularities.
Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-De Vries equation on a finite domain

In this paper, we study a class of initial boundary value problem (IBVP) of the Korteweg-de Vries equation posed on a finite interval with nonhomogeneous boundary conditions. The IBVP is known to be locally well-posed, but its global $L^2$- a priori estimate is not available and therefore it is not clear whether its solutions exist globally or blow up in finite time. It is shown in this paper that the solutions exist globally as long as their initial value and the associated boundary data are small, and moreover, those solutions decay exponentially if their boundary data decay exponentially.
Learning From Past Bids to Participate Strategically in Day-Ahead Electricity Markets

We consider the process of bidding by electricity suppliers in a day-ahead market context, where each supplier bids a linear non-decreasing function of her generating capacity with the goal of maximizing her individual profit given other competing suppliers’ bids. Based on the submitted bids, the market operator schedules suppliers to meet demand during each hour and determines hourly market clearing prices. Eventually, this game-theoretic process reaches a Nash equilibrium when no supplier is motivated to modify her bid. However, solving the individual profit maximization problem requires information of rivals’ bids, which are typically not available. To address this issue, we develop an inverse optimization approach for estimating rivals’ production cost functions given historical market clearing prices and production levels. We then use these functions to bid strategically and compute Nash equilibrium bids. We present numerical experiments illustrating our methodology, showing good agreement between bids based on the estimated production cost functions with the bids based on the true cost functions. We discuss an extension of our approach that takes into account network congestion resulting in location-dependent prices.
Rotational cavity optomechanics

We theoretically examine the optomechanical interaction between a rotating nanoparticle and an orbital angular momentum–carrying optical cavity mode. Specifically, we consider a dielectric nanosphere rotating uniformly in a ring-shaped optical potential inside a Fabry–Perot resonator. The motion of the particle is probed by a weak angular lattice created by introducing two additional degenerate Laguerre–Gaussian cavity modes carrying equal and opposite orbital angular momenta. We demonstrate that the rotation frequency of the nanoparticle is imprinted on the probe optical mode, via the Doppler shift, and thus may be sensed experimentally using homodyne detection. We show analytically that the effect of the optical probe on the particle rotation vanishes in the regime of linear response, resulting in an accurate frequency measurement. We also numerically characterize the degradation of the measurement accuracy when the system is driven in the nonlinear regime. Our results are relevant to rotational Doppler velocimetry and to studies of rotational Brownian motion in a periodic lattice.
Quantum representations and monodromies of fibered links

Abstract Andersen, Masbaum and Ueno conjectured that certain quantum representations of surface mapping class groups should send pseudo-Anosov mapping classes to elements of infinite order (for large enough level r). In this paper, we relate the AMU conjecture to a question about the growth of the Turaev-Viro invariants T V r of hyperbolic 3-manifolds. We show that if the r-growth of | T V r ( M ) | for a hyperbolic 3-manifold M that fibers over the circle is exponential, then the monodromy of the fibration of M satisfies the AMU conjecture. Building on earlier work [11] we give broad constructions of (oriented) hyperbolic fibered links, of arbitrarily high genus, whose S O ( 3 ) -Turaev-Viro invariants have exponential r-growth. As a result, for any g > n ⩾ 2 , we obtain infinite families of non-conjugate pseudo-Anosov mapping classes, acting on surfaces of genus g and n boundary components, that satisfy the AMU conjecture. We also discuss integrality properties of the traces of quantum representations and we answer a question of Chen and Yang about Turaev-Viro invariants of torus links.
Modeling Cell Size Regulation: From Single-Cell-Level Statistics to Molecular Mechanisms and Population-Level Effects

Most microorganisms regulate their cell size. In this article, we review some of the mathematical formulations of the problem of cell size regulation. We focus on coarse-grained stochastic models and the statistics that they generate. We review the biologically relevant insights obtained from these models. We then describe cell cycle regulation and its molecular implementations, protein number regulation, and population growth, all in relation to size regulation. Finally, we discuss several future directions for developing understanding beyond phenomenological models of cell size regulation.
Linearly Convergent Variable Sample-Size Schemes for Stochastic Nash Games: Best-Response Schemes and Distributed Gradient-Response Schemes

