cssi/SciSciGPT-SciSciNet huggingface dataset:
Sc6MTe2 (M = Mn, Fe, Co, Ni): members of the flexible Zr6CoAl2-type family of compounds.

The compounds Sc6MTe2 (M = Mn, Fe, Co, Ni) have been prepared by high-temperature solid-state techniques and their structures determined to be hexagonal P62m (No. 189), Z = 1, a = 7.662(1) A, 7.6795(2) A, 7.6977(4) A, 7.7235(4) A and c = 3.9041(9) A, 3.8368(2) A, 3.7855(3) A, 3.7656(3) A for M = Mn, Fe, Co, and Ni, respectively. Crystal structures were refined for M = Fe and Ni, while M = Mn and Co were assigned as isostructural on the basis of powder diffraction data. The Sc6MTe2 compounds belong to a large family with the Zr6CoAl2-type structure, an ordered variant of the Fe2P structure. The structure contains confacial tricapped trigonal prisms of scandium centered alternately by the late transition metal or tellurium atoms. The Sc6MTe2 compounds are the electron-poorest examples of this structure type. Extended Huckel band calculations for M = Fe and Ni show that both compounds exhibit largely 1D metal-metal bonding and are predicted to be metallic.
Reductions of aryl bromides in water at room temperature.

Micellar nanoreactors derived from commercially available ‘Nok’ (SPGS-550-M), in the presence of Fu’s catalyst and a mild hydride source (NaBH4), are useful for facile debromination of functionalized aromatic derivatives. This mild and environmentally responsible process is utilized in water at room temperature, and the reaction mixtures can be smoothly recycled.
Synthesis of 1-(T-Butoxycarbonyl)benzotriazole and 1-(p-Methoxybenzyloxycarbonyl)benzotriazole and Their Use in the Protection of Amino Acids

Abstract Benzotriazol-1-ylcarbonyl chloride, generated from benzotriazole and phosgene, reacts with t-butyl alcohol and p-methoxybenzyl alcohol to give 1-(t-butoxycarbonyl)benzotriazole (4) and 1-(p-methoxy-benzyloxycarbonyl)benzotriazole (5), respectively in good yields. The synthetic utility of reagents 4 and 5 is shown by effective amino protection in phenylalanine and phenylglycine.
Structural and spectroscopic studies of fluoroprotactinates.

Seven protactinium(V) fluoride compounds have been synthesized, and their crystal structures and Raman spectra are reported. (NH4)2PaF7, K2PaF7, Rb2PaF7, and Cs2PaF7 were found to crystallize in the monoclinic space group P21/c for the ammonium compound and C2/c for the K+-, Rb+-, and Cs+-containing compounds, with nine-coordinate Pa forming infinite chains through fluorine bridges. Na3PaF8 crystallizes in the tetragonal space group I4/mmm with eight-coordinate Pa in tetragonal geometry, while tetramethylammonium fluoroprotactinate shows two different structures: (Me4N)2(H3O)PaF8, an eight-coordinate molecular compound crystallizing in the monoclinic space group C2/c, and (Me4N)PaF6, an eight-coordinate Pa compound forming infinite chains and crystallizing in the orthorhombic space group Pnnm. A comparison of solid- and solution-state Raman data indicates that the PaF8– anion could be the predominant Pa(V) complex in concentrated solutions of aqueous HF.
Cyclopropyl-substituted pyrylium salts

The previously unknown 2,4,6-trisubstituted pyrylium salts 1-4, carrying cyclopropyl and methyl or phenyl substituents in the same molecule, and 5-8, substituted with isopropyl groups instead of cyclopropyl, were synthesized as perchlorates. The electronic spectra and the C-13 nmr spectra of the two groups of compounds were compared. A cyclopropyl group has a batochromic effect on the electronic spectrum roughly half that exerted by a phenyl; replacement of an alkyl by a cyclopropyl shifts the highest wavelength absorption band by about 20 nm. Presence of phenyl substituents reduces the batochromic effects of cyclopropyl substituents. The effects of both cyclopropyl and phenyl substituents on the electronic spectra are smaller for pyrylium than for tropylium. The nmr signals for all the ring carbons are shifted upfield upon replacement of isopropyl by cyclopropyl; in particular, the effect of substituents in position 2 upon the chemical shift of C(4) indicates that the electron-releasing effect varies in the series alkyl < phenyl < cyclopropyl, in agreement with the findings for 2,6-disubstituted pyrylium salts. The difference between the chemical shifts for the methine and methylene carbons of the three-membered ring is a function of the electron demand of the cationic heterocycle.
Rule activation and ventromedial prefrontal engagement support accurate stopping in self-paced learning.

