cssi/SciSciGPT-SciSciNet huggingface dataset:
DNF sparsification beyond sunflowers

There are two natural complexity measures associated with DNFs: their size, which is the number of clauses; and their width, which is the maximal number of variables in a clause. It is a folklore result that DNFs of small size can be approximated by DNFs of small width (logarithmic in the size). The other direction is much less clear. Gopalan, Meka and Reingold [Computational Complexity 2013] showed that the other direction – DNF sparsification – holds as well. Any DNF of width w can be approximated to within error e by a DNF of size (w log(1/e))O(w). Our main interest in this work is the dependence on the width w. The same dependence of ww appears in several other open problems in combinatorics and complexity, such as the Erdős-Rado sunflower conjecture and Mansour’s conjecture. In fact, there are deep connections between these three problems. Our main result is DNF compression with an improved dependence on the width, which overcomes the ww barrier. Concretely, we show that any DNF of width w can be approximated to within error e by a DNF of size (1/e)O(w). The proof centers around a new object which we call the DNF index function. Given a DNF, the DNF index function outputs for an input the first clause that satisfies it (if one exists). Our proof has two parts: a combinatorial part, where we exhibit a switching lemma for the DNF index function; and an analytic part, where we use the switching lemma to bound the noise sensitivity of the DNF index function, and then use it to obtain our DNF compression result.
Synthesis of 7-methoxybenzolactam-V8 using aminomercuration as a key reaction

Abstract 7-Methoxybenzolactam-V8 was synthesized using a short synthetic route that employs aminomercuration as a key reaction.
Exploiting Vulnerabilities of Load Forecasting Through Adversarial Attacks

Load forecasting plays a critical role in the operation and planning of power systems. By using input features such as historical loads and weather forecasts, system operators and utilities build forecast models to guide decision making in commitment and dispatch. As the forecasting techniques becomes more sophisticated, however, they also become more vulnerable to cybersecurity threats. In this paper, we study the vulnerability of a class of load forecasting algorithms and analyze the potential impact on the power system operations, such as load shedding and increased dispatch costs. Specifically, we propose data injection attack algorithms that require minimal assumptions on the ability of the adversary. The attacker does not need to have knowledge about the load forecasting model or the underlying power system. Surprisingly, our results indicate that standard load forecasting algorithms are quite vulnerable to the designed black-box attacks. By only injecting malicious data in temperature from online weather forecast APIs, an attacker could manipulate load forecasts in arbitrary directions and cause significant and targeted damages to system operations.
Syntheses and properties of benzodipyrrinones

2,3-Benzannelated dipyrrinone analogs (1 and 2) of xanthobilirubic acid (3) are prepared by base-catalyzed condensation of isoindolinone (5) and indolin-2-one (6) respectively, with methyl 3-(2-formyl-3,5-dimethyl-1H-pyrrol-4-yl)propanoate (4). Nuclear Overhauser effect H-nmr studies indicate that both 1 and 2 adopt preferentially a syn-Z configuration. The former forms a hydrogen-bonded homodimer in nonpolar solvents; the latter is intramolecularly hydrogen bonded.
Recent Advances in Rhodium-Catalyzed Cyclization Reactions

Mechanistic studies on silylformylation have led to the discovery of a series of new carbocyclizations involving alkynes and hydrosilanes. Cyclohydrocarbonylation processes have been devised by combining hydroformylation and cyclization. These new reactions serve as powerful methods for the rapid construction of monocyclic, bicyclic, and fused ring systems from readily obtainable starting materials.
LC3 and STRAP regulate actin filament assembly by JMY during autophagosome formation.

During autophagy, actin filament networks move and remodel cellular membranes to form autophagosomes that enclose and metabolize cytoplasmic contents. Two actin regulators, WHAMM and JMY, participate in autophagosome formation, but the signals linking autophagy to actin assembly are poorly understood. We show that, in nonstarved cells, cytoplasmic JMY colocalizes with STRAP, a regulator of JMY’s nuclear functions, on nonmotile vesicles with no associated actin networks. Upon starvation, JMY shifts to motile, LC3-containing membranes that move on actin comet tails. LC3 enhances JMY’s de novo actin nucleation activity via a cryptic actin-binding sequence near JMY’s N terminus, and STRAP inhibits JMY’s ability to nucleate actin and activate the Arp2/3 complex. Cytoplasmic STRAP negatively regulates autophagy. Finally, we use purified proteins to reconstitute LC3- and JMY-dependent actin network formation on membranes and inhibition of network formation by STRAP. We conclude that LC3 and STRAP regulate JMY’s actin assembly activities in trans during autophagy.
Anchor Me: The Benefits and Challenges of Fiscal Responsibility