This paper considers an $N$ -player stochastic Nash game in which the $i \mathbf{th}$ player minimizes a composite objective $f_{i}(x)+r_{i}(x_{i})$ , where $f_{i}$ is expectation-valued and $r_{i}$ has an efficient prox-evaluation. In this context, we make the following contributions. (i) Under a strong monotonicity assumption on the concatenated gradient map, we derive (optimal) rate statements and oracle complexity bounds for the proposed variable sample-size proximal stochastic gradient-response (VS-PGR) scheme; (ii) We overlay (VS-PGR) with a consensus phase with a view towards developing distributed protocols for aggregative stochastic Nash games. Notably, when the sample-size and the number of consensus steps at each iteration grow at a suitable rate, a linear rate of convergence can be achieved; (iii) Finally, under a suitable contractive property associated with the proximal best-response (BR) map, we design a variable sample-size proximal BR (VS-PBR) scheme, where the proximal BR is computed by solving a sample-average problem. If the batch-size for computing the sample-average is raised at a suitable rate, we show that the resulting iterates converge at a linear rate and derive the oracle complexity.
Safe sequential path planning of multi-vehicle systems via double-obstacle Hamilton-Jacobi-Isaacs variational inequality

We consider the problem of planning trajectories for a group of N vehicles, each aiming to reach its own target set while avoiding danger zones of other vehicles. The analysis of problems like this is extremely important practically, especially given the growing interest in utilizing unmanned aircraft systems for civil purposes. The direct solution of this problem by solving a single-obstacle Hamilton-Jacobi-Isaacs (HJI) variational inequality (VI) is numerically intractable due to the exponential scaling of computation complexity with problem dimensionality. Furthermore, the single-obstacle HJI VI cannot directly handle situations in which vehicles do not have a common scheduled arrival time. Instead, we perform sequential path planning by considering vehicles in order of priority, modeling higher-priority vehicles as time-varying obstacles for lower-priority vehicles. To do this, we solve a double-obstacle HJI VI which allows us to obtain the reach-avoid set, defined as the set of states from which a vehicle can reach its target while staying within a time-varying state constraint set. From the solution of the double-obstacle HJI VI, we can also extract the latest start time and the optimal control for each vehicle. This is a first application of the double-obstacle HJI VI which can handle systems with time-varying dynamics, target sets, and state constraint sets, and results in computation complexity that scales linearly, as opposed to exponentially, with the number of vehicles in consideration.
Surpassing Gradient Descent Provably: A Cyclic Incremental Method with Linear Convergence Rate

Recently, there has been growing interest in developing optimization methods for solving large-scale machine learning problems. Most of these boil down to the problem of minimizing an average of a finite set of smooth and strongly convex functions where the number of functions $n$ is large. The gradient descent (GD) method is successful in minimizing convex problems at a fast linear rate; however, it is not applicable to the considered large-scale optimization setting because of the high computational complexity. Incremental methods resolve this drawback of gradient methods by replacing the required gradient for the descent direction with an incremental gradient approximation. They operate by evaluating one gradient per iteration and executing the average of the $n$ available gradients as an approximate gradient. Although incremental methods reduce the computational cost of GD, their convergence rates do not justify their advantage relative to GD in terms of the total number of gradient evaluations until ...
The minimax risk of truncated series estimators for symmetric convex polytopes

We study the optimality of the minimax risk of truncated series estimators over symmetric convex polytopes. We show that the optimal truncated series estimator is within O(log m) factor of the optimal if the polytope is defined by m hyperplanes. This represents the first such bounds towards general convex bodies. In proving our result, we first define a geometric quantity, called the approximation radius, for lower bounding the minimax risk. We then derive our bounds by establishing a connection between the approximation radius and the Kolmogorov width, the quantity that provides upper bounds for the truncated series estimator. Besides, our proof contains several ingredients which might be of independent interest: 1. The notion of approximation radius depends on the volume of the body. It is an intuitive notion and is flexible to yield strong minimax lower bounds; 2. The connection between the approximation radius and the Kolmogorov width is a consequence of a novel duality relationship on the Kolmogorov width, developed by utilizing some classical results from convex geometry [1], [18], [6].
On the structure of the spectrum of small sets