Abstract When weighing evidence for a decision, individuals are continually faced with the choice of whether to gather more information or act on what has already been learned. The present experiment employed a self-paced category learning task and fMRI to examine the neural mechanisms underlying stopping of information search and how they contribute to choice accuracy. Participants learned to classify triads of face, object, and scene cues into one of two categories using a rule based on one of the stimulus dimensions. After each trial, participants were given the option to explicitly solve the rule or continue learning. Representational similarity analysis (RSA) was used to examine activation of rule-relevant information on trials leading up to a decision to solve the rule. We found that activation of rule-relevant information increased leading up to participants’ stopping decisions. Stopping was associated with widespread activation that included medial prefrontal cortex and visual association areas. Engagement of ventromedial prefrontal cortex (vmPFC) was associated with accurate stopping, and activation in this region was functionally coupled with signal in dorsolateral prefrontal cortex (dlPFC). Results suggest that activating rule information when deciding whether to stop an information search increases choice accuracy, and that the response profile of vmPFC during such decisions may provide an index of effective learning.
A New Method for the Preparation of 2-Thio Substituted Furans by Methylsulfanylation of γ-Dithiane Carbonyl Compounds

Several related methods for the preparation of differentially substituted 2-thiofurans are described. The general procedure involves the formation of a thionium ion from a gamma-dithianyl substituted carbonyl compound followed by cyclization of this reactive intermediate onto the tethered carbonyl group. Two methods for thionium ion generation were explored. One of these involved an acid-catalyzed reaction of beta-ketenedithioacetals, prepared from the condensation of 2,2-bis(methylsulfanyl)acetaldehyde with a variety of ketones. Cyclization followed by loss of methane thiol gave 2-thiofurans 17, 18 and 23, 24 in 70-90% yield. Attempts to prepare 5-heteroatom substituted 2-thiofurans from the corresponding beta-ketenedithioacetal amides or esters were unsuccessful, leading to 1,2-thio rearranged products. A more successful route involved the reaction of beta-acetoxy-gamma-thianyl carbonyl compounds with dimethyl(methylthio)sulfonium tetrafluoroborate (DMTSF). Treatment of the dithiane with this reagent resulted in the smooth generation of a thionium ion. Cyclization followed by loss of acetic acid afforded thiofurans 17, 18, 23, 47-49, 51, and 61-64 in 40-100% yield. The N-butenyl substituted thioamido furan furnished a rearranged hexahydropyrroloquinolin-2-one in high yield when heated at 110 degrees C.
Random walks and random tug of war in the Heisenberg group

We study mean value properties of $$\mathbf{p }$$ -harmonic functions on the first Heisenberg group $${\mathbb {H}}$$ , in connection to the dynamic programming principles of certain stochastic processes. We implement the approach of Peres and Sheffield (Duke Math J 145(1):91–120, 2008) to provide a game-theoretical interpretation of the sub-elliptic $$\mathbf{p }$$ -Laplacian; and of Manfredi et al. (Proc Am Math Soc 138(3):881–889, 2010) to characterize its viscosity solutions via asymptotic mean value expansions.
Capacity and Delay Scaling for Broadcast Transmission in Highly Mobile Wireless Networks

Futuristic communication network formed by autonomously operated, unmanned aerial vehicles, has piqued researchers interests in highly mobile wireless networks. Exchanging safety critical information, with low latency and high throughput, in such systems is of paramount importance. We study the broadcast capacity and minimum delay scaling laws for such highly mobile wireless networks, in which each node has to disseminate packets to all other nodes in the network. In particular, we consider a cell partitioned network under an IID mobility model, in which each node chooses a new position at random, every time slot. We derive scaling laws for broadcast capacity and minimum delay as a function of the network size. We propose a simple first-come-first-serve flooding scheme, which nearly achieve both capacity and minimum delay scaling. Thus, in contrast to what has been speculated in the literature, we show that there is nearly no tradeoff between capacity and delay. Our results also show that high mobility does not improve broadcast capacity. Our analysis makes use of the theory of Markov Evolving Graphs (MEGs), and develops two new bounds on flooding time in MEGs by relaxing the previously required expander property assumption. Simulation results verify our analysis, and throw up interesting open problems.
TED: Teaching AI to Explain its Decisions

Artificial intelligence systems are being increasingly deployed due to their potential to increase the efficiency, scale, consistency, fairness, and accuracy of decisions. However, as many of these systems are opaque in their operation, there is a growing demand for such systems to provide explanations for their decisions. Conventional approaches to this problem attempt to expose or discover the inner workings of a machine learning model with the hope that the resulting explanations will be meaningful to the consumer. In contrast, this paper suggests a new approach to this problem. It introduces a simple, practical framework, called Teaching Explanations for Decisions (TED), that provides meaningful explanations that match the mental model of the consumer. We illustrate the generality and effectiveness of this approach with two different examples, resulting in highly accurate explanations with no loss of prediction accuracy for these two examples.
Odorant Inhibition in Mosquito Olfaction