This paper discusses the benefits and challenges of implementing a rule‐based fiscal responsibility framework, using the Philippines as a case study. It estimates structural measures of the fiscal stance over the period 1980–2016 and applies a stochastic simulation model to determine the optimal set of fiscal rules. The empirical analysis indicates that discretionary fiscal policy has been procyclical, and the degree of procyclicality has increased in recent years. While the national government's nonbinding ceiling on the overall budget deficit is helpful, it does not constitute an appropriate operational target to guide fiscal policy over the economic cycle and necessarily ensure that the fiscal stance meets the government's intertemporal budget constraint. To this end, I use stochastic simulations and show the macroeconomic benefits of a well‐designed fiscal responsibility law that enshrines explicit fiscal rules designed for countercyclical policy and long‐term debt sustainability and an independent fiscal council that improves accountability and transparency.
A catalog of CasX genome editing sites in common model organisms

DpbCasX, also called Cas12e, is an RNA-guided DNA endonuclease isolated from Deltaproteobacteria. In this paper I characterized the CasX-compatible genome editing sites in the reference genomes of yeast (Saccharomyces cerevisiae), flatworms (Caenorhabditis elegans), flies (Drosophila melanogaster), zebrafish (Danio rerio), mouse (Mus musculus), rats (Rattus norvegicus), and humans (Homo sapiens). Across those genomes there were > 27,000 CasX sites per megabase on average. More than 90% of genes in each genome had at least one unique site overlapping an exon, with median unique sites per gene of 6–45. I also annotated sites in the GRCm38 reference and 15 additional mouse strain genomes. The presence of specific guide sequences varied amongst the strains, with CAST/EiJ and PWK/PhJ showing the greatest divergence from the reference strain. The high density of CasX sites and number of exon overlapping sites suggests that CasX has the potential to be used as a common genome editor.
Characterizing Round Spheres Using Half-Geodesics

A half-geodesic is a closed geodesic realizing the distance between any pair of its points. All geodesics in a round sphere are half-geodesics. Conversely, this paper establishes that Riemannian spheres with all geodesics closed and sufficiently many half-geodesics are round.
MassComp, a lossless compressor for mass spectrometry data

Mass Spectrometry (MS) is a widely used technique in biology research, and has become key in proteomics and metabolomics analyses. As a result, the amount of MS data has significantly increased in recent years. For example, the MS repository MassIVE contains more than 123TB of data. Somehow surprisingly, these data are stored uncompressed, hence incurring a significant storage cost. Efficient representation of these data is therefore paramount to lessen the burden of storage and facilitate its dissemination. We present MassComp, a lossless compressor optimized for the numerical (m/z)-intensity pairs that account for most of the MS data. We tested MassComp on several MS data and show that it delivers on average a 46% reduction on the size of the numerical data, and up to 89%. These results correspond to an average improvement of more than 27% when compared to the general compressor gzip and of 40% when compared to the state-of-the-art numerical compressor FPC. When tested on entire files retrieved from the MassIVE repository, MassComp achieves on average a 59% size reduction. MassComp is written in C++ and freely available at https://github.com/iochoa/MassComp . The compression performance of MassComp demonstrates its potential to significantly reduce the footprint of MS data, and shows the benefits of designing specialized compression algorithms tailored to MS data. MassComp is an addition to the family of omics compression algorithms designed to lessen the storage burden and facilitate the exchange and dissemination of omics data.
Ketones from Nickel‐Catalyzed Decarboxylative, Non‐Symmetric Cross‐Electrophile Coupling of Carboxylic Acid Esters

Synthesis of the C-C bonds of ketones relies upon one high-availability reagent (carboxylic acids) and one low-availability reagent (organometallic reagents or alkyl iodides). We demonstrate here a ketone synthesis that couples two different carboxylic acid esters, N-hydroxyphthalimide esters and S-2-pyridyl thioesters, to form aryl alkyl and dialkyl ketones in high yields. The keys to this approach are the use of a nickel catalyst with an electron-poor bipyridine or terpyridine ligand, a THF/DMA mixed solvent system, and ZnCl2 to enhance the reactivity of the NHP ester. The resulting reaction can be used to form ketones that have previously been difficult to access, such as hindered tertiary/tertiary ketones with strained rings and ketones with α-heteroatoms. The conditions can be employed in the coupling of complex fragments, including a 20-mer peptide fragment analog of Exendin(9-39) on solid support.
Bounds on volume growth of geodesic balls under Ricci flow

We prove a so called $\kappa$ non-inflating property for Ricci flow, which provides an upper bound for volume ratio of geodesic balls over Euclidean ones, under an upper bound for scalar curvature. This result can be regarded as the opposite statement of Perelman's $\kappa$ non-collapsing property for Ricci flow. These two results together imply volume doubling property for Ricci flow without assuming Ricci curvature lower bound.
Weighted Fourier frames on fractal measures

Abstract We generalize an idea of Picioroaga and Weber [10] to construct Parseval frames of weighted exponential functions for self-affine measures.
Lattices, graphs, and Conway mutation

The d-invariant of an integral, positive definite lattice Λ records the minimal norm of a characteristic covector in each equivalence class $({\textup{mod} \;}2\varLambda)$ . We prove that the 2-isomorphism type of a connected graph is determined by the d-invariant of its lattice of integral flows (or cuts). As an application, we prove that a reduced, alternating link diagram is determined up to mutation by the Heegaard Floer homology of the link’s branched double-cover. Thus, alternating links with homeomorphic branched double-covers are mutants.
Optimal Switching Synthesis for Jump Linear Systems With Gaussian Initial State Uncertainty

