cssi/SciSciGPT-SciSciNet huggingface dataset:
Continuous Interdomain Orientation Distributions Reveal Components of Binding Thermodynamics

The flexibility of biological macromolecules is an important structural determinant of function. Unfortunately, the correlations between different motional modes are poorly captured by discrete ensemble representations. Here, we present new ways to both represent and visualize correlated interdomain motions. Interdomain motions are determined directly from residual dipolar couplings, represented as a continuous conformational distribution, and visualized using the disk-on-sphere representation. Using the disk-on-sphere representation, features of interdomain motions, including correlations, are intuitively visualized. The representation works especially well for multidomain systems with broad conformational distributions.This analysis also can be extended to multiple probability density modes, using a Bingham mixture model. We use this new paradigm to study the interdomain motions of staphylococcal protein A, which is a key virulence factor contributing to the pathogenicity of Staphylococcus aureus. We capture the smooth transitions between important states and demonstrate the utility of continuous distribution functions for computing the reorientational components of binding thermodynamics. Such insights allow for the dissection of the dynamic structural components of functionally important intermolecular interactions.
Synthesis and Antiviral Activity of Oxaselenolane Nucleosides

As dioxolane and oxathiolane nucleosides have exhibited promising antiviral and anticancer activities, it was of interest to synthesize isoelectronically substituted oxaselenolane nucleosides, in which the 3‘-CH2 is replaced by a selenium atom. To study structure−activity relationships, various pyrimidine and purine oxaselenolane nucleosides were synthesized from the key intermediate, (±)-2-benzoyloxymethyl-1,2-oxaselenolane 5-acetate (6). Among the synthesized racemic nucleosides, cytosine and 5-fluorocytosine analogues exhibited potent anti-HIV and anti-HBV activities. It was of interest to obtain the enantiomerically pure isomers to determine if they have differential antiviral activities. However, due to the difficult and time-consuming nature of enantiomeric synthesis, a chiral HPLC separation was performed to obtain optical isomers from the corresponding racemic mixtures. Each pair of enantiomers of Se-ddC and Se-FddC was separated by an amylose chiral column using a mobile phase of 100% 2-propanol....
Revisiting the phylogeny of Zoanthidea (Cnidaria: Anthozoa): Staggered alignment of hypervariable sequences improves species tree inference

The recent rapid proliferation of novel taxon identification in the Zoanthidea has been accompanied by a parallel propagation of gene trees as a tool of species discovery, but not a corresponding increase in our understanding of phylogeny. This disparity is caused by the trade-off between the capabilities of automated DNA sequence alignment and data content of genes applied to phylogenetic inference in this group. Conserved genes or segments are easily aligned across the order, but produce poorly resolved trees; hypervariable genes or segments contain the evolutionary signal necessary for resolution and robust support, but sequence alignment is daunting. Staggered alignments are a form of phylogeny-informed sequence alignment composed of a mosaic of local and universal regions that allow phylogenetic inference to be applied to all nucleotides from both hypervariable and conserved gene segments. Comparisons between species tree phylogenies inferred from all data (staggered alignment) and hypervariable-excluded data (standard alignment) demonstrate improved confidence and greater topological agreement with other sources of data for the complete-data tree. This novel phylogeny is the most comprehensive to date (in terms of taxa and data) and can serve as an expandable tool for evolutionary hypothesis testing in the Zoanthidea. Spanish language abstract available in Text S1. Translation by L. O. Swain, DePaul University, Chicago, Illinois, 60604, USA.
Cloud bursting galaxy: federated identity and access management.

MOTIVATION Large biomedical datasets, such as those from genomics and imaging, are increasingly being stored on commercial and institutional cloud computing platforms. This is because cloud-scale computing resources, from robust backup to high-speed data transfer to scalable compute and storage, are needed to make these large datasets usable. However, one challenge for large-scale biomedical data on the cloud is providing secure access, especially when datasets are distributed across platforms. While there are open Web protocols for secure authentication and authorization, these protocols are not in wide use in bioinformatics and are difficult to use for even technologically sophisticated users. RESULTS We have developed a generic and extensible approach for securely accessing biomedical datasets distributed across cloud computing platforms. Our approach combines OpenID Connect and OAuth2, best-practice Web protocols for authentication and authorization, together with Galaxy (https://galaxyproject.org), a web-based computational workbench used by thousands of scientists across the world. With our enhanced version of Galaxy, users can access and analyze data distributed across multiple cloud computing providers without any special knowledge of access/authorization protocols. Our approach does not require users to share permanent credentials (e.g. username, password, API key), instead relying on automatically generated temporary tokens that refresh as needed. Our approach is generalizable to most identity providers and cloud computing platforms. To the best of our knowledge, Galaxy is the only computational workbench where users can access biomedical datasets across multiple cloud computing platforms using best-practice Web security approaches and thereby minimize risks of unauthorized data access and credential use. AVAILABILITY AND IMPLEMENTATION Freely available for academic and commercial use under the open-source Academic Free License (https://opensource.org/licenses/AFL-3.0) from the following Github repositories: https://github.com/galaxyproject/galaxy and https://github.com/galaxyproject/cloudauthz.
The Bonding of Metal-Alkynyl Complexes