How chemical signals are integrated at the peripheral sensory system of insects is still an enigma. Here we show that when coexpressed with Orco in Xenopus oocytes, an odorant receptor from the southern house mosquito, CquiOR32, generated inward (regular) currents when challenged with cyclohexanone and methyl salicylate, whereas eucalyptol and fenchone elicited inhibitory (upward) currents. Responses of CquiOR32-CquiOrco-expressing oocytes to odorants were reduced in a dose-dependent fashion by coapplication of inhibitors. This intrareceptor inhibition was also manifested in vivo in fruit flies expressing the mosquito receptor CquiOR32, as well in neurons on the antennae of the southern house mosquito. Likewise, an orthologue from the yellow fever mosquito, AaegOR71, showed intrareceptor inhibition in the Xenopus oocyte recording system and corresponding inhibition in antennal neurons. Inhibition was also manifested in mosquito behavior. Blood-seeking females were repelled by methyl salicylate, but repellence was significantly reduced when methyl salicylate was coapplied with eucalyptol.
Clinical Epidemiology, Risk Factors, and Outcomes of Encephalitis in Older Adults

BACKGROUND Encephalitis is associated with significant morbidity and mortality, with unknown etiologies in the majority of patients. Large prognostic studies evaluating elderly patients are currently lacking. METHODS We performed a retrospective cohort of encephalitis cases in 19 hospitals from New Orleans, Louisiana, and Houston, Texas, between the years 2000 and 2017. RESULTS A total of 340 adult (aged ≥17 years) patients with confirmed encephalitis were enrolled, and 194 (57%) had unknown etiologies. A cerebrospinal fluid polymerase chain reaction (PCR) for herpes simplex virus (HSV) and varicella zoster virus was done in 237 (69%) and 82 (24%) patients, respectively. Furthermore, an arboviral serology was done in 169 (49%) patients and measurements of anti-N-methyl-D-aspartate receptor antibodies were taken in 49 (14%) patients. A total of 172 out of 323 patients (53%) had adverse clinical outcomes (ACOs) at discharge. Older individuals (>65 years of age) had a lower prevalence of human immunodeficiency virus, had a higher number of comorbidities, were less likely to receive adjuvant steroids, were more likely to have a positive arbovirus serology, were more likely to have a positive HSV PCR, were more likely to have abnormal computerized tomography findings, and were more likely to have to have an ACO (all P values < .05). Prognostic factors independently associated with an ACO were age ≥65, fever, Glasgow Coma Scale (GCS) score <13, and seizures (all P values ≤0.01). CONCLUSIONS Encephalitis in adults remain with unknown etiologies and adverse clinical outcomes in the majority of patients. Independent prognostic factors include age ≥65 years, fever, GCS score <13, and seizures.
Efficient Mendler-Style Lambda-Encodings in Cedille

It is common to model inductive datatypes as least fixed points of functors. We show that within the Cedille type theory we can relax functoriality constraints and generically derive an induction principle for Mendler-style lambda-encoded inductive datatypes, which arise as least fixed points of covariant schemes where the morphism lifting is defined only on identities. Additionally, we implement a destructor for these lambda-encodings that runs in constant-time. As a result, we can define lambda-encoded natural numbers with an induction principle and a constant-time predecessor function so that the normal form of a numeral requires only linear space. The paper also includes several more advanced examples.
Fast Algorithms for Robust PCA via Gradient Descent

We consider the problem of Robust PCA in the fully and partially observed settings. Without corruptions, this is the well-known matrix completion problem. From a statistical standpoint this problem has been recently well-studied, and conditions on when recovery is possible (how many observations do we need, how many corruptions can we tolerate) via polynomial-time algorithms is by now understood. This paper presents and analyzes a non-convex optimization approach that greatly reduces the computational complexity of the above problems, compared to the best available algorithms. In particular, in the fully observed case, with $r$ denoting rank and $d$ dimension, we reduce the complexity from $O(r^2d^2\log(1/\epsilon))$ to $O(rd^2\log(1/\epsilon))$ -- a big savings when the rank is big. For the partially observed case, we show the complexity of our algorithm is no more than $O(r^4d\log(d)\log(1/\epsilon))$. Not only is this the best-known run-time for a provable algorithm under partial observation, but in the setting where $r$ is small compared to $d$, it also allows for near-linear-in-$d$ run-time that can be exploited in the fully-observed case as well, by simply running our algorithm on a subset of the observations.
Orderable Contact Structures on Liouville-fillable Contact Manifolds

We study the existence of positive loops of contactomorphisms on a Liouville-fillable contact manifold $(\Sigma,\xi=\ker(\alpha))$. Previous results show that a large class of Liouville-fillable contact manifolds admit contractible positive loops. In contrast, we show that for any Liouville-fillable $(\Sigma,\alpha)$ with $\dim(\Sigma) \geq 7$, there exists a Liouville-fillable contact structure $\xi'$ on $\Sigma$ which admits no positive loop at all. Further, $\xi'$ can be chosen to agree with $\xi$ on the complement of a Darboux ball.
Accelerated schemes for a class of variational inequalities