This paper provides a method to design an optimal switching sequence for jump linear systems with given Gaussian initial state uncertainty. In the practical perspective, the initial state contains some uncertainties that come from measurement errors or sensor inaccuracies and we assume that the type of this uncertainty has the form of Gaussian distribution. In order to cope with Gaussian initial state uncertainty and to measure the system performance, Wasserstein metric that defines the distance between probability density functions is used. Combining with the receding horizon framework, an optimal switching sequence for jump linear systems can be obtained by minimizing the objective function that is expressed in terms of Wasserstein distance. The proposed optimal switching synthesis also guarantees the mean square stability for jump linear systems. The validations of the proposed methods are verified by examples.
Algorithms versus Circuit Lower Bounds

Different techniques have been used to prove several transference theorems of the form “nontrivial algorithms for a circuit class C yield circuit lower bounds against C”. In this survey we revisit many of these results. We discuss how circuit lower bounds can be obtained from derandomization, compression, learning, and satisfiability algorithms. We also cover the connection between circuit lower bounds and useful properties, a notion that turns out to be fundamental in the context of these transference theorems. Along the way, we obtain a few new results, simplify several proofs, and show connections involving different frameworks. We hope that our presentation will serve as a self-contained introduction for those interested in pursuing research in this area. ∗Research supported by NSF grants CCF-1116702 and CCF-1115703.
Computing Quantum Phase Transitions

This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational challenges posed by quantum phase transitions, a number of successful computational approaches is discussed. The focus is on classical and quantum Monte Carlo methods, with the former being based on the quantum-to classical mapping while the latter directly attack the quantum problem. These methods are illustrated by several examples of quantum phase transitions in clean and disordered systems.
CONSTRUCTING DOUBLY-POINTED HEEGAARD DIAGRAMS COMPATIBLE WITH (1,1) KNOTS

A (1,1) knot K in a 3-manifold M is a knot that intersects each solid torus of a genus 1 Heegaard splitting of M in a single trivial arc. Choi and Ko developed a parametrization of this family of knots by a four-tuple of integers, which they call Schubert's normal form. This paper presents an algorithm for constructing a genus 1 doubly-pointed Heegaard diagram compatible with K, given a Schubert's normal form for K. The construction, coupled with results of Ozsvath and Szabo, provides a practical way to compute knot Floer homology groups for (1,1) knots. The construction uses train tracks, and its method is inspired by the work of Goda, Matsuda, and Morifuji.
On the distributed optimization over directed networks

Abstract In this paper, we propose a distributed algorithm, called Directed-Distributed Subgradient Descent (D-DSD), to solve multi-agent optimization problems over directed graphs. Existing algorithms mostly deal with similar problems under the assumption of undirected networks, i.e., requiring the weight matrices to be doubly-stochastic. The row-stochasticity of the weight matrix guarantees that all agents reach consensus, while the column-stochasticity ensures that each agent’s local (sub)gradient contributes equally to the global objective. In a directed graph, however, it may not be possible to construct a doubly-stochastic weight matrix in a distributed manner. We overcome this difficulty by augmenting an additional variable for each agent to record the change in the state evolution. In each iteration, the algorithm simultaneously constructs a row-stochastic matrix and a column-stochastic matrix instead of only a doubly-stochastic matrix. The convergence of the new weight matrix, depending on the row-stochastic and column-stochastic matrices, ensures agents to reach both consensus and optimality. The analysis shows that the proposed algorithm converges at a rate of O ( ln k k ) , where k is the number of iterations.
On-ratio PDMS bonding for multilayer microfluidic device fabrication

Integrated elastomeric valves, also referred to as Quake valves, enable precise control and manipulation of fluid within microfluidic devices. Fabrication of such valves requires bonding of multiple layers of the silicone polymer polydimethylsiloxane (PDMS). The conventional method for PDMS-PDMS bonding is to use varied ratios of base to crosslinking agent between layers, typically 20:1 and 5:1. This bonding technique, known as "off-ratio bonding," provides strong, effective PDMS-PDMS bonding for multi-layer soft-lithography, but it can yield adverse PDMS material properties and can be wasteful of PDMS. Here we demonstrate the effectiveness of "on-ratio" PDMS bonding, in which both layers use a 10:1 base-to-crosslinker ratio, for multilayer soft lithography. We show the efficacy of this technique among common variants of PDMS: Sylgard 184, RTV 615, and Sylgard 182.
Stability of the interface of an isotropic active fluid

