cssi/SciSciGPT-SciSciNet huggingface dataset:
Characterizing Dehn surgeries on links via trisections

We summarize and expand known connections between the study of Dehn surgery on links and the study of trisections of closed, smooth 4-manifolds. In particular, we propose a program in which trisections could be used to disprove the generalized property R conjecture, including a process that converts the potential counterexamples of Gompf, Scharlemann, and Thompson into genus four trisections of the standard 4-sphere that are unlikely to be standard. We also give an analog of the Casson–Gordon rectangle condition for trisections that obstructs reducibility of a given trisection.
Quantum differentiation and chain maps of bimodule complexes

We consider a finite group acting on a vector space and the corresponding skew group algebra generated by the group and the symmetric algebra of the space. This skew group algebra illuminates the resulting orbifold and serves as a replacement for the ring of invariant polynomials, especially in the eyes of cohomology. One analyzes the Hochschild cohomology of the skew group algebra using isomorphisms which convert between resolutions. We present an explicit chain map from the bar resolution to the Koszul resolution of the symmetric algebra which induces various isomorphisms on Hochschild homology and cohomology, some of which have appeared in the literature before. This approach unifies previous results on homology and cohomology of both the symmetric algebra and skew group algebra. We determine induced combinatorial cochain maps which invoke quantum differentiation (expressed by Demazure-BGG operators).
Sampling in the analysis transform domain

Abstract Many signal and image processing applications have benefited remarkably from the fact that the underlying signals reside in a low dimensional subspace. One of the main models for such a low dimensionality is the sparsity one. Within this framework there are two main options for the sparse modeling: the synthesis and the analysis ones, where the first is considered the standard paradigm for which much more research has been dedicated. In it the signals are assumed to have a sparse representation under a given dictionary. On the other hand, in the analysis approach the sparsity is measured in the coefficients of the signal after applying a certain transformation, the analysis dictionary, on it. Though several algorithms with some theory have been developed for this framework, they are outnumbered by the ones proposed for the synthesis methodology. Given that the analysis dictionary is either a frame or the two dimensional finite difference operator, we propose a new sampling scheme for signals from the analysis model that allows recovering them from their samples using any existing algorithm from the synthesis model. The advantage of this new sampling strategy is that it makes the existing synthesis methods with their theory also available for signals from the analysis framework.
Quantum Entanglement of Dark Matter

We suggest that the dark matter in the universe has quantum entanglement if the dark matter is a Bose-Einstein condensation of ultra-light scalar particles. In this theory, any two regions of a galaxy are quantum entangled due to the quantum nature of the condensate. We calculate the entanglement entropy of a typical galactic halo, which turns out to be at least O(ln(M/m)), where M is the mass of the halo and m is the mass of a dark matter particle. The entanglement can be inferred from the rotation curves of the galaxy or the interference patterns of the dark matter density.
New Properties of the Zeros of Krall Polynomials

We identify a new class of algebraic relations satisfied by the zeros of orthogonal polynomials that are eigenfunctions of linear differential operators of order higher than two, known as Krall polynomials. Given an orthogonal polynomial family , we relate the zeros of the polynomial pN with the zeros of pm for each m ≤ N (the case m = N corresponding to the relations that involve the zeros of pN only). These identities are obtained by finding exact expressions for the similarity transformation that relates the spectral and the (interpolatory) pseudospectral matrix representations of linear differential operators, while using the zeros of the polynomial pN as the interpolation nodes. The proposed framework generalizes known properties of classical orthogonal polynomials to the case of nonclassical polynomial families of Krall type. We illustrate the general result by proving new identities satisfied by the Krall-Legendre, the Krall-Laguerre and the Krall-Jacobi orthogonal polynomials.
Gluing of graph Laplacians and their spectra

ABSTRACTWe study two different types of gluing for graphs: interface (obtained by choosing a common subgraph as the gluing component) and bridge gluing (obtained by adding a set of edges to the giv...
Tiling spaces are Cantor set fiber bundles