Let G be a finite Abelian group and A a subset of G . The spectrum of A is the set of its large Fourier coefficients. Known combinatorial results on the structure of spectrum, such as Chang's theorem, become trivial in the regime |A|=|G| α | A | = | G | α whenever α≤c α ≤ c , where c≥1/2 c ≥ 1 / 2 is some absolute constant. On the other hand, there are statistical results, which apply only to a noticeable fraction of the elements, which give nontrivial bounds even to much smaller sets. One such theorem (due to Bourgain) goes as follows. For a noticeable fraction of pairs γ 1 ,γ 2 γ 1 , γ 2 in the spectrum, γ 1 +γ 2 γ 1 + γ 2 belongs to the spectrum of the same set with a smaller threshold. Here we show that this result can be made combinatorial by restricting to a large subset. That is, we show that for any set A there exists a large subset A ′ A ′ , such that the sumset of the spectrum of A ′ A ′ has bounded size. Our results apply to sets of size |A|=|G| α | A | = | G | α for any constant α>0 α > 0 , and even in some sub-constant regime.
Linear network coding for multiple groupcast sessions: An interference alignment approach

We consider the problem of linear network coding over communication networks, representable by directed acyclic graphs, with multiple groupcast sessions: the network comprises of multiple destination nodes, each desiring messages from multiple sources. We adopt an interference alignment perspective, providing new insights into designing practical network coding schemes as well as the impact of network topology on the complexity of the alignment scheme. In particular, we show that under certain (polynomial-time checkable) constraints on networks with K sources, it is possible to achieve a rate of 1/(L+d+1) per source using linear network coding coupled with interference alignment, where each destination receives messages from L sources (L < K), and d is a parameter, solely dependent on the network topology, that satisfies 0 ≤ d < K − L.
The infinitude of $\mathbb {Q}(\sqrt {-p})$ with class number divisible by 16

The density of primes $p$ such that the class number $h$ of $\mathbb{Q}(\sqrt{-p})$ is divisible by $2^k$ is conjectured to be $2^{-k}$ for all positive integers $k$. The conjecture is true for $1\leq k\leq 3$ but still open for $k\geq 4$. For primes $p$ of the form $p = a^2 + c^4$ with $c$ even, we describe the 8-Hilbert class field of $\mathbb{Q}(\sqrt{-p})$ in terms of $a$ and $c$. We then adapt a theorem of Friedlander and Iwaniec to show that there are infinitely many primes $p$ for which $h$ is divisible by $16$, and also infinitely many primes $p$ for which $h$ is divisible by $8$ but not by $16$.
Ramsey Numbers of Trees Versus Odd Cycles

Burr, Erd ő s, Faudree, Rousseau and Schelp initiated the study of Ramsey numbers of trees versus odd cycles, proving that $R(T_n, C_m) = 2n - 1$ for all odd $m \ge 3$ and $n \ge 756m^{10}$, where $T_n$ is a tree with $n$ vertices and $C_m$ is an odd cycle of length $m$. They proposed to study the minimum positive integer $n_0(m)$ such that this result holds for all $n \ge n_0(m)$, as a function of $m$. In this paper, we show that $n_0(m)$ is at most linear. In particular, we prove that $R(T_n, C_m) = 2n - 1$ for all odd $m \ge 3$ and $n \ge 25m$. Combining this with a result of Faudree, Lawrence, Parsons and Schelp yields $n_0(m)$ is bounded between two linear functions, thus identifying $n_0(m)$ up to a constant factor.
Kernel feature selection via conditional covariance minimization

We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to perform feature selection via a constrained optimization problem involving the trace of the conditional covariance operator. We prove various consistency results for this procedure, and also demonstrate that our method compares favorably with other state-of-the-art algorithms on a variety of synthetic and real data sets.
Upper and lower estimates for Schauder frames and atomic decompositions

We prove that a Schauder frame for any separable Banach space is shrinking if and only if it has an associated space with a shrinking basis, and that a Schauder frame for any separable Banach space is shrinking and boundedly complete if and only if it has a reflexive associated space. To obtain these results, we prove that the upper and lower estimate theorems for finite dimensional decompositions of Banach spaces can be extended and modified to Schauder frames. We show as well that if a separable infinite dimensional Banach space has a Schauder frame, then it also has a Schauder frame which is not shrinking.
Ion-Channeling in Direct Dark Matter Crystalline Detectors