Publisher Summary The chemistry of metal–alkynyl compounds is developing at a rapid pace. The bonds of alkynyl ligands, like those of organic alkynes have been shown to participate in a rich set of chemical transformations. Electronic-absorption band maxima and extinction coefficients have been reported for a large number of metal–alkynyl complexes. Casual comparisons of electronic-absorption band energies or intensities among a series of compounds in the absence of such experiments are not without the risk of misinterpretation because a variety of important effects not associated with the presence or absence of M-CCR π-bonding may be operative such as mixings between electronic states of identical symmetry but different orbital character. The best and simplest means of placing the M–C bond distances of metal–alkyl complexes in a context that allows insight into whether or not they manifest M-CCR π-interactions is to compare them to M–C bond distances of complexes where such effects are expected to be insignificant, as for metal–alkynyl compounds.
Rapid, quantitative, solvent-free synthesis of medium-ring diaza heterocycles from diketene–acetone adduct and diamines

Abstract The synthesis of medium-ring heterocycles remains a challenge largely due to unfavorable energetic factors. We are reporting syntheses of 7–9-member diaza heterocycles that go to completion in 5 min, require no solvents, and are quantitative with the only byproducts being acetone and water. The reaction products could be isolated in pure form by simply placing the mixture under vacuum. The reaction sequence possesses many of the hallmarks of a click reaction.
A facile and efficient direct aldol addition of simple thioesters.

Simple thioesters undergo direct aldol addition to aldehydes in the presence of MgBr2·OEt2 and i-Pr2NEt using untreated, reagent-grade CH2Cl2 under atmospheric conditions. The reactions proceed extremely rapidly and in excellent yield.
C-6 allylated pyranosides for the synthesis of complex oxygenated tetrahydrofurans

Abstract The iodoetherification of C6 allylated D-pyranosides containing an allylic benzyloxy substituent, and their acyclic 5-hexen-, 1,2,4-triol analogs were performed. Pyranosides of R configuration at the allylic ether gave exclusively a syn,syn -2,5-dialkyl-3-oxy-tetrahydrofuran which is primed for elaboration into several classes of naturally occurring THF's. By comparison, the stereoselectivity for the non-pyranoside derivative was much lower. In the S series, the bias was opposite for the pyranoside vs. the non-pyranoside substrates, but the selectivity in both cases was low.
Synthetic Design for Combinatorial Chemistry. Solution and Polymer-Supported Synthesis of Polycyclic Lactams by Intramolecular Cyclization of Azomethine Ylides

The rapidly expanding field of combinatorial chemistry has stimulated the development of new methods and synthetic strategies for assembly of compound libraries. We propose four criteria that are d...
Disrupted cholinergic modulation can underlie abnormal gamma rhythms in schizophrenia and auditory hallucination

The pathophysiology of auditory hallucination, a common symptom of schizophrenia, has yet been understood, but during auditory hallucination, primary auditory cortex (A1) shows paradoxical responses. When auditory stimuli are absent, A1 becomes hyperactive, while A1 responses to auditory stimuli are reduced. Such activation pattern of A1 responses during auditory hallucination is consistent with aberrant gamma rhythms in schizophrenia observed during auditory tasks, raising the possibility that the pathology underlying abnormal gamma rhythms can account for auditory hallucination. Moreover, A1 receives top-down signals in the gamma frequency band from an adjacent association area (Par2), and cholinergic modulation regulates interactions between A1 and Par2. In this study, we utilized a computational model of A1 to ask if disrupted cholinergic modulation could underlie abnormal gamma rhythms in schizophrenia. Furthermore, based on our simulation results, we propose potential pathology by which A1 can directly contribute to auditory hallucination.
Preparation of 6-Fluoro-8-quinolinol and Related 6-Fluoroquinolines

6-Fluoro-8-quinolinol was prepared from 2-amino-5-fluorophenol by a Skraup synthesis. No synergism was observed between 5-fluoro- and 6-fluoro-8-quinolinols or between 6-fluoro- and 7-fluoro-8-quinolinols against any of the six fungi in our test system (Aspergillus niger, A. oryzae, Myrothecium verrucaria, Trichoderma viride, Mucor cirinelloides, and Trichophyton mentagrophytes) in Sabouraud dextrose broth. Unlike the fluoro-8-quinolinols, the 8-quinolinols comparably substituted with chlorine or bromine did form synergistic mixtures. This is attributed to steric factors.
The Effect of Common Inversion Polymorphisms In(2L)t and In(3R)Mo on Patterns of Transcriptional Variation in Drosophila melanogaster