We prove that fairly general spaces of tilings of \mathbb{R}^d are fiber bundles over the torus T^d, with totally disconnected fiber. This was conjectured (in a weaker form) in the second author's recent work, and proved in certain cases. In fact, we show that each such space is homeomorphic to the d-fold suspension of a \mathbb{Z}^d subshift (or equivalently, a tiling space whose tiles are marked unit d-cubes). The only restrictions on our tiling spaces are that (1) the tiles are assumed to be polygons (polyhedra if d>2) that meet full-edge to full-edge (or full-face to full-face), (2) only a finite number of tile types are allowed, and (3) each tile type appears in only a finite number of orientations. The proof is constructive and we illustrate it by constructing a ‘square’ version of the Penrose tiling system.
Applications of the defect of a finitely presented functor

Abstract For an abelian category A , the defect sequence 0 ⟶ F 0 ⟶ F ⟶ φ ( w ( F ) , _ ) ⟶ F 1 ⟶ 0 of a finitely presented functor is used to establish the CoYoneda Lemma. An application of this result is the fp -dual formula which states that for any covariant finitely presented functor F, F ⁎ ≅ ( _ , w ( F ) ) . The defect sequence is shown to be isomorphic to both the double dual sequence 0 ⟶ Ext 1 ( Tr F , Hom ) ⟶ F ⟶ F ⁎ ⁎ ⟶ Ext 2 ( Tr F , Hom ) ⟶ 0 and the injective stabilization sequence 0 ⟶ F ‾ ⟶ F ⟶ R 0 F ⟶ F ˜ ⟶ 0 establishing the fp -injective stabilization formula F ‾ ≅ Ext 1 ( Tr F , Hom ) for any finitely presented functor F. The injectives of fp ( Mod ( R ) , Ab ) are used to compute the left derived functors L k ( _ ) ⁎ . These functors are shown to detect certain short exact sequences in Mod ( R ) .
A Mixed Classification-Regression Framework for 3D Pose Estimation from 2D Images

3D pose estimation from a single 2D image is an important and challenging task in computer vision with applications in autonomous driving, robot manipulation and augmented reality. Since 3D pose is a continuous quantity, a natural formulation for this task is to solve a pose regression problem. However, since pose regression methods return a single estimate of the pose, they have difficulties handling multimodal pose distributions (e.g. in the case of symmetric objects). An alternative formulation, which can capture multimodal pose distributions, is to discretize the pose space into bins and solve a pose classification problem. However, pose classification methods can give large pose estimation errors depending on the coarseness of the discretization. In this paper, we propose a mixed classification-regression framework that uses a classification network to produce a discrete multimodal pose estimate and a regression network to produce a continuous refinement of the discrete estimate. The proposed framework can accommodate different architectures and loss functions, leading to multiple classification-regression models, some of which achieve state-of-the-art performance on the challenging Pascal3D+ dataset.
A family of maps with many small fibers

The waist inequality states that for a continuous map from Sn to ℝq, not all fibers can have small (n - q)-dimensional volume. We construct maps for which most fibers have small (n - q)-dimensional volume and all fibers have bounded (n - q)-dimensional volume.
The global well-posedness and global attractor for the solutions to the 2D Boussinesq system with variable viscosity and thermal diffusivity

Abstract Global well-posedness of strong solutions and existence of the global attractor to the initial and boundary value problem of 2D Boussinesq system in a periodic channel with non-homogeneous boundary conditions for the temperature and viscosity and thermal diffusivity depending on the temperature are proved.
A combinatorial study of linear deterministic relay networks

The linear deterministic network model of Avestimehr, Diggavi and Tse has attracted attention because it captures certain physical aspects of wireless communication such as broadcasting and interference but is discrete and deterministic like traditional wireline network models. We study the unicast problem for this network model using results from matroid theory and submodular optimization, and we provide deterministic and polynomial-time coding schemes that can achieve the capacity.
Optimal traffic aggregation in multi-RAT heterogeneous wireless networks

