cssi/SciSciGPT-SciSciNet huggingface dataset:
Submodular functions are noise stable

We show that all non-negative submodular functions have high noise-stability. As a consequence, we obtain a polynomial-time learning algorithm for this class with respect to any product distribution on {- 1,1}n (for any constant accuracy parameter e). Our algorithm also succeeds in the agnostic setting. Previous work on learning submodular functions required either query access or strong assumptions about the types of submodular functions to be learned (and did not hold in the agnostic setting).Additionally we give simple algorithms that efficiently release differentially private answers to all Boolean conjunctions and to all halfspaces with constant average error, subsuming and improving recent work due to Gupta, Hardt, Roth and Ullman (STOC 2011).
On the surjectivity of the map of spectra associated to a tensor-triangulated functor

We prove a few results about the map $Spc(F)$ induced on tensor-triangular spectra by a tensor-triangulated functor $F$. First, $F$ is conservative if and only if $Spc(F)$ is surjective on closed points. Second, if $F$ detects tensor-nilpotence of morphisms then $Spc(F)$ is surjective on the whole spectrum. In fact, surjectivity of $Spc(F)$ is equivalent to $F$ detecting the nilpotence of some class of morphisms, namely those morphisms which are nilpotent on their cone.
R&D of commercially manufactured large GEM foils

Many experiments are currently using or proposing to use large area GEM foils in their detectors, which is creating a need for commercially available GEM foils. Currently CERN is the only main distributor of GEM foils, however with the growing interest in GEM technology keeping up with the increasing demand for GEM foils will be difficult. Thus the commercialization of GEM foils has been established by Tech-Etch Inc. of Plymouth, MA, USA using the single-mask technique, which is capable of producing GEM foils over a meter long. To date Tech-Etch has successfully manufactured 10 × 10 cm2 and 40 × 40 cm2 GEM foils. We will report on the electrical and geometrical properties, along with the inner and outer hole diameter size uniformity of these foils. Furthermore, Tech-Etch has now begun producing even larger GEM foils of 50 × 50 cm2, and are currently looking into how to accommodate GEM foils on the order of one meter long. The Tech-Etch foils were found to have excellent electrical properties. The measured mean optical properties were found to reflect the desired parameters and are consistent with those measured in double-mask GEM foils, as well as single-mask GEM foils produced at CERN. They also show good hole diameter uniformity over the active area.
Curvilinear Mesh Adaptation Using Radial Basis Function Interpolation and Smoothing

We present a new iterative technique based on radial basis function (RBF) interpolation and smoothing for the generation and smoothing of curvilinear meshes from straight-sided or other curvilinear meshes. Our technique approximates the coordinate deformation maps in both the interior and boundary of the curvilinear output mesh by using only scattered nodes on the boundary of the input mesh as data sites in an interpolation problem. Our technique produces high-quality meshes in the deformed domain even when the deformation maps are singular due to a new iterative algorithm based on modification of the RBF shape parameter. Due to the use of RBF interpolation, our technique is applicable to both 2D and 3D curvilinear mesh generation without significant modification.
How robust are reconstruction thresholds for community detection

The stochastic block model is one of the oldest and most ubiquitous models for studying clustering and community detection. In an exciting sequence of developments, motivated by deep but non-rigorous ideas from statistical physics, Decelle et al. conjectured a sharp threshold for when community detection is possible in the sparse regime. Mossel, Neeman and Sly and Massoulie proved the conjecture and gave matching algorithms and lower bounds. Here we revisit the stochastic block model from the perspective of semirandom models where we allow an adversary to make `helpful' changes that strengthen ties within each community and break ties between them. We show a surprising result that these `helpful' changes can shift the information-theoretic threshold, making the community detection problem strictly harder. We complement this by showing that an algorithm based on semidefinite programming (which was known to get close to the threshold) continues to work in the semirandom model (even for partial recovery). This suggests that algorithms based on semidefinite programming are robust in ways that any algorithm meeting the information-theoretic threshold cannot be. These results point to an interesting new direction: Can we find robust, semirandom analogues to some of the classical, average-case thresholds in statistics? We also explore this question in the broadcast tree model, and we show that the viewpoint of semirandom models can help explain why some algorithms are preferred to others in practice, in spite of the gaps in their statistical performance on random models.
Free products and the lack of state-preserving approximations of nuclear $C^{*}$-algebras

Let $A$ be a homogeneous C*-algebra and $\phi$ a state on $A.$ We show that if $\phi$ satisfies a certain faithfulness condition, then there is a net of finite-rank, unital completely positive, $\phi$-preserving maps on $A$ that tend to the identity pointwise. This combined with results of Ricard and Xu show that the reduced free product of homogeneous C*-algebras with respect to these states have the completely contractive approximation property. We also give an example of a faithful state on $M_2\otimes C[0,1]$ for which no such state-preserving approximation of the identity map exists, thus answering a question of Ricard and Xu.
Universal Simulation of Directed Systems in the Abstract Tile Assembly Model Requires Undirectedness