Chromosomal inversions are a ubiquitous feature of genetic variation. Theoretical models describe several mechanisms by which inversions can drive adaptation and be maintained as polymorphisms. While inversions have been shown previously to be under selection, or contain genetic variation under selection, the specific phenotypic consequences of inversions leading to their maintenance remain unclear. Here we use genomic sequence and expression data from the Drosophila Genetic Reference Panel (DGRP) to explore the effects of two cosmopolitan inversions, In(2L)t and In(3R)Mo, on patterns of transcriptional variation. We demonstrate that each inversion has a significant effect on transcript abundance for hundreds of genes across the genome. Inversion-affected loci (IAL) appear both within inversions as well as on unlinked chromosomes. Importantly, IAL do not appear to be influenced by the previously reported genome-wide expression correlation structure. We found that five genes involved with sterol uptake, four of which are Niemann-Pick Type 2 orthologs, are upregulated in flies with In(3R)Mo but do not have SNPs in linkage disequilibrium (LD) with the inversion. We speculate that this upregulation is driven by genetic variation in mod(mdg4) that is in LD with In(3R)Mo We find that there is little evidence for a regional or position effect of inversions on gene expression at the chromosomal level, but do find evidence for the distal breakpoint of In(3R)Mo interrupting one gene and possibly disassociating the two flanking genes from regulatory elements.
Synthesis and biological evaluation of (-)-16-normethyldictyostatin: a potent analogue of (-)-dictyostatin.

(−)-16-Normethyldictyostatin has been made by total synthesis and is a potent antitumor agent in cells expressing wild-type tubulin and in one mutant cell line that is resistant to paclitaxel, but it is much less active than dictyostatin in another paclitaxel-resistant cell line where Val is substituted for Phe270. This provides strong evidence that the C16 methyl group of the dictyostatins is oriented toward Phe270 in the paclitaxel-binding site on β-tubulin.
Matching the high momentum modes in a truncated determinant algorithm

Abstract Within a truncated determinant algorithm, two alternatives are discussed for including systematically the remaining ultraviolet modes. Evidence is presented that these modes are accurately described by an effective action involving only small Wilson loops.
Mild and efficient Cs2CO3-promoted synthesis of phosphonates

Abstract A mild and convenient synthesis for phosphonates using cesium carbonate (Cs2CO3), tetrabutylammonium iodide (TBAI) and DMF was developed at room temperature. Numerous dialkyl phosphites were screened using a diverse array of alkyl halides and these reaction conditions were found to be highly efficient producing various phosphonates exclusively in moderate to high yields.
How Much Is Data Privacy Worth? A Preliminary Investigation

Do consumers value data privacy? How much? In a survey of 2,416 Americans, we find that the median consumer is willing to pay just $5 per month to maintain data privacy (along specified dimensions), but would demand $80 to allow access to personal data. This is a “superendowment effect,” much higher than the 1:2 ratio often found between willingness to pay and willingness to accept. In addition, people demand significantly more money to allow access to personal data when primed that such data includes health-related data than when primed that such data includes demographic data. We analyze reasons for these disparities and offer some notations on their implications for theory and practice. A general theme is that because of a lack of information and behavioural biases, both willingness to pay and willingness to accept measures are highly unreliable guides to the welfare effects of retaining or giving up data privacy. Gertrude Stein’s comment about Oakland, California may hold for consumer valuations of data privacy: “There is no there there.” For guidance, policymakers should give little or no attention to either of those conventional measures of economic value, at least when steps are not taken to overcome deficits in information and behavioural biases.
GelSlim: A High-Resolution, Compact, Robust, and Calibrated Tactile-sensing Finger

This work describes the development of a high-resolution tactile-sensing finger for robot grasping. This finger, inspired by previous GelSight sensing techniques (Johnson and Adelson 2009), features an integration that is slimmer, more robust, and with more homogeneous output than previous vision-based tactile sensors. To achieve a compact integration, we redesign the optical path from illumination source to camera by combining light guides and an arrangement of mirror reflections. We parameterize the optical path with geometric design variables and describe the tradeoffs between the finger thickness, camera depth of field, and size of the tactile sensing area. The sensor sustains the wear from continuous use - and abuse - in grasping tasks by combining tougher materials for the compliant gel, a textured fabric skin, a structurally rigid body, and a calibration process that maintains homogeneous illumination and contrast of the tactile images during use. Finally, we evaluate the sensor's durability along four metrics that track the signal quality during more than 3000 grasping experiments.
Bi-Gyrogroup: The Group-Like Structure Induced by Bi-Decomposition of Groups