Traffic load balancing and radio resource management is key to harness the dense and increasingly heterogeneous deployment of next generation “5G” wireless infrastructure. Strategies for aggregating user traffic from across multiple radio access technologies (RATs) and/or access points (APs) would be crucial in such heterogeneous networks (HetNets), but are not well investigated. In this paper, we develop a low complexity solution for maximizing an α-optimal network utility leveraging the multi-link aggregation (simultaneous connectivity to multiple RATs/APs) capability of users in the network. The network utility maximization formulation has maximization of sum rate (α = 0), maximization of minimum rate (α → ∞), and proportional fair (α = 1) as its special cases. A closed form is also developed for the special case where a user aggregates traffic from at most two APs/RATs, and hence can be applied to practical scenarios like LTE-WLAN aggregation (LWA) and LTE dual-connectivity solutions. It is shown that the required objective may also be realized through a decentralized implementation requiring a series of message exchanges between the users and network. Using comprehensive system level simulations, it is shown that optimal leveraging of multi-link aggregation leads to substantial throughput gains over single RAT/AP selection techniques.
Fast imbalanced classification of healthcare data with missing values

In medical domain, data features often contain missing values. This can create serious bias in the predictive modeling. Typical standard data mining methods often produce poor performance measures. In this paper, we propose a new method to simultaneously classify large datasets and reduce the effects of missing values. The proposed method is based on a multilevel framework of the cost-sensitive SVM and the expected maximization imputation method for missing values, which relies on iterated regression analyses. We compare classification results of multilevel SVM-based algorithms on public benchmark datasets with imbalanced classes and missing values as well as real data in health applications, and show that our multilevel SVM-based method produces fast, and more accurate and robust classification results.
A Stochastic Geometry Analysis of Energy Harvesting in Large Scale Wireless Networks

In this paper, the theoretical sustainable capacity of wireless networks with radio frequency (RF) energy harvesting is analytically studied. Specifically, we consider a large scale wireless network where base stations (BSs) and low power wireless devices are deployed by homogeneous Poisson point process (PPP) with different spatial densities. Wireless devices exploit the downlink transmissions from the BSs for either information delivery or energy harvesting. Generally, a BS schedules downlink transmission to wireless devices. The scheduled device receives the data information while other devices harvest energy from the downlink signals. The data information can be successfully received by the scheduled device only if the device has sufficient energy for data processing, i.e., the harvested energy is larger than a threshold. Given the densities of BSs and users, we apply stochastic geometry to analyze the expected number of users per cell and the successful information delivery probability of a wireless device, based on which the total network throughput can be derived. It is shown that the maximum network throughput per cell can be achieved under the optimal density of BSs. Extensive simulations validate the analysis.
The number of subsets of integers with no $k$-term arithmetic progression

Addressing a question of Cameron and Erd\Ho s, we show that, for infinitely many values of $n$, the number of subsets of $\{1,2,\ldots, n\}$ that do not contain a $k$-term arithmetic progression is at most $2^{O(r_k(n))}$, where $r_k(n)$ is the maximum cardinality of a subset of $\{1,2,\ldots, n\}$ without a $k$-term arithmetic progression. This bound is optimal up to a constant factor in the exponent. For all values of $n$, we prove a weaker bound, which is nevertheless sufficient to transfer the current best upper bound on $r_k(n)$ to the sparse random setting. To achieve these bounds, we establish a new supersaturation result, which roughly states that sets of size $\Theta(r_k(n))$ contain superlinearly many $k$-term arithmetic progressions. For integers $r$ and $k$, Erd\Ho s asked whether there is a set of integers $S$ with no $(k+1)$-term arithmetic progression, but such that any $r$-coloring of $S$ yields a monochromatic $k$-term arithmetic progression. Nesetřil and Rodl, and independently Spencer, answered this question affirmatively. We show the following density version: for every $k\ge 3$ and $\delta>0$, there exists a reasonably dense subset of primes $S$ with no $(k+1)$-term arithmetic progression, yet every $U\subseteq S$ of size $|U|\ge\delta|S|$ contains a $k$-term arithmetic progression. Our proof uses the hypergraph container method, which has proven to be a very powerful tool in extremal combinatorics. The idea behind the container method is to have a small certificate set to describe a large independent set. We give two further applications in the appendix using this idea.
Families of Solution Curves for Some Non-autonomous Problems