The channeling of the recoiling nucleus in crystalline detectors after a WIMP collision would produce a larger scintillation or ionization signal in direct detection experiments than otherwise expected. I present estimates of the importance of this effect in NaI, Si and Ge crystals, using analytic models developed from the 1960's onwards to describe channeling and blocking effects.
Real-Time Grasp Planning for Multi-Fingered Hands by Finger Splitting

Grasp planning for multi-fingered hands is computationally expensive due to the joint-contact coupling, surface nonlinearities and high dimensionality, thus is generally not affordable for real-time implementations. Traditional planning methods by optimization, sampling or learning work well in planning for parallel grippers but remain challenging for multi-fingered hands. This paper proposes a strategy called finger splitting, to plan precision grasps for multi-fingered hands starting from optimal parallel grasps. The finger splitting is optimized by a dual-stage iterative optimization including a contact point optimization (CPO) and a palm pose optimization (PPO), to gradually split fingers and adjust both the contact points and the palm pose. The dual-stage optimization is able to consider both the object grasp quality and hand manipulability, address the nonlinearities and coupling, and achieve efficient convergence within one second. Simulation results demonstrate the effectiveness of the proposed approach. The simulation video is available at [1].
Optimizing Service Restoration in Distribution Systems With Uncertain Repair Time and Demand

This paper proposes a novel method to co-optimize the distribution system operation and repair crew routing for outage restoration after extreme weather events. A two-stage stochastic mixed integer linear program is developed. The first stage is to dispatch the repair crews to the damaged components. The second stage is distribution system restoration using distributed generators, and reconfiguration. We consider demand uncertainty in terms of a truncated normal forecast error distribution, and model the uncertainty of the repair time using a lognormal distribution. A new decomposition approach, combined with the progressive hedging algorithm, is developed for solving large-scale outage management problems in an effective and timely manner. The proposed method is validated on modified IEEE 34- and 8500-bus distribution test systems.
Accurate Computation of Survival Statistics in Genome-Wide Studies

A key challenge in genomics is to identify genetic variants that distinguish patients with different survival time following diagnosis or treatment. While the log-rank test is widely used for this purpose, nearly all implementations of the log-rank test rely on an asymptotic approximation that is not appropriate in many genomics applications. This is because: the two populations determined by a genetic variant may have very different sizes; and the evaluation of many possible variants demands highly accurate computation of very small p-values. We demonstrate this problem for cancer genomics data where the standard log-rank test leads to many false positive associations between somatic mutations and survival time. We develop and analyze a novel algorithm, Exact Log-rank Test (ExaLT), that accurately computes the p-value of the log-rank statistic under an exact distribution that is appropriate for any size populations. We demonstrate the advantages of ExaLT on data from published cancer genomics studies, finding significant differences from the reported p-values. We analyze somatic mutations in six cancer types from The Cancer Genome Atlas (TCGA), finding mutations with known association to survival as well as several novel associations. In contrast, standard implementations of the log-rank test report dozens-hundreds of likely false positive associations as more significant than these known associations.
Lifting Curves Simply

Let fρ(L) indicate the smallest integer so that every curve on a fixed hyperbolic surface (S, ρ) of length at most L lifts to a simple curve on a cover of degree at most fρ(L). We provide linear lower bounds for fρ(L), improving a recent result of Gupta-Kapovich [GK]. When (S, ρ) is without punctures, using work of Patel [Pat] and Lenzhen-RafiTao [LRT] we conclude that fρ(L)/L grows like the reciprocal of the systole of (S, ρ). When (S, ρ) has a puncture, we obtain lower bounds for fρ that are exponential in L.
Smoothness of definite unitary eigenvarieties at critical points

We compute an upper bound for the dimension of the tangent spaces at classical points of certain eigenvarieties associated with definite unitary groups, especially including the so-called critically refined cases. Our bound is given in terms of "critical types" and when our bound is minimized it matches the dimension of the eigenvariety. In those cases, which we explicitly determine, the eigenvariety is necessarily smooth and our proof also shows that the completed local ring on the eigenvariety is naturally a certain universal Galois deformation ring.
VADER: A flexible, robust, open-source code for simulating viscous thin accretion disks