‎The decomposition $Gamma=BH$ of a group $Gamma$ into a subset B ‎and a subgroup $H$ of $Gamma$ induces‎, ‎under general conditions‎, ‎a ‎group-like structure for B‎, ‎known as a gyrogroup‎. ‎The famous‎ concrete realization of a gyrogroup‎, ‎which motivated the emergence ‎of gyrogroups into the mainstream‎, ‎is the space of all ‎relativistically admissible velocities along with a binary ‎mbox{operation} given by the Einstein velocity addition law of ‎special relativity theory‎. ‎The latter leads to the Lorentz ‎transformation group $so{1,n}$‎, ‎$ninN$‎, ‎in pseudo-Euclidean ‎spaces of signature $(1‎, ‎n)$‎. ‎The study in this article is motivated ‎by generalized Lorentz groups $so{m‎, ‎n}$‎, ‎$m‎, ‎ninN$‎, ‎in ‎pseudo-Euclidean spaces of signature $(m‎, ‎n)$‎. ‎Accordingly‎, ‎this ‎article explores the bi-decomposition $Gamma = H_LBH_R$ of a group ‎$Gamma$ into a subset $B$ and subgroups $H_L$ and $H_R$ of ‎$Gamma$‎, ‎along with the novel bi-gyrogroup structure of $B$ induced ‎by the bi-decomposition of $Gamma$‎. ‎As an example‎, ‎we show by ‎methods of Clifford mbox{algebras} that the quotient group of the ‎spin group $spin{m‎, ‎n}$ possesses the bi-decomposition structure‎.
Algorithmic Social Intervention

Social and behavioral interventions are a critical tool for governments and communities to tackle deep-rooted societal challenges such as homelessness, disease, and poverty. However, real-world interventions are almost always plagued by limited resources and limited data, which creates a computational challenge: how can we use algorithmic techniques to enhance the targeting and delivery of social and behavioral interventions? The goal of my thesis is to provide a unified study of such questions, collectively considered under the name "algorithmic social intervention". This proposal introduces algorithmic social intervention as a distinct area with characteristic technical challenges, presents my published research in the context of these challenges, and outlines open problems for future work. A common technical theme is decision making under uncertainty: how can we find actions which will impact a social system in desirable ways under limitations of knowledge and resources? The primary application area for my work thus far is public health, e.g. HIV or tuberculosis prevention. For instance, I have developed a series of algorithms which optimize social network interventions for HIV prevention. Two of these algorithms have been pilot-tested in collaboration with LA-area service providers for homeless youth, with preliminary results showing substantial improvement over status-quo approaches. My work also spans other topics in infectious disease prevention and underlying algorithmic questions in robust and risk-aware submodular optimization.
From Geometry to Geology: An Invitation to Mathematical Pluralism Through the Phenomenon of Independence

This paper explores how a pluralist view can arise in a natural way out of the day-to-day practice of modern set theory. By contrast, the widely accepted orthodox view is that there is an ultimate universe of sets V, and it is in this universe that mathematics takes place. From this view, the purpose of set theory is “learning the truth about V.” It has become apparent, however, that the phenomenon of independence—those questions left unresolved by the axioms—holds a central place in the investigation. This paper introduces the notion of independence, explores the primary tool (“soundness”) for establishing independence results, and shows how a plurality of models arises through the investigation of this phenomenon. Building on a familiar example from Euclidean geometry, a template for independence proofs is established. Applying this template in the domain of set theory leads to a consideration of forcing, the tool par excellence for constructing universes of sets. Fifty years of forcing has resulted in a profusion of universes exhibiting a wide variety of characteristics—a multiverse of set theories. Direct study of this multiverse presents technical challenges due to its second-order nature. Nonetheless, there are certain nice “local neighborhoods” of the multiverse that are amenable to first-order analysis, and set-theoretic geology studies just such a neighborhood, the collection of grounds of a given universe V of set theory. I will explore some of the properties of this collection, touching on major concepts, open questions, and recent developments.
Lower bounds for exact model counting and applications in probabilistic databases

The best current methods for exactly computing the number of satisfying assignments, or the satisfying probability, of Boolean formulas can be seen, either directly or indirectly, as building decision-DNNF (decision decomposable negation normal form) representations of the input Boolean formulas. Decision-DNNFs are a special case of d-DNNFs where d stands for deterministic. We show that any decision-DNNF can be converted into an equivalent FBDD (free binary decision diagram) - also known as a read-once branching program (ROBP or 1-BP) -with only a quasipolynomial increase in representation size in general, and with only a polynomial increase in size in the special case of monotone k-DNF formulas. Leveraging known exponential lower bounds for FBDDs, we then obtain similar exponential lower bounds for decision-DNNFs which provide lower bounds for the recent algorithms. We also separate the power of decision-DNNFs from d-DNNFs and a generalization of decision-DNNFs known as AND-FBDDs. Finally we show how these imply exponential lower bounds for natural problems associated with probabilistic databases.
Thermodynamically Consistent Coarse-Graining of Polymers