As a mathematical model of tile-based self-assembling systems, Winfree's abstract Tile Assembly Model (aTAM) has proven to be a remarkable platform for studying and understanding the behaviors and powers of self-assembling systems. Furthermore, as it is capable of Turing universal computation, the aTAM allows algorithmic self-assembly, in which the components can be designed so that the rules governing their behaviors force them to inherently execute prescribed algorithms as they combine. This power has yielded a wide variety of theoretical results in the aTAM utilizing algorithmic self-assembly to design systems capable of performing complex computations and forming extremely intricate structures. Adding to the completeness of the model, in FOCS 2012 the aTAM was shown to also be intrinsically universal, which means that there exists one single tile set such that for any arbitrary input aTAM system, that tile set can be configured into a "seed" structure which will then cause self-assembly using that tile set to simulate the input system, capturing its full dynamics modulo only a scale factor. However, the "universal simulator" of that result makes use of nondeterminism in terms of the tiles placed in several key locations when different assembly sequences are followed. This nondeterminism remains even when the simulator is simulating a system which is directed, meaning that it has exactly one unique terminal assembly and for any given location, no matter which assembly sequence is followed, the same tile type is always placed there. The question which then arose was whether or not that nondeterminism is fundamentally required, and if any universal simulator must in fact utilize more nondeterminism than directed systems when simulating them. In this paper, we answer that question in the affirmative: the class of directed systems in the aTAM is not intrinsically universal, meaning there is no universal simulator for directed systems which itself is always directed. This result provides a powerful insight into the role of nondeterminism in self-assembly, which is itself a fundamentally nondeterministic process occurring via unguided local interactions. Furthermore, to achieve this result we leverage powerful results of computational complexity hierarchies, including tight bounds on both best and worst-case complexities of decidable languages, to tailor design systems with precisely controllable space resources available to computations embedded within them. We also develop novel techniques for designing systems containing subsystems with disjoint, mutually exclusive computational powers. The main result will be important in the development of future simulation systems, and the supporting design techniques and lemmas will provide powerful tools for the development of future aTAM systems as well as proofs of their computational abilities.
NAK for Ext and ascent of module structures

We investigate the interplay between properties of Ext modules and the ascent of module structures along local ring homomorphisms. Specifically, let φ : (R,m, k) → (S,mS, k) be a flat local ring homomorphism. We show that if M is a finitely generated R-module such that ExtR(S,M) satisfies NAK (e.g. if ExtR(S,M) is finitely generated over S) for i = 1, . . . , dimR(M), then ExtR(S,M) = 0 for all i = 0 and M has an S-module structure that is compatible with its R-module structure via φ. We provide explicit computations of ExtR(S,M) to indicate how large it can be when M does not have a compatible S-module structure.
Signatures of Young Planets in the Continuum Emission from Protostellar Disks

Many protostellar disks show central cavities, rings, or spiral arms likely caused by low-mass stellar or planetary companions, yet few such features are conclusively tied to bodies embedded in the disks. We note that even small features on the disk's surface cast shadows, because the starlight grazes the surface. We therefore focus on accurately computing the disk's thickness, which depends on its temperature. We present models with temperatures set by the balance between starlight heating and radiative cooling, that are also in vertical hydrostatic equilibrium. The planet has 20, 100, or 1000~M$_\oplus$, ranging from barely enough to perturb the disk significantly, to clearing a deep tidal gap. The hydrostatic balance strikingly alters the model disk's appearance. The planet-carved gap's outer wall puffs up under starlight heating, throwing a shadow across the disk beyond. The shadow appears in scattered light as a dark ring that could be mistaken for a gap opened by another more distant planet. The surface brightness contrast between outer wall and shadow for the 1000-M$_\oplus$ planet is an order of magnitude greater than a model neglecting the temperature disturbances. The shadow is so deep it largely hides the planet-launched spiral wave's outer arm. Temperature gradients are such that outer low-mass planets undergoing orbital migration will converge within the shadow. Furthermore the temperature perturbations affect the shape, size, and contrast of features at millimeter and centimeter wavelengths. Thus radiative heating and cooling are key to the appearance of protostellar disks with embedded planets.
Evidence against tetrapod-wide digit identities and for a limited frame shift in bird wings

In crown group tetrapods, individual digits are homologized in relation to a pentadactyl ground plan. However, testing hypotheses of digit homology is challenging because it is unclear whether digits represent distinct and conserved gene regulatory states. Here we show dramatic evolutionary dynamism in the gene expression profiles of digits, challenging the notion that five digits have conserved developmental identities across amniotes. Transcriptomics shows diversity in the patterns of gene expression differentiation of digits, although the anterior-most digit of the pentadactyl limb has a unique, conserved expression profile. Further, we identify a core set of transcription factors that are differentially expressed among the digits of amniote limbs; their spatial expression domains, however, vary between species. In light of these results, we reevaluate the frame shift hypothesis of avian wing evolution and conclude only the identity of the anterior-most digit has shifted position, suggesting a 1,3,4 digit identity in the bird wing.
An improved analysis of the ER-SpUD dictionary learning algorithm