Abstract The evolution of thin axisymmetric viscous accretion disks is a classic problem in astrophysics. While models based on this simplified geometry provide only approximations to the true processes of instability-driven mass and angular momentum transport, their simplicity makes them invaluable tools for both semi-analytic modeling and simulations of long-term evolution where two- or three-dimensional calculations are too computationally costly. Despite the utility of these models, the only publicly-available frameworks for simulating them are rather specialized and non-general. Here we describe a highly flexible, general numerical method for simulating viscous thin disks with arbitrary rotation curves, viscosities, boundary conditions, grid spacings, equations of state, and rates of gain or loss of mass (e.g., through winds) and energy (e.g., through radiation). Our method is based on a conservative, finite-volume, second-order accurate discretization of the equations, which we solve using an unconditionally-stable implicit scheme. We implement Anderson acceleration to speed convergence of the scheme, and show that this leads to factor of ∼5 speed gains over non-accelerated methods in realistic problems, though the amount of speedup is highly problem-dependent. We have implemented our method in the new code Viscous Accretion Disk Evolution Resource ( VADER ), which is freely available for download from https://bitbucket.org/krumholz/vader/ under the terms of the GNU General Public License.
Canonical complexes associated to a matrix

Let Φ be an f×g matrix with entries from a commutative Noetherian ring R, with g≤f. Recall the family of generalized Eagon–Northcott complexes {CΦi} associated to Φ. (See, for example, Appendix A2 in “Commutative Algebra with a View Toward Algebraic Geometry” by D. Eisenbud.) For each integer i, CΦi is a complex of free R-modules. For example, CΦ0 is the original “Eagon–Northcott” complex with zero-th homology equal to the ring R/Ig(Φ) defined by ideal generated by the maximal order minors of Φ; and CΦ1 is the “Buchsbaum–Rim” complex with zero-th homology equal to the cokernel of the transpose of Φ. If Φ is sufficiently general, then each CΦi, with −1≤i, is acyclic; and, if Φ is generic, then these complexes resolve half of the divisor class group of R/Ig(Φ). The family {CΦi} exhibits duality; and, if −1≤i≤f−g+1, then the complex CΦi exhibits depth-sensitivity with respect to the ideal Ig(Φ) in the sense that the tail of CΦi of length equal to grade(Ig(Φ)) is acyclic. The entries in the differentials of CΦi are linear in the entries of Φ at every position except at one, where the entries of the differential are g×g minors of Φ. This paper expands the family {CΦi} to a family of complexes {CΦi,a} for integers i and a with 1≤a≤g. The entries in the differentials of {CΦi,a} are linear in the entries of Φ at every position except at two consecutive positions. At one of the exceptional positions the entries are a×a minors of Φ, at the other exceptional position the entries are (g−a+1)×(g−a+1) minors of Φ. The complexes {CΦi} are equal to {CΦi,1} and {CΦi,g}. The complexes {CΦi,a} exhibit all of the properties of {CΦi}. In particular, if −1≤i≤f−g and 1≤a≤g, then CΦi,a exhibits depth-sensitivity with respect to the ideal Ig(Φ).
Equivariant noncommutative motives

Given a finite group G, we develop a theory of G-equivariant noncommutative motives. This theory provides a well-adapted framework for the study of G-schemes, Picard groups of schemes, G-algebras, 2-cocycles, G-equivariant algebraic K-theory, etc. Among other results, we relate our theory with its commutative counterpart as well as with Panin’s theory. As a first application, we extend Panin’s computations, concerning twisted projective homogeneous varieties, to a large class of invariants. As a second application, we prove that whenever the category of perfect complexes of a G-scheme X admits a full exceptional collection of G-invariant (≠G-equivariant) objects, the G-equivariant Chow motive of X is of Lefschetz type. Finally, we construct a G-equivariant motivic measure with values in the Grothendieck ring of G-equivariant noncommutative Chow motives.
A noncommutative de Finetti theorem for boolean independence

Abstract We introduce a family of quantum semigroups and its natural coactions on noncommutative polynomials. We define three invariance conditions for the joint distribution of sequences of selfadjoint noncommutative random variables associated with these coactions. For one of the invariance conditions, we show that the joint distribution of an infinite sequence of noncommutative random variables satisfy it is equivalent to the fact that the sequence of the random variables is identically distributed and boolean independent with respect to the conditional expectation onto its tail algebra. This is a boolean analogue of de Finetti theorem on exchangeable sequences. In the end of the paper, we also discuss the other two invariance conditions which lead to some trivial results.
Observational cosmology with semi-relativistic stars