We propose a novel stochastic method, namely the stochastic accelerated mirror-prox (SAMP) method, for solving a class of monotone stochastic variational inequalities (SVI). The main idea of the proposed algorithm is to incorporate a multi-step acceleration scheme into the stochastic mirror-prox method. The developed SAMP method computes weak solutions with the optimal iteration complexity for SVIs. In particular, if the operator in SVI consists of the stochastic gradient of a smooth function, the iteration complexity of the SAMP method can be accelerated in terms of their dependence on the Lipschitz constant of the smooth function. For SVIs with bounded feasible sets, the bound of the iteration complexity of the SAMP method depends on the diameter of the feasible set. For unbounded SVIs, we adopt the modified gap function introduced by Monteiro and Svaiter for solving monotone inclusion, and show that the iteration complexity of the SAMP method depends on the distance from the initial point to the set of strong solutions. It is worth noting that our study also significantly improves a few existing complexity results for solving deterministic variational inequality problems. We demonstrate the advantages of the SAMP method over some existing algorithms through our preliminary numerical experiments.
ALMOST OPTIMAL SEQUENTIAL TESTS OF DISCRETE COMPOSITE HYPOTHESES

We consider the problem of sequentially testing a simple null hypothesis, H0, versus a composite alternative hypothesis, H1, that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based likelihood ratio statistics and weighted generalized likelihood rati o statistics. It is shown that both sequential tests have several asymptotic optimality properties as error probabilities go to zero. First, for any weights, they minimize the expected sample size within a con- stant term under every scenario in H1 and at least to first order under H0. Second, for appropriate weights that are specified up to a prior distribu tion, they minimize within an asymptotically negligible term a weighted expected sample size in H1. Third, for a particular prior distribution, they are almost minimax wi th respect to the expected Kullback-Leibler divergence until stopping. Furthermore, based on high-order asymp- totic expansions for the operating characteristics, we pro pose prior distributions that lead to a robust behavior. Finally, based on asymptotic analysis as well as on simula- tion experiments, we argue that both tests have the same performance when they are designed with the same weights.
Deforming group actions on Koszul algebras

We give Braverman-Gaitsgory style conditions for general PBW deformations of skew group algebras formed from finite groups acting on Koszul algebras. When the characteristic divides the order of the group, this includes deformations of the group action as well as of the Koszul relations.
Facial expression recognition in the wild using rich deep features

Facial Expression Recognition is an active area of research in computer vision with a wide range of applications. Several approaches have been developed to solve this problem for different benchmark datasets. However, Facial Expression Recognition in the wild remains an area where much work is still needed to serve real-world applications. To this end, in this paper we present a novel approach towards facial expression recognition. We fuse rich deep features with domain knowledge through encoding discriminant facial patches. We conduct experiments on two of the most popular benchmark datasets; CK and TFE. Moreover, we present a novel dataset that, unlike its precedents, consists of natural — not acted — expression images. Experimental results show that our approach achieves state-of-the-art results over standard benchmarks and our own dataset.
Simplicial Homotopy Theory, Link Homology and Khovanov Homology

The purpose of this note is to point out that simplicial methods and the well-known Dold-Kan construction in simplicial homotopy theory can be fruitfully applied to convert link homology theories into homotopy theories. Dold and Kan prove that there is a functor from the category of chain complexes over a commutative ring with unit to the category of simplicial objects over that ring such that chain homotopic maps go to homotopic maps in the simplicial category. Furthermore, this is an equivalence of categories. In this way, given a link homology theory, we construct a mapping taking link diagrams to a category of simplicial objects such that up to looping or delooping, link diagrams related by Reidemeister moves will give rise to homotopy equivalent simplicial objects, and the homotopy groups of these objects will be equal to the link homology groups of the original link homology theory. The construction is independent of the particular link homology theory. A simplifying point in producing a homotopy simplicial object in relation to a chain complex occurs when the chain complex is itself derived (via face maps) from a simplicial object that satisfies the Kan extension condition. Under these circumstances one can use that simplicial object rather than apply the Dold-Kan functor to the chain complex. We will give examples of this situation in regard to Khovanov homology. We will investigate detailed working out of this correspondence in separate papers. The purpose of this note is to announce the basic relationships for using simplicial methods in this domain. Thus we do more than just quote the Dold-Kan Theorem. We give a review of simplicial theory and we point to specific constructions, particularly in relation to Khovanov homology, that can be used to make simplicial homotopy types directly.
Ordered set partitions, generalized coinvariant algebras, and the Delta Conjecture