∗ Author to whom correspondence should be addressed. Electronic mail: mguenza@uoregon.edu 1 ar X iv :1 50 9. 08 54 6v 1 [ co nd -m at .s of t] 2 9 Se p 20 15 Molecular dynamics simulations have become an essential tool in developing and testing theories in complex systems of either biological or synthetic origins. However, explicit atom molecular dynamics simulations are computationally costly, which limits their applicability to a restricted range of length and time-scales. A way to overcome this limitation is to design specific coarse-graining (CG) models. These models can be highly efficient with respect to atomistic descriptions because they represent the system at a lower resolution, thus greatly reducing the degrees of freedom that need to be sampled during the simulation.[1–6] However, reducing the degrees of freedom comes with the consequence that some thermodynamic properties and the dynamical quantities are modified in a way that depend on the extent of coarse-graining. This can be intuitively understood by considering that when a system is coarse-grained, a number of atomistic units are combined together into a new, effective, fictitious unit. Those CG units interact by means of an effective potential that is simplified and, in general, is smoother than the original atomistic potential. While the atomistic units spend time sampling a myriad of local configurations, the effective CG units can slide freely on a smoother free energy landscape. A coarse-graining procedure is formally equivalent to applying the Mori-Zwanzig projection operator technique to a macromolecular liquid, originally described at the level of the Hamiltonian by a Liouville equation. The projection simplifies the system to a number of coarse-grained units interacting through an effective free-energy-type potential in the reduced representation. The dynamics of the coarse-grained units is then described by a Langevin equation where dissipation emerges from the procedure. Because the potential between units in the coarse-grained description is a free energy, it is parameter dependent and changes with the thermodynamic settings and the type of molecular system. We should expect a different potential to act between the coarse-grained units when the value of the temperature, the density, the molecular concentration, the number of monomers in the coarse-grained unit, or even the degree of polymerization of the molecule is varied. This is a problem for the proper design of a coarse-grained description if the potential is numerically derived, i.e. an analytical solution is not possible, leading to representability problems for the potential. Most of the effective potentials in traditional Molecular Dynamics simulations, such as the Lennard-Jones potential or the united atom potential,[7] are dependent on thermodynamic and molecular parameters in a trivial way. They depend on temperature and on the
Quantized Weyl algebras at roots of unity

We classify the centers of the quantized Weyl algebras that are polynomial identity algebras and derive explicit formulas for the discriminants of these algebras over a general class of polynomial central subalgebras. Two different approaches to these formulas are given: one based on Poisson geometry and deformation theory, and the other using techniques from quantum cluster algebras. Furthermore, we classify the PI quantized Weyl algebras that are free over their centers and prove that their discriminants are locally dominating and effective. This is applied to solve the automorphism and isomorphism problems for this family of algebras and their tensor products.
Form factors from lattice QCD

Precision computation of hadronic physics with lattice QCD is becoming feasible. The last decade has seen precent-level calculations of many simple properties of mesons, and the last few years have seen calculations of baryon masses, including the nucleon mass, accurate to a few percent. As computational power increases and algorithms advance, the precise calculation of a variety of more demanding hadronic properties will become realistic. With this in mind, I discuss the current lattice QCD calculations of generalized parton distributions with an emphasis on the prospects for well-controlled calculations for these observables as well. I will do this by way of several examples: the pion and nucleon form factors and moments of the nucleon parton and generalized-parton distributions.
Deformations of Axially Symmetric Initial Data and the Mass-Angular Momentum Inequality

We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. This procedure is based on a certain deformation of the initial data which preserves the relevant geometry, while achieving the maximal condition and its implied inequality (in a weak sense) for the scalar curvature; this answers a question posed by R. Schoen. The primary equation involved, bears a strong resemblance to the Jang-type equations studied in the context of the positive mass theorem and the Penrose inequality. Each equation in the system is analyzed in detail individually, and it is shown that appropriate existence/uniqueness results hold with the solution satisfying desired asymptotics. Lastly, it is shown that the same reduction argument applies to the basic inequality yielding a lower bound for the area of black holes in terms of mass and angular momentum.
Universally weakly secure coset coding schemes for minimum storage regenerating (MSR) codes

We consider the problem of designing codes for distributed storage that protect user data against eavesdroppers that can gain access to network links as well as individual nodes. Our goal is to achieve weak (block) security that requires that the eavesdroppers would not be able to decode individual files or combinations of a small number of files. The standard approach for achieving block security is to use a joint design scheme that consists of (inner) storage code and the (outer) coset code. However, jointly designing the codes requires that the user, who pre-process and stores the files, should know the underlying storage code in order to design the (outer) linear transformation for achieving weak security. In many practical scenarios, such as storing the files on the third party cloud storage system, it may not be possible for the user to know the underlying storage code. In this work, we present a universal scheme that separates the outer code design from the storage code design for minimum storage regenerating codes (MSR). Our scheme allows the independent design of the storage code and the outer code. Our scheme uses small field size and can be used in a broad range of practical settings.
FM backscatter: enabling connected cities and smart fabrics

This paper enables connectivity on everyday objects by transforming them into FM radio stations. To do this, we show for the first time that ambient FM radio signals can be used as a signal source for backscatter communication. Our design creates backscatter transmissions that can be decoded on any FM receiver including those in cars and smartphones. This enables us to achieve a previously infeasible capability: backscattering information to cars and smartphones in outdoor environments. Our key innovation is a modulation technique that transforms backscatter, which is a multiplication operation on RF signals, into an addition operation on the audio signals output by FM receivers. This enables us to embed both digital data as well as arbitrary audio into ambient analog FM radio signals. We build prototype hardware of our design and successfully embed audio transmissions over ambient FM signals. Further, we achieve data rates of up to 3.2 kbps and ranges of 5-60 feet, while consuming as little as 11.07 µW of power. To demonstrate the potential of our design, we also fabricate our prototype on a cotton t-shirt by machine sewing patterns of a conductive thread to create a smart fabric that can transmit data to a smartphone. We also embed FM antennas into posters and billboards and show that they can communicate with FM receivers in cars and smartphones.
Geometry of Mean Value Sets for General Divergence Form Uniformly Elliptic Operators