We study the linear stability of an isotropic active fluid in three different geometries: a film of active fluid on a rigid substrate, a cylindrical thread of fluid, and a spherical fluid droplet. The active fluid is modeled by the hydrodynamic theory of an active nematic liquid crystal in the isotropic phase. In each geometry, we calculate the growth rate of sinusoidal modes of deformation of the interface. There are two distinct branches of growth rates; at long wavelength, one corresponds to the deformation of the interface, and one corresponds to the evolution of the liquid crystalline degrees of freedom. The passive cases of the film and the spherical droplet are always stable. For these geometries, a sufficiently large activity leads to instability. Activity also leads to propagating damped or growing modes. The passive cylindrical thread is unstable for perturbations with wavelength longer than the circumference. A sufficiently large activity can make any wavelength unstable, and again leads to propagating damped or growing modes. Our calculations are carried out for the case of zero Frank elasticity. While Frank elasticity is a stabilizing mechanism as it penalizes distortions of the order parameter tensor, we show that it has a small effect on the instabilities considered here.
Robust and Scalable Models of Microbiome Dynamics

Microbes are everywhere, including in and on our bodies, and have been shown to play key roles in a variety of prevalent human diseases. Consequently, there has been intense interest in the design of bacteriotherapies or "bugs as drugs," which are communities of bacteria administered to patients for specific therapeutic applications. Central to the design of such therapeutics is an understanding of the causal microbial interaction network and the population dynamics of the organisms. In this work we present a Bayesian nonparametric model and associated efficient inference algorithm that addresses the key conceptual and practical challenges of learning microbial dynamics from time series microbe abundance data. These challenges include high-dimensional (300+ strains of bacteria in the gut) but temporally sparse and non-uniformly sampled data; high measurement noise; and, nonlinear and physically non-negative dynamics. Our contributions include a new type of dynamical systems model for microbial dynamics based on what we term interaction modules, or learned clusters of latent variables with redundant interaction structure (reducing the expected number of interaction coefficients from $O(n^2)$ to $O((\log n)^2)$); a fully Bayesian formulation of the stochastic dynamical systems model that propagates measurement and latent state uncertainty throughout the model; and introduction of a temporally varying auxiliary variable technique to enable efficient inference by relaxing the hard non-negativity constraint on states. We apply our method to simulated and real data, and demonstrate the utility of our technique for system identification from limited data and gaining new biological insights into bacteriotherapy design.
Generic A-family of exponential sums

Let s→:=(s1,s2,…,sm) with s1<⋯<sm being positive integers. Let A(s→) be the space of all 1-variable polynomials f(x)=∑l=1malxsl parameterized by coefficients a→=(a1,…,am) with am≠0. We study the p-adic valuation of the roots of the L-function of exponential sum of f¯ for modulo p reduction of any generic point f∈A(s→)(Q¯). Let NP(f¯) be the normalized p-adic Newton polygon of the L function of exponential sums of f¯. Let GNP(A(s→),F¯p) be the generic Newton polygon for A(s→) over F¯p, and let HP(A(s→)):=NPp(∏i=1d−1(1−pidT)) be the absolute lower bound of NP(A(s→)). One knows that NP(f¯)≺GNP(A(s→);F¯p)≺HP(f¯) for all prime p and for all f¯∈A(s→)(Q¯), and these equalities hold only when p≡1modd. In the case s→=(s,d) with s<d coprime we provide a computational method to determine GNP(A(s,d),F¯p) explicitly by constructing its generating polynomial Hr∈Q[Xr,1,Xr,2,…,Xr,d−1] for each residue class p≡rmodd. For p≡rmodd (with 2≤r≤d−1 coprime to d) large enough Hr=∑n=1d−1hr,n,kr,nXr,nkr,n with ∏n=1d−1hr,n,kr,n≠0 if and only if GNP(A(s,d),F¯p) has its breaking points after the origin at ((n,n(n+1)2d+(1−sd)kr,np−1))n=1,2,…,d−1. If a≠0 then for any f=xd+axs∈A(s,d)(Q¯) and for any prime p≡rmodd large enough we have that NP(f¯)=GNP(A(s,d),F¯p) and limp→∞NP(f¯)=HP(A(s,d)). Our method applies to compute the generic Newton polygon of Artin–Schreier family yp−y=xd+axs parameterized by a for p large enough.
Optimal haplotype assembly from high-throughput mate-pair reads

Humans have 23 pairs of homologous chromosomes. The homologous pairs are identical except on certain documented positions called single nucleotide polymorphisms (SNPs). A haplotype of an individual is the pair of sequences of SNPs on the two homologous chromosomes. In this paper, we study the problem of inferring haplotypes of individuals from mate-pair reads of their genome. We give a simple formula for the coverage needed for haplotype assembly, under a generative model. The analysis here leverages connections of this problem with decoding convolutional codes.
Eliciting Expertise without Verification

A central question of crowdsourcing is how to elicit expertise from agents. This is even more difficult when answers cannot be directly verified. A key challenge is that sophisticated agents may strategically withhold effort or information when they believe their payoff will be based upon comparison with other agents whose reports will likely omit this information due to lack of effort or expertise. Our work defines a natural model for this setting based on the assumption that more sophisticated agents know the beliefs of less sophisticated agents. We then provide a mechanism design framework for this setting. From this framework, we design several novel mechanisms, for both the single and multiple tasks settings, that (1) encourage agents to invest effort and provide their information honestly; (2) output a correct "hierarchy" of the information when agents are rational.
Zarankiewicz's problem for semi-algebraic hypergraphs