Abstract The symmetric group S n acts on the polynomial ring Q [ x n ] = Q [ x 1 , … , x n ] by variable permutation. The invariant ideal I n is the ideal generated by all S n -invariant polynomials with vanishing constant term. The quotient R n = Q [ x n ] I n is called the coinvariant algebra. The coinvariant algebra R n has received a great deal of study in algebraic and geometric combinatorics. We introduce a generalization I n , k ⊆ Q [ x n ] of the ideal I n indexed by two positive integers k ≤ n . The corresponding quotient R n , k : = Q [ x n ] I n , k carries a graded action of S n and specializes to R n when k = n . We generalize many of the nice properties of R n to R n , k . In particular, we describe the Hilbert series of R n , k , give extensions of the Artin and Garsia–Stanton monomial bases of R n to R n , k , determine the reduced Grobner basis for I n , k with respect to the lexicographic monomial order, and describe the graded Frobenius series of R n , k . Just as the combinatorics of R n are controlled by permutations in S n , we will show that the combinatorics of R n , k are controlled by ordered set partitions of { 1 , 2 , … , n } with k blocks. The Delta Conjecture of Haglund, Remmel, and Wilson is a generalization of the Shuffle Conjecture in the theory of diagonal coinvariants. We will show that the graded Frobenius series of R n , k is (up to a minor twist) the t = 0 specialization of the combinatorial side of the Delta Conjecture. It remains an open problem to give a bigraded S n -module V n , k whose Frobenius image is even conjecturally equal to any of the expressions in the Delta Conjecture; our module R n , k solves this problem in the specialization t = 0 .
AbuSniff: Automatic Detection and Defenses Against Abusive Facebook Friends.

Adversaries leverage social network friend relationships to collect sensitive data from users and target them with abuse that includes fake news, cyberbullying, malware, and propaganda. Case in point, 71 out of 80 user study participants had at least 1 Facebook friend with whom they never interact, either in Facebook or in real life, or whom they believe is likely to abuse their posted photos or status updates, or post offensive, false or malicious content. We introduce AbuSniff, a system that identifies Facebook friends perceived as strangers or abusive, and protects the user by unfriending, unfollowing, or restricting the access to information for such friends. We develop a questionnaire to detect perceived strangers and friend abuse.We introduce mutual Facebook activity features and show that they can train supervised learning algorithms to predict questionnaire responses. We have evaluated AbuSniff through several user studies with a total of 263 participants from 25 countries. After answering the questionnaire, participants agreed to unfollow and restrict abusers in 91.6% and 90.9% of the cases respectively, and sandbox or unfriend non-abusive strangers in 92.45% of the cases. Without answering the questionnaire, participants agreed to take the AbuSniff suggested action against friends predicted to be strangers or abusive, in 78.2% of the cases. AbuSniff increased the participant self-reported willingness to reject invitations from strangers and abusers, their awareness of friend abuse implications and their perceived protection from friend abuse.
Dynamics of Geodesic Flows with Random Forcing on Lie Groups with Left-Invariant Metrics

We consider stochastic perturbations of geodesic flow for left-invariant metrics on finite-dimensional Lie groups and study the Hormander condition and some properties of the solutions of the corresponding Fokker–Planck equations.
Guessing models imply the singular cardinal hypothesis

In this article we prove three main theorems: (1) guessing models are internally unbounded, (2) for any regular cardinal $\kappa \ge \omega_2$, $\textsf{ISP}(\kappa)$ implies that $\textsf{SCH}$ holds above $\kappa$, and (3) forcing posets which have the $\omega_1$-approximation property also have the countable covering property. These results solve open problems of Viale and Hachtman-Sinapova.
Eignets for function approximation on manifolds

Abstract Let X be a compact, smooth, connected, Riemannian manifold without boundary, G : X × X → R be a kernel. Analogous to a radial basis function network, an eignet is an expression of the form ∑ j = 1 M a j G ( ○ , y j ) , where a j ∈ R , y j ∈ X , 1 ⩽ j ⩽ M . We describe a deterministic, universal algorithm for constructing an eignet for approximating functions in L p ( μ ; X ) for a general class of measures μ and kernels G. Our algorithm yields linear operators. Using the minimal separation among the centers y j as the cost of approximation, we give modulus of smoothness estimates for the degree of approximation by our eignets, and show by means of a converse theorem that these are the best possible for every individual function. We also give estimates on the coefficients a j in terms of the norm of the eignet. Finally, we demonstrate that if any sequence of eignets satisfies the optimal estimates for the degree of approximation of a smooth function, measured in terms of the minimal separation, then the derivatives of the eignets also approximate the corresponding derivatives of the target function in an optimal manner.
Anomalous parity-time symmetry transition away from an exceptional point

Parity-time (PT) symmetric systems have two distinguished phases, e.g., one with real energy eigenvalues and the other with complex conjugate eigenvalues. To enter one phase from the other, it is believed that the system must pass through an exceptional point, which is a non-Hermitian degenerate point with coalesced eigenvalues and eigenvectors. In this talk I will discuss an anomalous PT transition that takes place away from an exceptional point in a nonlinear system: as the nonlinearity increases, the original linear system evolves along two distinct PT-symmetric trajectories, each of which can have an exceptional point. However, the two trajectories collide and vanish away from these exceptional points, after which the system is left with a PT-broken phase. This phenomenon is first illustrated using a coupled mode theory and then exemplified using paraxial wave propagation in a transverse periodic potential.
Integral Gassman equivalence of algebraic and hyperbolic manifolds