In the Fermi Lectures on the obstacle problem in 1998, Caffarelli gave a proof of the mean value theorem which extends to general divergence form uniformly elliptic operators. In the general setting, the result shows that for any such operator L and at any point x0 in the domain, there exists a nested family of sets {Dr(x0)} where the average over any of those sets is related to the value of the function at x0. Although it is known that the {Dr(x0)} are nested and are comparable to balls in the sense that there exists c,C depending only on L such that Bcr(x0) ⊂ Dr(x0) ⊂ BCr(x0) for all r > 0 and x0 in the domain, otherwise their geometric and topological properties are largely unknown. In this paper we begin the study of these topics and we prove a few results about the geometry of these sets and give a couple of applications of the theorems.
Learning to Adapt in Dynamic, Real-World Environments Through Meta-Reinforcement Learning

Although reinforcement learning methods can achieve impressive results in simulation, the real world presents two major challenges: generating samples is exceedingly expensive, and unexpected perturbations or unseen situations cause proficient but specialized policies to fail at test time. Given that it is impractical to train separate policies to accommodate all situations the agent may see in the real world, this work proposes to learn how to quickly and effectively adapt online to new tasks. To enable sample-efficient learning, we consider learning online adaptation in the context of model-based reinforcement learning. Our approach uses meta-learning to train a dynamics model prior such that, when combined with recent data, this prior can be rapidly adapted to the local context. Our experiments demonstrate online adaptation for continuous control tasks on both simulated and real-world agents. We first show simulated agents adapting their behavior online to novel terrains, crippled body parts, and highly-dynamic environments. We also illustrate the importance of incorporating online adaptation into autonomous agents that operate in the real world by applying our method to a real dynamic legged millirobot. We demonstrate the agent's learned ability to quickly adapt online to a missing leg, adjust to novel terrains and slopes, account for miscalibration or errors in pose estimation, and compensate for pulling payloads.
Recovering the topology of surfaces from cluster algebras

We present an effective method for recovering the topology of a bordered oriented surface with marked points from its cluster algebra. The information is extracted from the maximal triangulations of the surface, those that have exchange quivers with maximal number of arrows in the mutation class. The method gives new proofs of the automorphism and isomorphism problems for the surface cluster algebras as well as the uniqueness of the Fomin–Shapiro–Thurston block decompositions of the exchange quivers of the surface cluster algebras. The previous proofs of these results followed a different approach based on Gu’s direct proof of the last result. The method also explains the exceptions to these results due to pathological problems with the maximal triangulations of several surfaces.
Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots

Abstract Some time ago Ranada (1989) obtained new nontrivial solutions of the Maxwellian gauge fields without sources. These were reinterpreted in Kholodenko (2015) [10] (part I) as particle-like (monopoles, dyons, etc.). They were obtained by the method of Abelian reduction of the non-Abelian Yang–Mills functional. The developed method uses instanton-type calculations normally employed for the non-Abelian gauge fields. By invoking the electric–magnetic duality it then becomes possible to replace all known charges/masses by the particle-like solutions of the source-free Abelian gauge fields. To employ these results in high energy physics, it is essential to extend Ranada’s results by carefully analyzing and classifying all dynamically generated knotted/linked structures in gauge fields, including those discovered by Ranada. This task is completed in this work. The study is facilitated by the recent progress made in solving the Moffatt conjecture. Its essence is stated as follows: in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. By employing the correspondence between the ideal hydrodynamics and electrodynamics discussed in part I and by superimposing it with the already mentioned method of Abelian reduction, it is demonstrated that in the absence of boundaries only the iterated torus knots and links could be dynamically generated. Obtained results allow to develop further particle-knot/link correspondence studied in Kholodenko (2015) [13].
Betti-linear ideals

Abstract We introduce the notion of a Betti-linear monomial ideal, which generalizes the notion of lattice-linear monomial ideal introduced by Clark. We provide a characterization of Betti-linearity in terms of Tchernev's poset construction. As an application we obtain an explicit canonical construction for the minimal free resolutions of monomial ideals having pure resolutions.
On the Kähler Ricci Flow on Projective Manifolds of General Type

We consider the K\"ahler Ricci flow on a smooth minimal model of general type, we show that if the Ricci curvature is uniformly bounded below along the K\"ahler-Ricci flow, then the diameter is uniformly bounded. As a corollary we show that under the Ricci curvature lower bound assumption, the Gromov-Hausdorff limit of the flow is homeomorphic to the canonical model. Moreover, we can give a purely analytic proof of a recent result of Tosatti-Zhang (\cite{TZ}) that if the canonical line bundle $K_X$ is big and nef, but not ample, then the flow is of Type IIb.
Optimal Control for Diffusions on Graphs