Abstract Zarankiewicz's problem asks for the largest possible number of edges in a graph that does not contain a K u , u subgraph for a fixed positive integer u. Recently, Fox, Pach, Sheffer, Sulk and Zahl [12] considered this problem for semi-algebraic graphs, where vertices are points in R d and edges are defined by some semi-algebraic relations. In this paper, we extend this idea to semi-algebraic hypergraphs. For each k ≥ 2 , we find an upper bound on the number of hyperedges in a k-uniform k-partite semi-algebraic hypergraph without K u 1 , … , u k for fixed positive integers u 1 , … , u k . When k = 2 , this bound matches the one of Fox et al. and when k = 3 , it is O ( ( m n p ) 2 d 2 d + 1 + e + m ( n p ) d d + 1 + e + n ( m p ) d d + 1 + e + p ( m n ) d d + 1 + e + m n + n p + p m ) , where m , n , p are the sizes of the parts of the tripartite hypergraph and e is an arbitrarily small positive constant. We then present applications of this result to a variant of the unit area problem, the unit minor problem and intersection hypergraphs.
Modeling and stabilization results for a charge or current-actuated active constrained layer (ACL) beam model with the electrostatic assumption

An infinite dimensional model for a three-layer active constrained layer (ACL) beam model, consisting of a piezoelectric elastic layer at the top and an elastic host layer at the bottom constraining a viscoelastic layer in the middle, is obtained for clamped-free boundary conditions by using a thorough variational approach. The Rao-Nakra thin compliant layer approximation is adopted to model the sandwich structure, and the electrostatic approach (magnetic effects are ignored) is assumed for the piezoelectric layer. Instead of the voltage actuation of the piezoelectric layer, the piezoelectric layer is proposed to be activated by a charge (or current) source. We show that, the closed-loop system with all mechanical feedback is shown to be uniformly exponentially stable. Our result is the outcome of the compact perturbation argument and a unique continuation result for the spectral problem which relies on the multipliers method. Finally, the modeling methodology of the paper is generalized to the multilayer ACL beams, and the uniform exponential stabilizability result is established analogously.
Adaptive algorithms for online convex optimization with long-term constraints

We present an adaptive online gradient descent algorithm to solve online convex optimization problems with long-term constraints, which are constraints that need to be satisfied when accumulated over a finite number of rounds T, but can be violated in intermediate rounds. For some user-defined trade-off parameter β ∈ (0; 1), the proposed algorithm achieves cumulative regret bounds of O(Tmax{β,1-β}) and O(T1-β/2), respectively for the loss and the constraint violations. Our results hold for convex losses, can handle arbitrary convex constraints and rely on a single computationally efficient algorithm. Our contributions generalize over the best known cumulative regret bounds of Mahdavi et al. (2012a), which are respectively O(T1/2) and O(T3/4) for general convex domains, and respectively O(T2/3) and O(T2/3) when the domain is further restricted to be a polyhedral set. We supplement the analysis with experiments validating the performance of our algorithm in practice.
Efficient High-Dimensional Entanglement Imaging with a Compressive-Sensing Double-Pixel Camera

Combining a technique that compresses information during measurement with standard detector arrays allows high-dimensional quantum entanglement to be efficiently characterized.
A high-order wideband direct solver for electromagnetic scattering from bodies of revolution

Abstract The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric conductors and dielectric bodies. Furthermore, these representations, and resulting integral equations, are fully stable in the static limit as ω → 0 in multiply connected geometries. In this paper, we present the first high-order accurate solver based on this representation for bodies of revolution. The resulting solver uses a Nystrom discretization of a one-dimensional generating curve and high-order integral equation methods for applying and inverting surface differentials. The accuracy and speed of the solvers are demonstrated in several numerical examples.
Modal regression using kernel density estimation: A review

We review recent advances in modal regression studies using kernel density estimation. Modal regression is an alternative approach for investigating relationship between a response variable and its covariates. Specifically, modal regression summarizes the interactions between the response variable and covariates using the conditional mode or local modes. We first describe the underlying model of modal regression and its estimators based on kernel density estimation. We then review the asymptotic properties of the estimators and strategies for choosing the smoothing bandwidth. We also discuss useful algorithms and similar alternative approaches for modal regression, and propose future direction in this field.
From r -linearized polynomial equations to r m -linearized polynomial equations

Abstract Let r be a prime power and q = r m . For 0 ≤ i ≤ m − 1 , let f i ∈ F r [ X ] be q-linearized and a i ∈ F q . Assume that z ∈ F ‾ r satisfies the equation ∑ i = 0 m − 1 a i f i ( z ) r i = 0 , where ∑ i = 0 m − 1 a i f i r i ∈ F q [ X ] is an r-linearized polynomial. It is shown that z satisfies a q-linearized polynomial equation with coefficients in F r . This result provides an explanation for numerous permutation polynomials previously obtained through computer search.
A New Formulation of the 3D Compressible Euler Equations with Dynamic Entropy: Remarkable Null Structures and Regularity Properties