In this paper we construct arbitrarily large families of smooth projective varieties and closed Riemannian manifolds that share many algebraic and analytic invariants. For instance, every non-arithmetic, closed hyperbolic 3-manifold admits arbitrarily large collections of non-isometric finite covers which are strongly isospectral, length isospectral, and have isomorphic integral cohomology where the isomorphisms commute with restriction and co-restriction. We can also construct arbitrarily large collections of pairwise non-isomorphic smooth projective surfaces where these isomorphisms in cohomology are natural with respect to Hodge structure or as Galois modules. In particular, the projective varieties have isomorphic Picard and Albanese varieties, and they also have isomorphic effective Chow motives. Our construction employs an integral refinement of the Gassman–Sunada construction that has recently been utilized by D. Prasad. One application of our work shows the non-injectivity of the map from the Grothendieck group of varieties over $$\overline{\mathbf {Q}}$$ to the Grothendieck group of the category of effective Chow motives. We also answer a question of D. Prasad.
Consistent Parameter Estimation for LASSO and Approximate Message Passing

This paper studies the optimal tuning of the regularization parameter in LASSO or the threshold parameters in approximate message passing (AMP). Considering a model in which the design matrix and noise are zero-mean i.i.d. Gaussian, we propose a data-driven approach for estimating the regularization parameter of LASSO and the threshold parameters in AMP. Our estimates are consistent, that is, they converge to their asymptotically optimal values in probability as $n$, the number of observations, and $p$, the ambient dimension of the sparse vector, grow to infinity, while $n/p$ converges to a fixed number $\delta$. As a byproduct of our analysis, we will shed light on the asymptotic properties of the solution paths of LASSO and AMP.
An Online Algorithm for Power-Proportional Data Centers with Switching Cost

Recent studies have shown that power-proportional data centers can save energy cost by dynamically “right-sizing” the data centers based on real-time workload. More servers are activated when the workload increases while some servers can be put into the sleep mode during periods of low load. In this paper, we revisit the dynamic right-sizing problem for heterogeneous data centers with various operational cost and switching cost. We propose a new online algorithm based on a regularization technique, which achieves a better competitive ratio compared to the state-of-the-art greedy algorithm in [17]. We further introduce a switching cost offset into the model and extend our algorithm to this new setting. Simulations based on real workload and renewable energy traces show that our algorithms outperform the greedy algorithm in both settings.
Cloud-based centralized/decentralized multi-agent optimization with communication delays

We present and analyze a hybrid computational architecture for performing multi-agent optimization. The optimization problems under consideration have convex objective and constraint functions with mild smoothness conditions imposed on them. For such problems, we provide a primal-dual algorithm implemented in the hybrid architecture, which consists of a decentralized network of agents into which an updated dual vector is occasionally injected, and we establish its convergence properties. In this setting, a central cloud computer is responsible for aggregating information, computing dual variable updates, and distributing these updates to the agents. The agents update their (primal) state variables and also communicate among themselves with each agent sharing and receiving state information with some number of its neighbors. Throughout, communications with the cloud are not assumed to be synchronous or instantaneous, and communication delays are explicitly accounted for in the modeling and analysis of the system. Experimental results for a team of robots are presented to support the theoretical developments made.
Scheduling Policies for Minimizing Age of Information in Broadcast Wireless Networks

In this paper, we consider a wireless broadcast network with a base station sending time-sensitive information to a number of clients through unreliable channels. The Age of Information (AoI), namely the amount of time that elapsed since the most recently delivered packet was generated, captures the freshness of the information. We formulate a discrete-time decision problem to find a transmission scheduling policy that minimizes the expected weighted sum AoI of the clients in the network. We first show that in symmetric networks, a greedy policy, which transmits the packet for the client with the highest current age, is optimal. For general networks, we develop three low-complexity scheduling policies: a randomized policy, a Max-Weight policy and a Whittle’s Index policy, and derive performance guarantees as a function of the network configuration. To the best of our knowledge, this is the first work to derive performance guarantees for scheduling policies that attempt to minimize AoI in wireless networks with unreliable channels. Numerical results show that both the Max-Weight and Whittle’s Index policies outperform the other scheduling policies in every configuration simulated, and achieve near optimal performance.
On Distinguishing Interstellar Objects Like ‘Oumuamua From Products of Solar System Scattering

Schneider (2018) explored the possibility that 'Oumuamua is a Solar System object, and concluded that if it is, it must have been scattered by "another, yet unknown planet." I provide an extremely conservative upper limit on post-scattering velocities in the Solar System to show that 'Oumuamua is moving far to quickly to be the result of any hypothetical single scattering event between any bound Solar System objects within 21 au (a distance within which our understanding of objects capable of scattering 'Oumuamua is presumably complete).
Superpixel-Enhanced Pairwise Conditional Random Field for Semantic Segmentation