Galaxy mergers lead to the formation of massive black hole binaries which can accelerate background stars close to the speed of light. We estimate the comoving density of ejected stars with a peculiar velocity in excess of $0.1c$ or $0.5c$ to be $\sim 10^{10}$ and $10^5$ Gpc$^{-3}$ respectively, in the present-day Universe. Semi-relativistic giant stars will be detectable with forthcoming telescopes out to a distance of a few Mpc, where their proper motion, radial velocity, and age, can be spectroscopically measured. In difference from traditional cosmological messengers, such as photons, neutrinos, or cosmic-rays, these stars shine and so their trajectories need not be directed at the observer for them to be detected. Tracing the stars to their parent galaxies as a function of speed and age will provide a novel test of the equivalence principle and the standard cosmological parameters. Semi-relativistic stars could also flag black hole binaries as gravitational wave sources for the future eLISA observatory.
Excluding a large theta graph

Abstract A theta graph, denoted θ a , b , c , is a graph of order a + b + c − 1 consisting of a pair of vertices and three internally-disjoint paths between them of lengths a, b, and c. In this paper we study graphs that do not contain a large θ a , b , c minor. More specifically, we describe the structure of θ 1 , 2 , t -, θ 2 , 2 , t -, θ 1 , t , t -, θ 2 , t , t -, and θ t , t , t -free graphs where t is large. The main result is a characterization of θ t , t , t -free graphs for large t. The 3-connected θ t , t , t -free graphs are formed by 3-summing graphs without a long path to certain planar graphs. The 2-connected θ t , t , t -free graphs are then built up in a similar fashion by 2- and 3-sums. This result implies a well-known theorem of Robertson and Chakravarti on graphs that do not have a bond containing three specified edges.
Minimal input selection for robust control

This paper studies the problem of selecting a minimum-size set of input nodes to guarantee stability of a networked system in the presence of uncertainties and time delays. Current approaches to input selection in networked dynamical systems focus on nominal systems with known parameter values in the absence of delays. We derive sufficient conditions for existence of a stabilizing controller for an uncertain system that are based on a subset of system modes lying within the controllability subspace induced by the set of inputs. We then formulate the minimum input selection problem and prove that it is equivalent to a submodular optimization problem, leading to polynomial-time algorithms with provable optimality bounds. We show that our approach is applicable to different types of uncertainties, including additive and multiplicative uncertainties in the system matrices as well as uncertain time delays. We demonstrate our approach in a numerical case study on the IEEE 39-bus test power system.
The Andoni-Krauthgamer-Razenshteyn characterization of sketchable norms fails for sketchable metrics

Andoni, Krauthgamer and Razenshteyn (AKR) proved (STOC'15) that a finite-dimensional normed space (X, ||·||x) admits a O(1) sketching algorithm (namely, with O(1) sketch size and O(1) approximation) if and only if for every e ∈ (0, 1) there exist α ⩾ 1 and an embedding f : X → l1−e such that ||x − y||x ⩽ ||f(x) − f(y)||1-e ⩽ α||x − y||x for all x, y ∈ X. The "if part" of this theorem follows from a sketching algorithm of Indyk (FOCS 2000). The contribution of AKR is therefore to demonstrate that the mere availability of a sketching algorithm implies the existence of the aforementioned geometric realization. Indyk's algorithm shows that the "if part" of the AKR characterization holds true for any metric space whatsoever, i.e., the existence of an embedding as above implies sketchability even when X is not a normed space. Due to this, a natural question that AKR posed was whether the assumption that the underlying space is a normed space is needed for their characterization of sketchability. We resolve this question by proving that for arbitrarily large n ∈ N there is an n-point metric space (M(n), dM(n)) which is O(1)-sketchable yet for every e ϵ (0, [MATH HERE]), if α(n) ⩾ 1 and fn : M(n) → l1−e are such that dM(n)(x,y)⩾||fn(x)- fn(y)||1-e ⩾ α(n)dM(n) (x,y) for all x, y e M(n), then necessarily limn→∞α(n) = ∞.
On the complexity of smooth spline surfaces from quad meshes