Starting from a unit mass on a vertex of a graph, we investigate the minimum number of controlled diffusion steps needed to transport a constant mass $p$ outside of the ball of radius $n$. In a ste...
Understanding Deep Architectures using a Recursive Convolutional Network

A key challenge in designing convolutional network models is sizing them appropriately. Many factors are involved in these decisions, including number of layers, feature maps, kernel sizes, etc. Complicating this further is the fact that each of these influence not only the numbers and dimensions of the activation units, but also the total number of parameters. In this paper we focus on assessing the independent contributions of three of these linked variables: The numbers of layers, feature maps, and parameters. To accomplish this, we employ a recursive convolutional network whose weights are tied between layers; this allows us to vary each of the three factors in a controlled setting. We find that while increasing the numbers of layers and parameters each have clear benefit, the number of feature maps (and hence dimensionality of the representation) appears ancillary, and finds most of its benefit through the introduction of more weights. Our results (i) empirically confirm the notion that adding layers alone increases computational power, within the context of convolutional layers, and (ii) suggest that precise sizing of convolutional feature map dimensions is itself of little concern; more attention should be paid to the number of parameters in these layers instead.
Prime II$_1$ factors arising from irreducible lattices in products of rank one simple Lie groups

We prove that if $\Gamma$ is an icc irreducible lattice in a product of connected non-compact rank one simple Lie groups with finite center, then the II$_1$ factor $L(\Gamma)$ is prime. In particular, we deduce that the II$_1$ factors associated to the arithmetic groups $\text{PSL}_2(\mathbb Z[\sqrt{d}])$ and $\text{PSL}_2(\mathbb Z[S^{-1}])$ are prime, for any square-free integer $d\geq 2$ with $d\not\equiv 1 mod{4}$ and any finite non-empty set of primes $S$. This provides the first examples of prime II$_1$ factors arising from lattices in higher rank semisimple Lie groups. More generally, we describe all tensor product decompositions of $L(\Gamma)$ for icc countable groups $\Gamma$ that are measure equivalent to a product of non-elementary hyperbolic groups. In particular, we show that $L(\Gamma)$ is prime, unless $\Gamma$ is a product of infinite groups, in which case we prove a unique prime factorization result for $L(\Gamma)$.
AUTOMATED BIFURCATION ANALYSIS FOR NONLINEAR ELLIPTIC PARTIAL DIFFERENCE EQUATIONS ON GRAPHS

We seek solutions u ∈ ℝn to the semilinear elliptic partial difference equation -Lu + fs(u) = 0, where L is the matrix corresponding to the Laplacian operator on a graph G and fs is a one-parameter family of nonlinear functions. This article combines the ideas introduced by the authors in two papers: (a) Nonlinear elliptic partial difference equations on graphs (J. Experimental Mathematics, 2006), which introduces analytical and numerical techniques for solving such equations, and (b) Symmetry and automated branch following for a semilinear elliptic PDE on a fractal region (SIAM J. Dynamical Systems, 2006), wherein we present some of our recent advances concerning symmetry, bifurcation and automation for PDE. We apply the symmetry analysis found in the SIAM paper to arbitrary graphs in order to obtain better initial guesses for Newton's method, create informative graphics, and better understand the role of symmetry in the underlying variational structure. We use two modified implementations of the gradient Newton–Galerkin algorithm (GNGA, Neuberger and Swift) to follow bifurcation branches in a robust way. By handling difficulties that arise when encountering accidental degeneracies and higher-dimensional critical eigenspaces, we can find many solutions of many symmetry types to the discrete nonlinear system. We present a selection of experimental results which demonstrate our algorithm's capability to automatically generate bifurcation diagrams and solution graphics starting with only an edgelist of a graph. We highlight interesting symmetry and variational phenomena.
Unipotent invariant matrices

Abstract We describe the variety of fixed points of a unipotent operator acting on the space of matrices. We compute the determinant and the rank of a generic (symmetric, or anti-symmetric) matrix in the fixed variety, yielding information about the generic singular locus of the corresponding bilinear form.
Integrate multi-omic data using affinity network fusion (ANF) for cancer patient clustering

Clustering cancer patients into subgroups and identifying cancer subtypes is an important task in cancer genomics. Clustering based on comprehensive multi-omic molecular profiling can often achieve better results than those using a single data type, since each omic data type may contain complementary information. However, it is challenging to integrate heterogeneous omic data directly. Based on one popular method – Similarity Network Fusion (SNF), we presented Affinity Network Fusion (ANF), an “upgrade” of SNF with several advantages. Similar to SNF, ANF treats each omic data type as one view of patients and learns a fused affinity matrix for clustering. We applied ANF to a harmonized TCGA dataset consisting of 2193 patients, and generated promising results on clustering patients into correct disease types. Our experimental results also demonstrated the power of feature selection and transformation combined with using ANF in patient clustering. Moreover, eigengap analysis suggests that the learned affinity matrices of four cancer types using our proposed framework may have successfully captured patient group structure and can be used for discovering unknown cancer subtypes.
TRIONS IN COUPLED QUANTUM WELLS AND WIGNER CRYSTALLIZATION