Superpixel-based Higher-order Conditional Random Fields (CRFs) are effective in enforcing long-range consistency in pixel-wise labeling problems, such as semantic segmentation. However, their major short coming is considerably longer time to learn higher-order potentials and extra hyperparameters and/or weights compared with pairwise models. This paper proposes a superpixel-enhanced pairwise CRF framework that consists of the conventional pairwise as well as our proposed superpixel-enhanced pairwise (SP-Pairwise) potentials. SP-Pairwise potentials incorporate the superpixel-based higher-order cues by conditioning on a segment filtered image and share the same set of parameters as the conventional pairwise potentials. Therefore, the proposed superpixel-enhanced pairwise CRF has a lower time complexity in parameter learning and at the same time it outperforms higher-order CRF in terms of inference accuracy. Moreover, the new scheme takes advantage of the pre-trained pairwise models by reusing their parameters and/or weights, which provides a significant accuracy boost on the basis of CRF-RNN [25] even without training. Experiments on MSRC-21 and PASCAL VOC 2012 dataset confirm the effectiveness of our method.
Distributed convex optimization of time-varying cost functions with swarm tracking behavior for continuous-time dynamics

In this paper, a distributed convex optimization problem with swarm tracking behavior is studied for continuous-time multi-agent systems. The agents' task is to drive their center to track an optimal trajectory which minimizes the sum of local time-varying cost functions through local interaction, while maintaining connectivity and avoiding inter-agent collision. Each local cost function is known only to an individual agent and the team's optimal solution is time-varying. Here two cases are considered, single-integrator dynamics and double-integrator dynamics. For each case, a distributed convex optimization algorithm with swarm tracking behavior is proposed where each agent relies only on its own position and the relative positions (and velocities in the double-integrator case) between itself and its neighbors. It is shown that the center of the agents tracks the optimal trajectory, the the connectivity of the agents will be maintained and inter-agent collision is avoided. Finally, numerical a example is included for illustration.
Graph Reconstruction by Discrete Morse Theory

Recovering hidden graph-like structures from potentially noisy data is a fundamental task in modern data analysis. Recently, a persistence-guided discrete Morse-based framework to extract a geometric graph from low-dimensional data has become popular. However, to date, there is very limited theoretical understanding of this framework in terms of graph reconstruction. This paper makes a first step towards closing this gap. Specifically, first, leveraging existing theoretical understanding of persistence-guided discrete Morse cancellation, we provide a simplified version of the existing discrete Morse-based graph reconstruction algorithm. We then introduce a simple and natural noise model and show that the aforementioned framework can correctly reconstruct a graph under this noise model, in the sense that it has the same loop structure as the hidden ground-truth graph, and is also geometrically close. We also provide some experimental results for our simplified graph-reconstruction algorithm.
Powers of the theta divisor and relations in the tautological ring

We show that the vanishing of the $(g+1)$-st power of the theta divisor on the universal abelian variety $\mathcal{X}_g$ implies, by pulling back along a collection of Abel--Jacobi maps, the vanishing results in the tautological ring of $\mathcal{M}_{g,n}$ of Looijenga, Ionel, Graber--Vakil, and Faber--Pandharipande. We also show that Pixton's double ramification cycle relations, which generalize the theta vanishing relations and were recently proved by the first and third authors, imply Theorem~$\star$ of Graber and Vakil, and we provide an explicit algorithm for expressing any tautological class on $\overline{\mathcal{M}}_{g,n}$ of sufficiently high codimension as a boundary class.
The Internet of Battle Things

On the battlefields of the future, multitudes of intelligent things will be communicating, acting, and collaborating with one another and with human warfighters. This will demand major advances in science and technology.
Depth Prediction without the Sensors: Leveraging Structure for Unsupervised Learning from Monocular Videos

Learning to predict scene depth from RGB inputs is a challenging task both for indoor and outdoor robot navigation. In this work we address unsupervised learning of scene depth and robot ego-motion where supervision is provided by monocular videos, as cameras are the cheapest, least restrictive and most ubiquitous sensor for robotics. Previous work in unsupervised image-to-depth learning has established strong baselines in the domain. We propose a novel approach which produces higher quality results, is able to model moving objects and is shown to transfer across data domains, e.g. from outdoors to indoor scenes. The main idea is to introduce geometric structure in the learning process, by modeling the scene and the individual objects; camera ego-motion and object motions are learned from monocular videos as input. Furthermore an online refinement method is introduced to adapt learning on the fly to unknown domains. The proposed approach outperforms all state-of-the-art approaches, including those that handle motion e.g. through learned flow. Our results are comparable in quality to the ones which used stereo as supervision and significantly improve depth prediction on scenes and datasets which contain a lot of object motion. The approach is of practical relevance, as it allows transfer across environments, by transferring models trained on data collected for robot navigation in urban scenes to indoor navigation settings. The code associated with this paper can be found at https://sites.google.com/view/struct2depth.
Representations of spin quiver Hecke algebras for orthosymplectic Lie superalgebras

We construct all the irreducible representations of spin quiver Hecke algebras for orthosymplectic Lie superalgebras osp(1|2n), and show that their highest weights are given by the dominant words. We use the dominant Lyndon words to construct the cuspidal modules and show that the irreducible representations are the simple heads of standard representations constructed by induction from the cuspidal modules.
On equivariant Chern-Weil forms and determinant lines