In dictionary learning we observe Y = AX + E for some Y in R^{n*p}, A in R^{m*n}, and X in R^{m*p}, where p >= max{n, m}, and typically m >=n. The matrix Y is observed, and A, X, E are unknown. Here E is a "noise" matrix of small norm, and X is column-wise sparse. The matrix A is referred to as a dictionary, and its columns as atoms. Then, given some small number p of samples, i.e. columns of Y , the goal is to learn the dictionary A up to small error, as well as the coefficient matrix X. In applications one could for example think of each column of Y as a distinct image in a database. The motivation is that in many applications data is expected to sparse when represented by atoms in the "right" dictionary A (e.g. images in the Haar wavelet basis), and the goal is to learn A from the data to then use it for other applications. Recently, the work of [Spielman/Wang/Wright, COLT'12] proposed the dictionary learning algorithm ER-SpUD with provable guarantees when E = 0 and m = n. That work showed that if X has independent entries with an expected Theta n non-zeroes per column for 1/n ~ n^2 log^2 n with high probability ER-SpUD outputs matrices A', X' which equal A, X up to permuting and scaling columns (resp. rows) of A (resp. X). They conjectured that p >~ n log n suffices, which they showed was information theoretically necessary for any algorithm to succeed when Theta =~ 1/n. Significant progress toward showing that p >~ n log^4 n might suffice was later obtained in [Luh/Vu, FOCS'15]. In this work, we show that for a slight variant of ER-SpUD, p >~ n log(n/delta) samples suffice for successful recovery with probability 1 - delta. We also show that without our slight variation made to ER-SpUD, p >~ n^{1.99} samples are required even to learn A, X with a small success probability of 1/ poly(n). This resolves the main conjecture of [Spielman/Wang/Wright, COLT'12], and contradicts a result of [Luh/Vu, FOCS'15], which claimed that p >~ n log^4 n guarantees high probability of success for the original ER-SpUD algorithm.
Monotonicity of dissipative flow networks renders robust maximum profit problem tractable: General analysis and application to natural gas flows

We consider general, steady, balanced flows of a commodity over a network where an instance of the network flow is characterized by edge flows and nodal potentials. Edge flows in and out of a node are assumed to be conserved, thus representing standard network flow relations. The remaining freedom in the flow distribution over the network is constrained by potentials so that the difference of potentials at the head and the tail of an edge is expressed as a nonlinear function of the edge flow. We consider networks with nodes divided into three categories: sources that inject flows into the network for a certain cost, terminals which buy the flow at a fixed price, and “internal” customers each withdrawing an uncertain amount of flow, which has a priority and thus it is not priced. Our aim is to operate the network such that the profit, i.e. amount of flow sold to terminals minus cost of injection, is maximized, while maintaining the potentials within prescribed bounds. We also require that the operating point is robust with respect to the uncertainty of internal customers' withdrawal. In this setting we prove that potentials are monotonic functions of the withdrawals. This observation enables us to replace in the maximum profit optimization infinitely many nodal constraints, each representing a particular value of withdrawal uncertainty, by only two constraints representing the cases where all nodes with uncertainty consume their minimum and maximum amounts respectively. We illustrate this general result on an example of the natural gas transmission network. In this enabling example, gas withdrawals by internal customers are assumed uncertain, the potentials are gas pressures squared, the potential drop functions are bilinear in the flow and its intensity with an added tunable factor representing compression.
Particle Acceleration and Plasma Dynamics during Magnetic Reconnection in the Magnetically Dominated Regime

Magnetic reconnection is thought to be the driver for many explosive phenomena in the universe. The energy release and particle acceleration during reconnection have been proposed as a mechanism for producing high-energy emissions and cosmic rays. We carry out two- and three-dimensional (3D) kinetic simulations to investigate relativistic magnetic reconnection and the associated particle acceleration. The simulations focus on electron–positron plasmas starting with a magnetically dominated, force-free current sheet (σ ≡ B2 / (4πnemec2) >> 1). For this limit, we demonstrate that relativistic reconnection is highly efficient at accelerating particles through a first-order Fermi process accomplished by the curvature drift of particles along the electric field induced by the relativistic flows. This mechanism gives rise to the formation of hard power-law spectra f α (γ - 1)-p and approaches p = 1 for sufficiently large σ and system size. Eventually most of the available magnetic free energy is converted into nonthermal particle kinetic energy. An analytic model is presented to explain the key results and predict a general condition for the formation of power-law distributions. The development of reconnection in these regimes leads to relativistic inflow and outflow speeds and enhanced reconnection rates relative to nonrelativistic regimes. In the 3Dmore » simulation, the interplay between secondary kink and tearing instabilities leads to strong magnetic turbulence, but does not significantly change the energy conversion, reconnection rate, or particle acceleration. This paper suggests that relativistic reconnection sites are strong sources of nonthermal particles, which may have important implications for a variety of high-energy astrophysical problems.« less
Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces

AtheoremofLusinstatesthateveryBorelfunctiononRisequalalmosteverywheretothederivative of a continuous function. This result was later generalized to R n in works of Alberti and Moonens-Pfeer. In this note, we prove direct analogs of these results on a large class of metric measure spaces, those with doubling measures and Poincare inequalities, which admit a form of dierentiation by a famous theorem of Cheeger.
Smoothed Online Convex Optimization in High Dimensions via Online Balanced Descent

We study Smoothed Online Convex Optimization, a version of online convex optimization where the learner incurs a penalty for changing her actions between rounds. Given a $\Omega(\sqrt{d})$ lower bound on the competitive ratio of any online algorithm, where $d$ is the dimension of the action space, we ask under what conditions this bound can be beaten. We introduce a novel algorithmic framework for this problem, Online Balanced Descent (OBD), which works by iteratively projecting the previous point onto a carefully chosen level set of the current cost function so as to balance the switching costs and hitting costs. We demonstrate the generality of the OBD framework by showing how, with different choices of "balance," OBD can improve upon state-of-the-art performance guarantees for both competitive ratio and regret, in particular, OBD is the first algorithm to achieve a dimension-free competitive ratio, $3 + O(1/\alpha)$, for locally polyhedral costs, where $\alpha$ measures the "steepness" of the costs. We also prove bounds on the dynamic regret of OBD when the balance is performed in the dual space that are dimension-free and imply that OBD has sublinear static regret.
Modules of constant Jordan type, pullbacks of bundles and generic kernel filtrations

Abstract Let kE denote the group algebra of an elementary abelian p-group of rank r over an algebraically closed field of characteristic p. We investigate the functors F i from kE-modules of constant Jordan type to vector bundles on P r − 1 ( k ) , constructed by Benson and Pevtsova. For a kE-module M of constant Jordan type, we show that restricting the sheaf F i ( M ) to a dimension s − 1 linear subvariety of P r − 1 ( k ) is equivalent to restricting M along a corresponding rank s shifted subgroup of kE and then applying F i . In the case r = 2 , we examine the generic kernel filtration of M in order to show that F i ( M ) may be computed on certain subquotients of M whose Loewy lengths are bounded in terms of i. More precise information is obtained by applying similar techniques to the nth power generic kernel filtration of M. The latter approach also allows us to generalise our results to higher ranks r.
Robust decentralized voltage control of DC-DC converters with applications to power sharing and ripple sharing

This paper addresses the problem of output voltage regulation for multiple DC-DC converters connected to a grid, and prescribes a robust scheme for sharing power among different sources. Also it develops a method for sharing 120 Hz ripple among DC power sources in a prescribed proportion, which accommodates the different capabilities of DC power sources to sustain the ripple. We present a decentralized control architecture, where a nested (inner-outer) control design is used at every converter. An interesting aspect of the proposed design is that the analysis and design of the entire multi-converter system can be done using an equivalent single converter system, where the multi-converter system inherits the performance and robustness achieved by a design for the single-converter system. Another key aspect of this work is that the voltage regulation problem is addressed as a disturbance-rejection problem, where unknown load current is viewed as an external signal, and thus, no prior information is required on the nominal loading conditions. The control design is obtained using robust optimal-control framework. Case studies presented show the enhanced performance of prescribed optimal controllers.
INTRINSIC FLAT ARZELA-ASCOLI THEOREMS

In this paper two Arzela-Ascoli Theorems are proven: one for uniformly Lip- schitz functions whose domains are converging in the intrinsic flat sense, and one for se- quences of uniformly local isometries between spaces which are converging in the intrinsic flat sense. A basic Bolzano-Weierstrass Theorem is proven fo r sequences of points in such sequences of spaces. In addition it is proven that when a sequence of manifolds has a pre- compact intrinsic flat limit then the metric completion of th e limit is the Gromov-Hausdorff limit of regions within those manifolds. Open problems with suggested applications are provided throughout the paper.
On cohomology theory of (di)graphs

To a digraph with a choice of certain integral basis, we construct a CW complex, whose integral singular cohomology is canonically isomorphic to the path cohomology of the digraph as introduced in \cite{GLMY}. The homotopy type of the CW complex turns out to be independent of the choice of basis. After a very brief discussion of functoriality, this construction immediately implies some of the expected but perhaps combinatorially subtle properties of the digraph cohomology and homotopy proved very recently \cite{GLMY2}. Furthermore, one gets a very simple expected formula for the cup product of forms on the digraph. On the other hand, we present an approach of using sheaf theory to reformulate (di)graph cohomologies. The investigation of the path cohomology from this framework, leads to a subtle version of Poincare lemma for digraphs, which follows from the construction of the CW complex.
Weakly Nonlinear Time-Adiabatic Theory