This paper derives strong relations that boundary curves of a smooth complex of patches have to obey when the patches are computed by local averaging. These relations restrict the choice of reparameterizations for geometric continuity. In particular, when one bicubic tensor-product B-spline patch is associated with each facet of a quadrilateral mesh with n-valent vertices and we do not want segments of the boundary curves forced to be linear, then the relations dictate the minimal number and multiplicity of knots: For general data, the tensor-product spline patches must have at least two internal double knots per edge to be able to model a G^1-connected complex of C^1 splines. This lower bound on the complexity of any construction is proven to be sharp by suitably interpreting an existing surface construction. That is, we have a tight bound on the complexity of smoothing quad meshes with bicubic tensor-product B-spline patches.
The design of long-life, high-efficiency PEM fuel cell power supplies for low power sensor networks

Abstract Field sensor networks have important applications in environmental monitoring, wildlife preservation, in disaster monitoring and in border security. The reduced cost of electronics, sensors and actuators make it possible to deploy hundreds if not thousands of these sensor modules. However, power technology has not kept pace. Current power supply technologies such as batteries limit many applications due to their low specific energy. Photovoltaics typically requires large bulky panels and is dependent on varying solar insolation and therefore requires backup power sources. Polymer Electrolyte Membrane (PEM) fuel cells are a promising alternative, because they are clean, quiet and operate at high efficiencies. However, challenges remain in achieving long lives due to factors such as degradation and hydrogen storage. In this work, we devise a framework for designing fuel cells power supplies for field sensor networks. This design framework utilize lithium hydride hydrogen storage technology that offers high energy density of up to 5000 Wh/kg. Using this design framework, we identify operating conditions to maximize the life of the power supply, meet the required power output and minimize fuel consumption. We devise a series of controllers to achieve this capability and demonstrate it using a bench-top experiment that operated for 5000 h. The laboratory experiments point towards a pathway to demonstrate these fuel cell power supplies in the field. Our studies show that the proposed PEM fuel cell hybrid system fueled using lithium hydride offers at least a 3 fold reduction in mass compared to state-of-the-art batteries and 3-5 fold reduction in mass compared to current fuel cell technologies.
Optimal Coded Multicast in Cache Networks with Arbitrary Content Placement

A new class of caching schemes, called coded caching, can significantly reduce the communication bandwidth requirement for satisfying users' demands by utilizing the multicasting gain among multiple users. Most existing works assume that the users follow the prescriptions for content placement made by the system. However, users may prefer to decide what files to cache or discard some part of their caches due to lack of space. In order to address this issue, we study a caching system where the content placement phase has been already carried out by the users arbitrarily. More specifically, we consider a network consisting of a file server connected through a shared link to $K$ users, each equipped with a cache. Given arbitrary content placement by the users, the goal is to find a coded multicast strategy for the server that minimizes the load of the shared link. We first formulate the optimal coded multicast design problem as an Integer Linear Program (ILP). Using a connection with the weighted set cover problem, we propose an approximation algorithm for solving this problem. We show that our proposed algorithm provides $(1 + \log K)$-approximation for the optimal coded multicast design problem, while the approximation ratio for the existing coded delivery schemes is linear in $K$. Numerical simulations show that our proposed algorithm provides a considerable bandwidth reduction over the existing coded delivery schemes for uniformly-random generated content placement.
iCAN: Instance-Centric Attention Network for Human-Object Interaction Detection.

Recent years have witnessed rapid progress in detecting and recognizing individual object instances. To understand the situation in a scene, however, computers need to recognize how humans interact with surrounding objects. In this paper, we tackle the challenging task of detecting human-object interactions (HOI). Our core idea is that the appearance of a person or an object instance contains informative cues on which relevant parts of an image to attend to for facilitating interaction prediction. To exploit these cues, we propose an instance-centric attention module that learns to dynamically highlight regions in an image conditioned on the appearance of each instance. Such an attention-based network allows us to selectively aggregate features relevant for recognizing HOIs. We validate the efficacy of the proposed network on the Verb in COCO and HICO-DET datasets and show that our approach compares favorably with the state-of-the-arts.