We derive a new formulation of the 3D compressible Euler equations exhibiting remarkable null structures and regularity properties. Our results hold for an arbitrary equation of state (which yields the pressure in terms of the density and the entropy) in non-vacuum regions where the speed of sound is positive. Our work here is an extension of our prior joint work with J. Luk, in which we derived a similar new formulation in the special case of a barotropic fluid, that is, when the equation of state depends only on the density. The new formulation comprises covariant wave equations for the Cartesian components of the velocity and the logarithmic density coupled to a transport equation for the specific vorticity (defined to be vorticity divided by density), transport equations for the entropy and its gradient, and some additional transport–divergence–curl-type equations involving special combinations of the derivatives of the solution variables. The good geometric structures in the equations allow one to use the full power of the vectorfield method in treating the “wave part” of the system. In a forthcoming application, we will use the new formulation to give a sharp, constructive proof of finite-time shock formation, tied to the intersection of acoustic “wave characteristics,” for solutions with nontrivial vorticity and entropy at the singularity. In the present article, we derive the new formulation and provide an overview of the central role that it plays in the proof of shock formation. Although the equations are significantly more complicated than they are in the barotropic case, they enjoy many of same remarkable features, including: (i) all derivative-quadratic inhomogeneous terms are null forms relative to the acoustical metric, which is the Lorentzian metric driving the propagation of sound waves and (ii) the transport–divergence–curl-type equations allow one to show that the entropy is one degree more differentiable than the velocity and that the vorticity is exactly as differentiable as the velocity, assuming that the initial data enjoy the same gain in regularity. This represents a gain of one derivative compared to standard estimates. This gain of a derivative, which seems to be new for the entropy, is essential for closing the energy estimates in our forthcoming proof of shock formation, since the second derivatives of the entropy and the first derivatives of the vorticity appear as inhomogeneous terms in the wave equations.
Visualizing the "Heartbeat" of a City with Tweets

Describing the dynamics of a city is a crucial step to both understanding the human activity in urban environments and to planning and designing cities accordingly. Here, we describe the collective dynamics of New York City (NYC) and surrounding areas as seen through the lens of Twitter usage. In particular, we observe and quantify the patterns that emerge naturally from the hourly activities in different areas of NYC, and discuss how they can be used to understand the urban areas. Using a dataset that includes more than 6 million geolocated Twitter messages we construct a movie of the geographic density of tweets. We observe the diurnal “heartbeat” of the NYC area. The largest scale dynamics are the waking and sleeping cycle and commuting from residential communities to office areas in Manhattan. Hourly dynamics reflect the interplay of commuting, work and leisure, including whether people are preoccupied with other activities or actively using Twitter. Differences between weekday and weekend dynamics point to changes in when people wake and sleep, and engage in social activities. We show that by measuring the average distances to a central location one can quantify the weekly differences and the shift in behavior during weekends. We also identify locations and times of high Twitter activity that occur because of specific activities. These include early morning high levels of traffic as people arrive and wait at air transportation hubs, and on Sunday at the Meadowlands Sports Complex and Statue of Liberty. We analyze the role of particular individuals where they have large impacts on overall Twitter activity. Our analysis points to the opportunity to develop insight into both geographic social dynamics and attention through social media analysis. © 2015 Wiley Periodicals, Inc. Complexity, 2015
Parallelizable Stack Long Short-Term Memory.

Stack Long Short-Term Memory (StackLSTM) is useful for various applications such as parsing and string-to-tree neural machine translation, but it is also known to be notoriously difficult to parallelize for GPU training due to the fact that the computations are dependent on discrete operations. In this paper, we tackle this problem by utilizing state access patterns of StackLSTM to homogenize computations with regard to different discrete operations. Our parsing experiments show that the method scales up almost linearly with increasing batch size, and our parallelized PyTorch implementation trains significantly faster compared to the Dynet C++ implementation.
Submultiplicativity of the numerical radius of commuting matrices of order two

Abstract Denote by w ( T ) the numerical radius of a matrix T. An elementary proof is given to the fact that w ( A B ) ≤ w ( A ) w ( B ) for a pair of commuting matrices of order two, and characterization is given for the matrix pairs that attain the quality.
Decentralized Submodular Maximization: Bridging Discrete and Continuous Settings

In this paper, we showcase the interplay between discrete and continuous optimization in network-structured settings. We propose the first fully decentralized optimization method for a wide class of non-convex objective functions that possess a diminishing returns property. More specifically, given an arbitrary connected network and a global continuous submodular function, formed by a sum of local functions, we develop Decentralized Continuous Greedy (DCG), a message passing algorithm that converges to the tight (1-1/e) approximation factor of the optimum global solution using only local computation and communication. We also provide strong convergence bounds as a function of network size and spectral characteristics of the underlying topology. Interestingly, DCG readily provides a simple recipe for decentralized discrete submodular maximization through the means of continuous relaxations. Formally, we demonstrate that by lifting the local discrete functions to continuous domains and using DCG as an interface we can develop a consensus algorithm that also achieves the tight (1-1/e) approximation guarantee of the global discrete solution once a proper rounding scheme is applied.
Categoricity in multiuniversal classes