We revisit the time-adiabatic theorem of quantum mechanics and show that it can be extended to weakly nonlinear situations, that is to nonlinear Schrodinger equations in which either the nonlinear coupling constant or, equivalently, the solution is asymptotically small. To this end, a notion of criticality is introduced at which the linear bound states stay adiabatically stable, but nonlinear effects start to show up at leading order in the form of a slowly varying nonlinear phase modulation. In addition, we prove that in the same regime a class of nonlinear bound states also stays adiabatically stable, at least in terms of spectral projections.
Learning pseudo-Boolean k-DNF and submodular functions

We prove that any submodular function f: {0, 1}n → {0, 1,..., k} can be represented as a pseudo-Boolean 2k-DNF formula. Pseudo-Boolean DNFs are a natural generalization of DNF representation for functions with integer range. Each term in such a formula has an associated integral constant. We show that an analog of Hastad's switching lemma holds for pseudo-Boolean k-DNFs if all constants associated with the terms of the formula are bounded.This allows us to generalize Mansour's PAC-learning algorithm for k-DNFs to pseudo-Boolean k-DNFs, and hence gives a PAC-learning algorithm with membership queries under the uniform distribution for submodular functions of the form f: {0, 1}n → {0, 1,..., k}. Our algorithm runs in time polynomial in n,
On the Sensitivity of Shape Fitting Problems

In this article, we study shape fitting problems, epsilon-coresets, and total sensitivity. We focus on the (j,k)-projective clustering problems, including k-median/k-means, k-line clustering, j-subspace approximation, and the integer (j,k)-projective clustering problem. We derive upper bounds of total sensitivities for these problems, and obtain epsilon-coresets using these upper bounds. Using a dimension-reduction type argument, we are able to greatly simplify earlier results on total sensitivity for the k-median/k-means clustering problems, and obtain positively-weighted epsilon-coresets for several variants of the (j,k)-projective clustering problem. We also extend an earlier result on epsilon-coresets for the integer (j,k)-projective clustering problem in fixed dimension to the case of high dimension.
Efficient probabilistic inference with partial ranking queries

Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as smoothness, sparsity, or probabilistic independence about these underlying distributions. We approach the modeling problem from the computational principle that one should make structural assumptions which allow for efficient calculation of typical probabilistic queries. For ranking models, "typical" queries predominantly take the form of partial ranking queries (e.g., given a user's top-k favorite movies, what are his preferences over remaining movies?). In this paper, we argue that riffled independence factorizations proposed in recent literature [7, 8] are a natural structural assumption for ranking distributions, allowing for particularly efficient processing of partial ranking queries.
Normal and Jones surfaces of knots

We describe a normal surface algorithm that decides whether a knot, with known degree of the colored Jones polynomial, satisfies the Strong Slope Conjecture. We also discuss possible simplification...
Eisenstein Series of Weight One, q-Averages of the 0-Logarithm and Periods of Elliptic Curves

For any elliptic curve E over \(k\subset {\mathbb {R}}\) with \(E({\mathbb {C}})={\mathbb {C}}^\times /q^{{\mathbb {Z}}}\), \(q=e^{2\pi iz}, \mathrm{Im}(z)>0\), we study the q-average \(D_{0,q}\), defined on \(E({\mathbb {C}})\), of the function \(D_0(z) = \mathrm{Im}(z/(1-z))\). Let \(\Omega ^+(E)\) denote the real period of E. We show that there is a rational function \(R \in {\mathbb {Q}}(X_1(N))\) such that for any non-cuspidal real point \(s\in X_1(N)\) (which defines an elliptic curve E(s) over \({\mathbb {R}}\) together with a point P(s) of order N), \(\pi D_{0,q}(P(s))\) equals \(\Omega ^+(E(s))R(s)\). In particular, if s is \({\mathbb {Q}}\)-rational point of \(X_1(N)\), a rare occurrence according to Mazur, R(s) is a rational number.
An extension of the Koplienko–Neidhardt trace formulae

Abstract Koplienko (Sibirsk. Mat. Zh. 25(5) (1984) 62) found a trace formula for perturbations of self-adjoint operators by operators of Hilbert Schmidt class S 2 . A similar formula in the case of unitary operators was obtained by Neidhardt (Math. Nachr. 138 (1988) 7). In this paper we improve their results and obtain sharp conditions under which the Koplienko–Neidhardt trace formulae hold.
Learning to Inpaint for Image Compression

We study the design of deep architectures for lossy image compression. We present two architectural recipes in the context of multi-stage progressive encoders and empirically demonstrate their importance on compression performance. Specifically, we show that: 1) predicting the original image data from residuals in a multi-stage progressive architecture facilitates learning and leads to improved performance at approximating the original content and 2) learning to inpaint (from neighboring image pixels) before performing compression reduces the amount of information that must be stored to achieve a high-quality approximation. Incorporating these design choices in a baseline progressive encoder yields an average reduction of over 60% in file size with similar quality compared to the original residual encoder.
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms

Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic programming. The recent advances in various topics of modern optimization have also been revamping the area of machine learning. Motivated by the crucial role of optimization theory in the design, analysis, control and operation of real-world systems, this tutorial paper offers a detailed overview of some major advances in this area, namely conic optimization and its emerging applications. First, we discuss the importance of conic optimization in different areas. Then, we explain seminal results on the design of hierarchies of convex relaxations for a wide range of nonconvex problems. Finally, we study different numerical algorithms for large-scale conic optimization problems.
An Efficient Evolutionary Algorithm for Minimum Cost Submodular Cover.

In this paper, the Minimum Cost Submodular Cover problem is studied, which is to minimize a modular cost function such that the monotone submodular benefit function is above a threshold. For this problem, an evolutionary algorithm EASC is introduced that achieves a constant, bicriteria approximation in expected polynomial time; this is the first polynomial-time evolutionary approximation algorithm for Minimum Cost Submodular Cover. To achieve this running time, ideas motivated by submodularity and monotonicity are incorporated into the evolutionary process, which likely will extend to other submodular optimization problems. In a practical application, EASC is demonstrated to outperform the greedy algorithm and converge faster than competing evolutionary algorithms for this problem.
Rational dilation of tetrablock contractions revisited

Abstract A classical result of Sz.-Nagy asserts that a Hilbert-space contraction operator T can be lifted to an isometry V. A more general multivariable setting of recent interest for these ideas is the case where (i) the unit disk is replaced by a certain domain contained in C 3 (called the tetrablock), (ii) the contraction operator T is replaced by a commutative triple ( T 1 , T 2 , T ) of Hilbert-space operators having E as a spectral set (a tetrablock contraction). The rational dilation question for this setting is whether a tetrablock contraction ( T 1 , T 2 , T ) can be lifted to a tetrablock isometry ( V 1 , V 2 , V ) (a commutative operator tuple which extends to a tetrablock-unitary tuple ( U 1 , U 2 , U ) —a commutative tuple of normal operators with joint spectrum contained in the distinguished boundary of the tetrablock). We discuss necessary conditions for a tetrablock contraction to have a tetrablock-isometric lift. We present an example of a tetrablock contraction which does have a tetrablock-isometric lift but violates a condition previously thought to be necessary for the existence of such a lift. Thus the question of whether a tetrablock contraction always has a tetrablock-isometric lift appears to be unresolved at this time.
Frontier Markets: Punching Below their Weight? A Risk Parity Perspective on Asset Allocation

Are frontier markets the next emerging markets? And if so, should global equity investors include them in their portfolios? From a risk parity perspective, investors could benefit from a frontier markets allocation well in excess of the market weight of the asset class. A risk parity portfolio tends to outperform a market cap-weighted portfolio during periods of positive equity returns while delivering comparable returns during crisis periods. Even if portfolio managers could not follow a risk parity asset allocation strategy due to benchmark tracking considerations, overweighting frontier markets could help them outperform their benchmarks during upside periods without increasing downside risks significantly.
Counting using Hall algebras III: Quivers with potentials

For a quiver with potential, we can associate a vanishing cycle to each representation space. If there is a nice torus action on the potential, the vanishing cycles can be expressed in terms of truncated Jacobian algebras. We study how these vanishing cycles change under the mutation of Derksen-Weyman-Zelevinsky. The wall-crossing formula leads to a categorification of quantum cluster algebras under some assumption. This is a special case of A. Efimov's result, but our approach is more concrete and down-to-earth. We also obtain a counting formula relating the representation Grassmannians under sink-source reflections.
Germline Maintenance Through the Multifaceted Activities of GLH/Vasa in Caenorhabditis elegans P Granules

Vasa homologs are ATP-dependent DEAD-box helicases, multipotency factors, and critical components that specify and protect the germline. They regulate translation, amplify piwi-interacting RNAs (piRNAs), and act as RNA solvents; however, the limited availability of mutagenesis-derived alleles and their wide range of phenotypes have complicated their analysis. Now, with clustered regularly interspaced short palindromic repeats (CRISPR/Cas9), these limitations can be mitigated to determine why protein domains have been lost or retained throughout evolution. Here, we define the functional motifs of GLH-1/Vasa in Caenorhabditis elegans using 28 endogenous, mutant alleles. We show that GLH-1’s helicase activity is required to retain its association with P granules. GLH-1 remains in P granules when changes are made outside of the helicase and flanking domains, but fertility is still compromised. Removal of the glycine-rich repeats from GLH proteins progressively diminishes P-granule wetting-like interactions at the nuclear periphery. Mass spectrometry of GLH-1-associated proteins implies conservation of a transient piRNA-amplifying complex, and reveals a novel affinity between GLH-1 and three structurally conserved PCI (26S Proteasome Lid, COP9, and eIF3) complexes or “zomes,” along with a reciprocal aversion for assembled ribosomes and the 26S proteasome. These results suggest that P granules compartmentalize the cytoplasm to exclude large protein assemblies, effectively shielding associated transcripts from translation and associated proteins from turnover. Within germ granules, Vasa homologs may act as solvents, ensuring mRNA accessibility by small RNA surveillance and amplification pathways, and facilitating mRNA export through germ granules to initiate translation.
The impact of BMI on mental health: Further evidence from genetic markers