A strong from of invariance under a group G is manifested in a family over the classifying space BG. We advocate a differential-geometric avatar of BG when G is a Lie group. Applied to G-equivariant connections on smooth principal or vector bundles, the equivariance-->families principle converts the G-equivariant extensions of curvature and Chern-Weil forms to the standard nonequivariant versions. An application of this technique yields the moment map of the determinant line of a G-equivariant Dirac operator, which in turn sheds light on some anomaly formulas in quantum field theory.
On the circuit-size of inverses

We reprove a result of Boppana and Lagarias: If then there exists a partial function f that is computable by a polynomial-size family of circuits, but no inverse of f is computable by a polynomial-size family of circuits. We strengthen this result by showing, if , that there exist length-preserving total functions that are one-way by circuit size and that are computable in uniform polynomial time. We also prove, if , that there exist polynomially balanced total surjective functions that are one-way by circuit size; here non-uniformity is used.
Armstrong's Axioms and Navigation Strategies

The paper investigates navigability with imperfect information. It shows that the properties of navigability with perfect recall are exactly those captured by Armstrong's axioms from the database theory. If the assumption of perfect recall is omitted, then Armstrong's transitivity axiom is not valid, but it can be replaced by two new weaker principles. The main technical results are soundness and completeness theorems for the logical systems describing properties of navigability with and without perfect recall.
Geometric endoscopy and mirror symmetry

The geometric Langlands correspondence has been interpreted as the mirror symmetry of the Hitchin fibrations for two dual reductive groups. This mirror symmetry, in turn, reduces to T -duality on the generic Hitchin fibers, which are smooth tori. In this paper, we study what happens when the Hitchin fibers on the B-model side develop orbifold singularities. These singularities correspond to local systems with finite groups of automorphisms. In the classical Langlands program, local systems of this type are called endoscopic. They play an important role in the theory of automorphic representations, in particular, in the stabilization of the trace formula. Our goal is to use the mirror symmetry of the Hitchin fibrations to expose the special role played by these local systems in the geometric theory. The study of the categories of A-branes on the dual Hitchin fibers allows us to uncover some interesting phenomena associated with the endoscopy in the geometric Langlands correspondence. We then follow our predictions back to the classical theory of automorphic functions. This enables us to test and confirm them. The geometry we use is similar to that which is exploited in recent work by Ngo, a fact which could be significant for understanding the trace formula.
A Simple Harmonic Universe

We explore simple but novel bouncing solutions of general relativity that avoid singularities. These solutions require curvature k = +1, and are supported by a negative cosmological term and matter with −1 < w < −1/3. In the case of moderate bounces (where the ratio of the maximal scale factor a + to the minimal scale factor a − is $ \mathcal{O}(1) $ ), the solutions are shown to be classically stable and cycle through an infinite set of bounces. For more extreme cases with large a + /a −, the solutions can still oscillate many times before classical instabilities take them out of the regime of validity of our approximations. In this regime, quantum particle production also leads eventually to a departure from the realm of validity of semiclassical general relativity, likely yielding a singular crunch. We briefly discuss possible applications of these models to realistic cosmology.
Liquid Drops on a Rough Surface

We consider a liquid drop sitting on a rough solid surface at equilibrium, a volume constrained minimizer of the total interfacial energy. The large-scale shape of such a drop strongly depends on the micro-structure of the solid surface. Surface roughness enhances hydrophilicity and hydrophobicity properties of the surface, altering the equilibrium contact angle between the drop and the surface. Our goal is to understand the shape of the drop with fixed small scale roughness. To achieve this, we develop a quantitative description of the drop and its contact line in the context of periodic homogenization theory, building on the qualitative theory of Alberti and DeSimone.
Bounds for the first several prime character nonresidues

Let $\varepsilon > 0$. We prove that there are constants $m_0=m_0(\varepsilon)$ and $\kappa=\kappa(\varepsilon) > 0$ for which the following holds: For every integer $m > m_0$ and every nontrivial Dirichlet character modulo $m$, there are more than $m^{\kappa}$ primes $\ell \le m^{\frac{1}{4\sqrt{e}}+\varepsilon}$ with $\chi(\ell)\notin \{0,1\}$. The proof uses the fundamental lemma of the sieve, Norton's refinement of the Burgess bounds, and a result of Tenenbaum on the distribution of smooth numbers satisfying a coprimality condition. For quadratic characters, we demonstrate a somewhat weaker lower bound on the number of primes $\ell \le m^{\frac14+\epsilon}$ with $\chi(\ell)=1$.
Mekler's construction and generalized stability

Mekler’s construction gives an interpretation of any structure in a finite relational language in a group (nilpotent of class 2 and exponent p > 2, but not finitely generated in general). Even though this construction is not a bi-interpretation, it is known to preserve some model-theoretic tameness properties of the original structure including stability and simplicity. We demonstrate that k-dependence of the theory is preserved, for all k ∈ N, and that NTP2 is preserved. We apply this result to obtain first examples of strictly k-dependent groups (with no additional structure).