Abstract The third author has shown that Shelah's eventual categoricity conjecture holds in universal classes: class of structures closed under isomorphisms, substructures, and unions of chains. We extend this result to the framework of multiuniversal classes. Roughly speaking, these are classes with a closure operator that is essentially algebraic closure (instead of, in the universal case, being essentially definable closure). Along the way, we prove in particular that Galois (orbital) types in multiuniversal classes are determined by their finite restrictions, generalizing a result of the second author.
Closed Symmetric 2-Differentials of the 1st Kind

A closed symmetric differential of the 1st kind is a differential that locally is the product of closed holomorphic 1-forms. We show that closed symmetric 2-differentials of the 1st kind on a projective manifold $X$ come from maps of $X$ to cyclic or dihedral quotients of Abelian varieties and that their presence implies that the fundamental group of $X$ (case of rank 2) or of the complement $X\setminus E$ of a divisor $E$ with negative properties (case of rank 1) contains subgroup of finite index with infinite abelianization. Other results include: i) the identification of the differential operator characterizing closed symmetric 2-differentials on surfaces (which provides in this case a connection to flat Riemannian metrics) and ii) projective manifolds $X$ having symmetric 2-differentials $w$ that are the product of two closed meromorphic 1-forms are irregular, in fact if $w$ is not of the 1st kind (which can happen), then $X$ has a fibration $f:X \to C$ over a curve of genus $\ge 1$.
The impact of high density receptor clusters on VEGF signaling

Vascular endothelial growth factor (VEGF) signaling is involved in the process of blood vessel development and maintenance. Signaling is initiated by binding of the bivalent VEGF ligand to the membrane-bound receptors (VEGFR), which in turn stimulates receptor dimerization. Herein, we discuss experimental evidence that VEGF receptors localize in caveloae and other regions of the plasma membrane, and for other receptors, it has been shown that receptor clustering has an impact on dimerization and thus also on signaling. Overall, receptor clustering is part of a complex ecosystem of interactions and how receptor clustering impacts dimerization is not well understood. To address these questions, we have formulated the simplest possible model. We have postulated the existence of a single high affinity region in the cell membrane, which acts as a transient trap for receptors. We have defined an ODE model by introducing high- and low-density receptor variables and introduce the corresponding reactions from a realistic model of VEGF signal initiation. Finally, we use the model to investigate the relation between the degree of VEGFR concentration, ligand availability, and signaling. In conclusion, our simulation results provide a deeper understanding of the role of receptor clustering in cell signaling.
Solving Toda field theories and related algebraic and differential properties

Abstract Toda field theories are important integrable systems. They can be regarded as constrained WZNW models, and this viewpoint helps to give their explicit general solutions, especially when a Drinfeld–Sokolov gauge is used. The main objective of this paper is to carry out this approach of solving the Toda field theories for the classical Lie algebras, following Balog et al. (1990) [5] . In this process, we discover and prove some algebraic identities for principal minors of special matrices. The known elegant solutions of Leznov (1980) [10] fit in our scheme in the sense that they are the general solutions to our conditions discovered in this solving process. To prove this, we find and prove some differential identities for iterated integrals. It can be said that altogether our paper gives complete mathematical proofs for Leznov’s solutions.
Learning to Acquire Information.

We consider the problem of diagnosis where a set of simple observations are used to infer a potentially complex hidden hypothesis. Finding the optimal subset of observations is intractable in general, thus we focus on the problem of active diagnosis, where the agent selects the next most-informative observation based on the results of previous observations. We show that under the assumption of uniform observation entropy, one can build an implication model which directly predicts the outcome of the potential next observation conditioned on the results of past observations, and selects the observation with the maximum entropy. This approach enjoys reduced computation complexity by bypassing the complicated hypothesis space, and can be trained on observation data alone, learning how to query without knowledge of the hidden hypothesis.
When Was That Made

In this paper, we explore deep learning methods for estimating when the objects were made. Temporal estimation of objects is a challenging task which requires expertise in the object domain. With temporal information of objects, historian, genealogists, sociologist, archaeologist or conservationists can study the past through the objects. Toward this goal, we utilize features from existing deep networks and fine-tune new networks for temporal estimation task. The results demonstrate that the deep learning approach outperforms both a color-based baseline and visual data mining approach which is the previous state of the art method for the temporal estimation. To gain the insights into the deep network performance, we provide the analyses of neuron activations and their entropy including neuron temporal sensitivity, neuron activity and the correlation between discriminative parts from the deep network and the data mining approach. Finally, we demonstrate the potential of the temporal estimation pipeline for an interesting application such as fashion trend analysis.
Projections and Phase retrieval