Abstract We estimate the effect of BMI on mental health for young adults and elderly individuals using data from the National Longitudinal Study of Adolescent Health and the Health & Retirement Study. To tackle confounding due to unobserved factors, we exploit variation in a polygenic score (PGS) for BMI within two related econometric methods that differ in the assumptions they employ. First, we use the BMI PGS as an IV and adjust for PGSs for other factors (depression and educational attainment) that may invalidate this IV. We find a large statistically significant effect of BMI on mental health for the elderly: a 5 kg/m2 increase in BMI (a difference equivalent to moving from overweight to obese) increases the probability of depression by 29 %. In contrast, for young adults the IV estimates are statistically and economically insignificant. We show that IV estimates likely have to be interpreted as identifying a weighted average of effects of BMI on mental health mostly for compliers on the upper quantiles of the BMI distribution. Second, we use the BMI PGS as an “imperfect” IV and estimate an upper bound on the average treatment effect for the population. The estimated upper bounds are consistent with the conclusions from the IV estimates.
Groups acting acylindrically on hyperbolic spaces

The goal of this article is to survey some recent developments in the study of groups acting on hyperbolic spaces. We focus on the class of acylindrically hyperbolic groups; it is broad enough to include many examples of interest, yet a significant part of the theory of hyperbolic and relatively hyperbolic groups can be generalized in this context. In particular, we discuss group theoretic Dehn filling and small cancellation theory in acylindrically hyperbolic groups. Many results discussed here rely on the new generalization of relative hyperbolicity based on the notion of a hyperbolically embedded subgroup.
Power-efficient ReRAM-aware CNN model generation

Abstract This is the first work to propose a co-design approach for generation of the network model of a convolutional neural network (CNN) and its implementation using the ReRAM technology to achieve power efficiency. State-of-the-art in this area is based on implementation of an already fixed CNN model. It uses parallel crossbar structures to achieve a desired precision quantization of the edge weights using the limited precision provided by individual ReRAM devices. In contrast, in this work we keep the ReRAM crossbar structure in mind during model generation, and target altering a base CNN model such that the resulting implementation will be more power efficient. This is by means of eliminating the parallel crossbars as much as possible, thus reducing the number of required analog-to-digital and digital-to-analog converters which are dominant sources of power consumption. We study four architectural techniques which are applicable to convolutional or fully-connected layers in a CNN to alter the network model, thus enabling it to work with lower precision of the weights with negligible loss in accuracy. In our experiments, we achieve at least 50% power savings with almost no loss in accuracy for popular CNNs compared to ReRAM implementation of the base model. Further, we propose 2 independent power reduction techniques and investigate the impact of replacing the conventional analog Sigmoid activation function with a simpler design in digital mode on power. The results show that the power consumption of the network can be further decreased to at least 30% of the base model.
Identification of Spikes in Time Series

Identification of unexpectedly high values in a time series is useful for epidemiologists, economists, and other social scientists interested in the effect of an exposure spike on an outcome variable. However, the best method to identify spikes in time series is not known. This paper aims to fill this gap by testing the performance of several spike detection methods in a simulation setting. We created simulations parameterized by monthly violence rates in nine California cities that represented different series features, and randomly inserted spikes into the series. We then compared the ability to detect spikes of the following methods: ARIMA modeling, Kalman filtering and smoothing, wavelet modeling with soft thresholding, and an iterative outlier detection method. We varied the magnitude of spikes from 10-50% of the mean rate over the study period and varied the number of spikes inserted from 1 to 10. We assessed performance of each method using sensitivity and specificity. The Kalman filtering and smoothing procedure had the best overall performance. We applied Kalman filtering and smoothing to the monthly violence rates in nine California cities and identified spikes in the rate over the 2005-2012 period.
CaATP prolongs strong actomyosin binding and promotes futile myosin stroke.