We consider a restricted three-body problem, where two interacted particles are located in a two-dimensional (2D) plane and interact with the third one located in the parallel spatially separated plane. The system of such type can be formed in the semiconductor coupled quantum wells, where the electrons (holes) and direct excitons spatially separated in different parallel neighboring quantum wells are sufficiently close to interact and form negative X- or positive X+ indirect trions. It is shown that at large interwell separations, when the interwell separation is much greater than the exciton Bohr radius, this problem can be solved analytically using the cluster approach. Analytical results for the energy spectrum and the wavefunctions of the spatially indirect trion are obtained, their dependencies on the interwell separations is analyzed and a conditional probability distribution is calculated. The formation of 2D Wigner crystal of trions at the low densities is predicted. It is shown that the critical density of the formation of the trion Wigner crystal is sufficiently greater than the critical density of the electron Wigner crystal in the same material.
Capacity of multiple one-bit transceivers in a Rayleigh environment

We analyze the channel capacity of a system with a large number of one-bit transceivers in a classical Rayleigh environment with perfect channel information at the receiver. With M transmitters and N =αM receivers, we derive an expression of the capacity per transmitter C, where C ≤ min(1,α), as a function of a and signal-to-noise ratio (SNR) ρ, when M → ∞. We show that our expression is a good approximation for small M, and provide simple approximations of C for various ranges of α and ρ. We conclude that at high SNR, C reaches its upper limit of one only if α > 1.24. Expressions for determining when C “saturates” as a function of α and ρ are given.
Deterministic Policy Optimization by Combining Pathwise and Score Function Estimators for Discrete Action Spaces

Policy optimization methods have shown great promise in solving complex reinforcement and imitation learning tasks. While model-free methods are broadly applicable, they often require many samples to optimize complex policies. Model-based methods greatly improve sample-efficiency but at the cost of poor generalization, requiring a carefully handcrafted model of the system dynamics for each task. Recently, hybrid methods have been successful in trading off applicability for improved sample-complexity. However, these have been limited to continuous action spaces. In this work, we present a new hybrid method based on an approximation of the dynamics as an expectation over the next state under the current policy. This relaxation allows us to derive a novel hybrid policy gradient estimator, combining score function and pathwise derivative estimators, that is applicable to discrete action spaces. We show significant gains in sample complexity, ranging between 1.7 and 25 times, when learning parameterized policies on Cart Pole, Acrobot, Mountain Car and Hand Mass. Our method is applicable to both discrete and continuous action spaces, when competing pathwise methods are limited to the latter.
Online Adaptive Machine Learning Based Algorithm for Implied Volatility Surface Modeling

Abstract In this work, we design a machine learning based method – online adaptive primal support vector regression (SVR) – to model the implied volatility surface (IVS). The algorithm proposed is the first derivation and implementation of an online primal kernel SVR. It features enhancements that allow efficient online adaptive learning by embedding the idea of local fitness and budget maintenance to dynamically update support vectors upon pattern drifts. For algorithm acceleration, we implement its most computationally intensive parts in a Field Programmable Gate Arrays hardware, where a 132x speedup over CPU is achieved during online prediction. Using intraday tick data from the E-mini S&P 500 options market, we show that the Gaussian kernel outperforms the linear kernel in regulating the size of support vectors, and that our empirical IVS algorithm beats two competing online methods with regards to model complexity and regression errors (the mean absolute percentage error of our algorithm is up to 13%). Best results are obtained at the center of the IVS grid due to its larger number of adjacent support vectors than the edges of the grid. Sensitivity analysis is also presented to demonstrate how hyper parameters affect the error rates and model complexity.
Coxeter elements and root bases

Abstract Let g be a Lie algebra of type A , D , E with fixed Cartan subalgebra h , root system R and Weyl group W . We show that a choice of Coxeter element C ∈ W gives a root basis for g . Moreover, using the results of Kirillov and Thind (2010) [KT] we show that this root basis gives a purely combinatorial construction of g , where root vectors correspond to vertices of a certain quiver Γ ˆ , and with respect to this basis the structure constants of the Lie bracket are given by paths in Γ ˆ . This construction is then related to the constructions of Ringel and Peng and Xiao.
Optimal factorizations of rational numbers using factorization trees

Let mt(α) denote the t-metric Mahler measure of the algebraic number α. Recent work of the first author established that the infimum in mt(α) is attained by a single point for all sufficiently large t. Nevertheless, no efficient method for locating is known. In this paper, we define a new tree data structure, called a factorization tree, which enables us to find when α ∈ ℚ. We establish several basic properties of factorization trees, and use these properties to locate in previously unknown cases.