Abstract We characterize collections of orthogonal projections for which it is possible to reconstruct a vector from the magnitudes of the corresponding projections. As a result we are able to show that in an M-dimensional real vector space a vector can be reconstructed from the magnitudes of its projections onto a generic collection of N ≥ 2 M − 1 subspaces. We also show that this bound is sharp when N = 2 k + 1 . The results of this paper answer a number of questions raised in [5] .
Deep TAMER: Interactive Agent Shaping in High-Dimensional State Spaces

While recent advances in deep reinforcement learning have allowed autonomous learning agents to succeed at a variety of complex tasks, existing algorithms generally require a lot oftraining data. One way to increase the speed at which agent sare able to learn to perform tasks is by leveraging the input of human trainers. Although such input can take many forms, real-time, scalar-valued feedback is especially useful in situations where it proves difficult or impossible for humans to provide expert demonstrations. Previous approaches have shown the usefulness of human input provided in this fashion (e.g., the TAMER framework), but they have thus far not considered high-dimensional state spaces or employed the use of deep learning. In this paper, we do both: we propose DeepTAMER, an extension of the TAMER framework that leverages the representational power of deep neural networks inorder to learn complex tasks in just a short amount of time with a human trainer. We demonstrate Deep TAMER’s success by using it and just 15 minutes of human-provided feedback to train an agent that performs better than humans on the Atari game of Bowling - a task that has proven difficult for even state-of-the-art reinforcement learning methods.
Aff2Vec: Affect-Enriched Distributional Word Representations.

Human communication includes information, opinions and reactions. Reactions are often captured by the affective-messages in written as well as verbal communications. While there has been work in affect modeling and to some extent affective content generation, the area of affective word distributions is not well studied. Synsets and lexica capture semantic relationships across words. These models, however, lack in encoding affective or emotional word interpretations. Our proposed model, Aff2Vec, provides a method for enriched word embeddings that are representative of affective interpretations of words. Aff2Vec outperforms the state-of-the-art in intrinsic word-similarity tasks. Further, the use of Aff2Vec representations outperforms baseline embeddings in downstream natural language understanding tasks including sentiment analysis, personality detection, and frustration prediction.
Stability of epsilon -Kernels.

Given a set P of n points in |R^d, an eps-kernel K subset P approximates the directional width of P in every direction within a relative (1-eps) factor. In this paper we study the stability of eps-kernels under dynamic insertion and deletion of points to P and by changing the approximation factor eps. In the first case, we say an algorithm for dynamically maintaining a eps-kernel is stable if at most O(1) points change in K as one point is inserted or deleted from P. We describe an algorithm to maintain an eps-kernel of size O(1/eps^{(d-1)/2}) in O(1/eps^{(d-1)/2} + log n) time per update. Not only does our algorithm maintain a stable eps-kernel, its update time is faster than any known algorithm that maintains an eps-kernel of size O(1/eps^{(d-1)/2}). Next, we show that if there is an eps-kernel of P of size k, which may be dramatically less than O(1/eps^{(d-1)/2}), then there is an (eps/2)-kernel of P of size O(min {1/eps^{(d-1)/2}, k^{floor(d/2)} log^{d-2} (1/eps)}). Moreover, there exists a point set P in |R^d and a parameter eps > 0 such that if every eps-kernel of P has size at least k, then any (eps/2)-kernel of P has size Omega(k^{floor(d/2)}).
Representation-Tame Algebras Need not be Homologically Tame

We show that even within the class of special biserial algebras, one of the most thoroughly studied classes of representation-tame finite dimensional algebras, the (left) big finitistic dimension may be strictly larger than the little. In fact, we find that the discrepancies Fin dim Λ – fin dim Λ fail to be bounded as Λ traces the special biserial algebras. More precisely: For every positive integer r, we exhibit a special biserial algebra Λ with the property that fin dim Λ = r+1, while Fin dim Λ=2r+1.
Photometric Mesh Optimization for Video-Aligned 3D Object Reconstruction

In this paper, we address the problem of 3D object mesh reconstruction from RGB videos. Our approach combines the best of multi-view geometric and data-driven methods for 3D reconstruction by optimizing object meshes for multi-view photometric consistency while constraining mesh deformations with a shape prior. We pose this as a piecewise image alignment problem for each mesh face projection. Our approach allows us to update shape parameters from the photometric error without any depth or mask information. Moreover, we show how to avoid a degeneracy of zero photometric gradients via rasterizing from a virtual viewpoint. We demonstrate 3D object mesh reconstruction results from both synthetic and real-world videos with our photometric mesh optimization, which is unachievable with either naive mesh generation networks or traditional pipelines of surface reconstruction without heavy manual post-processing.
Mathematics at the eve of a historic transition in biology

A century ago physicists and mathematicians worked in tandem and established quantum mechanism. Indeed, algebras, partial differential equations, group theory, and functional analysis underpin the foundation of quantum mechanism. Currently, biology is undergoing a historic transition from qualitative, phenomenological and descriptive to quantitative, analytical and predictive. Mathematics, again, becomes a driving force behind this new transition in biology.