Calcium plays an essential role in muscle contraction, regulating actomyosin interaction by binding troponin of thin filaments. There are several buffers for calcium in muscle, and those buffers play a crucial role in the formation of the transient calcium wave in sarcomere upon muscle activation. One such calcium buffer in muscle is ATP. ATP is a fuel molecule, and the important role of MgATP in muscle is to bind myosin and supply energy for the power stroke. Myosin is not a specific ATPase, and CaATP also supports myosin ATPase activity. The concentration of CaATP in sarcomeres reaches 1% of all ATP available. Since 294 myosin molecules form a thick filament, naive estimation gives three heads per filament with CaATP bound, instead of MgATP. We found that CaATP dissociates actomyosin slower than MgATP, thus increasing the time of the strong actomyosin binding. The rate of the basal CaATPase is faster than that of MgATPase, myosin readily produces futile stroke with CaATP. When calcium is upregulated, as in malignant hyperthermia, kinetics of myosin and actomyosin interaction with CaATP suggest that myosin CaATPase activity may contribute to observed muscle rigidity and enhanced muscle thermogenesis.
Shareholder Litigation Rights and Capital Structure Decisions

Abstract We exploit the staggered adoption of the universal demand (UD) laws across U.S. states, which impedes shareholder rights to initiate derivative lawsuits, as a quasi-natural experiment to examine the relation between shareholder litigation rights and firm capital structures. We find that weaker shareholder litigation rights due to the UD laws adoption lead to higher financial leverage, which enhances firm value. Furthermore, the positive relation between the UD laws adoption and financial leverage is more pronounced for firms exposed to higher shareholder litigation risk ex ante or financially constrained firms. Our evidence is consistent with lower shareholder litigation threats motivating firms to increase financial leverage.
When Social Sensing Meets Edge Computing: Vision and Challenges

This paper overviews the state of the art, research challenges, and future opportunities in an emerging research direction: Social Sensing based Edge Computing (SSEC). Social sensing has emerged as a new sensing application paradigm where measurements about the physical world are collected from humans or from devices on their behalf. The advent of edge computing pushes the frontier of computation, service, and data along the cloud-to-things continuum. The merging of these two technical trends generates a set of new research challenges that need to be addressed. In this paper, we first define the new SSEC paradigm that is motivated by a few underlying technology trends. We then present a few representative real-world case studies of SSEC applications and several key research challenges that exist in those applications. Finally, we envision a few exciting research directions in future SSEC. We hope this paper will stimulate discussions of this emerging research direction in the community.
Quantified Uncertainty of Flexible Protein-Protein Docking Algorithms.

The strength or weakness of an algorithm is ultimately governed by the confidence of its result. When the domain of the problem is large (e.g. traversal of a high-dimensional space), a perfect solution cannot be obtained, so approximations must be made. These approximations often lead to a reported quantity of interest (QOI) which varies between runs, decreasing the confidence of any single run. When the algorithm further computes this final QOI based on uncertain or noisy data, the variability (or lack of confidence) of the final QOI increases. Unbounded, these two sources of uncertainty (algorithmic approximations and uncertainty in input data) can result in a reported statistic that has low correlation with ground truth. In biological applications, this is especially applicable, as the search space is generally approximated at least to some degree (e.g. a high percentage of protein structures are invalid or energetically unfavorable) and the explicit conversion from continuous to discrete space for protein representation implies some uncertainty in the input data. This research applies uncertainty quantification techniques to the difficult protein-protein docking problem, first showing the variability that exists in existing software, and then providing a method for computing probabilistic certificates in the form of Chernoff-like bounds. Finally, this paper leverages these probabilistic certificates to accurately bound the uncertainty in docking from two docking algorithms, providing a QOI that is both robust and statistically meaningful.
Blood DNA methylation biomarkers of cumulative lead exposure in adults.

Lead is a ubiquitous toxicant following three compartment kinetics with the longest half-life found in bones. Patella and tibia lead levels—validated measures of cumulative exposure—require specialized X-ray-fluorescence-spectroscopy available only in a few centers worldwide. We developed minimally invasive biomarkers reflecting individual cumulative lead exposure using blood DNA methylation profiles—obtainable via Illumina 450K or IlluminaEPIC bead-chip assays. We developed and tested two methylation-based biomarkers from 348 Normative Aging Study (NAS) elderly men. We selected methylation sites with strong associations with bone lead levels via robust regressions analysis and constructed the biomarkers using elastic nets. Results were validated in a NAS subset, reporting specificity, and sensitivity. Participants were 73 years old on average (standard deviation, SD = 6), with moderate lead levels of (mean ± SD patella: 27 ± 18 µg/g; tibia:21 ± 13 µg/g). Methylation-based biomarkers for lead in patella and tibia included 59 and 138 DNA methylation sites, respectively. Estimated lead levels were significantly correlated with actual measured values, (r = 0.62 patella, r = 0.59 tibia) and had low mean square error (MSE) (MSE = 0.68 patella, MSE = 0.53 tibia). Means and distributions of the estimated and actual lead levels were not significantly different across patella and tibia bones (p > 0.05). Methylation-based biomarkers discriminated participants highly exposed (>median) to lead with a specificity of 74 and 73% for patella and tibia lead levels, respectively, with 70% sensitivity. DNA methylation-based lead biomarkers are novel tools that can be used to reconstruct decades’ worth of individual cumulative lead exposure using only blood DNA methylation profiles and may help identify the consequences of cumulative exposure.