The paper studies families of positive solution curves for non-autonomous two-point problems u?+?f(u)?μg(x)=0,?1
The Geometry of Most Probable Trajectories in Noise-Driven Dynamical Systems

This paper presents a heuristic derivation of a geometric minimum action method that can be used to determine most-probable transition paths in noise-driven dynamical systems. Particular attention is focused on systems that violate detailed balance, and the role of the stochastic vorticity tensor is emphasized. The general method is explored through a detailed study of a two-dimensional quadratic shear flow which exhibits bifurcating most-probable transition pathways.
Coherent adequate sets and forcing square

We introduce the idea of a coherent adequate set of models, which can be used as side conditions in forcing. As an application we define a forcing poset which adds a square sequence on ω2 using finite conditions. In previous work [3] we introduced the idea of an adequate set of models and showed how to use adequate sets as side conditions in forcing with finite conditions. We gave several examples of forcing with adequate sets, including forcing posets for adding a generic function on ω2, adding a nonreflecting stationary subset of ω2, adding a Kurepa tree on ω1, and in [4] adding a club to a fat stationary subset of ω2. The main result of the present paper is to define a forcing poset using adequate sets which adds a ω1-sequence. The idea of using models as side conditions in forcing goes back to Todorcevic [6], where the method was applied to add generic objects of size ω1 with finite approximations. In the original context of applications of PFA, the preservation of ω2 was not necessary. To preserve ω2, Todorcevic introduced the requirement of a system of isomorphisms on the models in a condition. In the present paper we introduce the idea of a coherent adequate set of models. A coherent adequate set is essentially an adequate set in the sense of [3] which also satisfies the existence of a system of isomorphisms in the sense of Todorcevic. Combining these two ideas turns out to provide a powerful method for forcing with side conditions. As an application we define a forcing poset which adds a square sequence on ω2 with finite conditions. We assume that the reader is familiar with the basic theory of adequate sets as described in Sections 1–3 of [3]. Our treatment of coherent adequate sets owes a lot to the presentation of nicely arranged families given by Abraham and Cummings [1]. Forcing a square sequence with finite conditions was first achieved by Dolinar and Dzamonja [2] using the Mitchell style of models as side conditions [5]. An important difference is that the clubs which appear in the square sequence added by their forcing poset belong to the ground model, whereas for us the clubs are themselves generically approximated by finite fragments.
Classifying families of character degree graphs of solvable groups

‎We investigate prime character degree graphs of solvable groups‎. ‎In particular‎, ‎we consider a family of graphs $Gamma_{k,t}$ constructed by adjoining edges between two complete graphs in a one-to-one fashion‎. ‎In this paper we determine completely which graphs $Gamma_{k,t}$ occur as the prime character degree graph of a solvable group‎.
Galerkin v. least-squares Petrov-Galerkin projection in nonlinear model reduction

Least-squares Petrov-Galerkin (LSPG) model-reduction techniques such as the Gauss-Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible flow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform optimal projection associated with residual minimization at the time-continuous level, while LSPG techniques do so at the time-discrete level.This work provides a detailed theoretical and computational comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge-Kutta schemes. We present a number of new findings, including conditions under which the LSPG ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and computationally that decreasing the time step does not necessarily decrease the error for the LSPG ROM; instead, the time step should be 'matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible-flow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the LSPG reduced-order model by an order of magnitude.
CUBE DIAGRAMS AND 3-DIMENSIONAL REIDEMEISTER-LIKE MOVES FOR KNOTS

In this paper we introduce a representation of knots and links called a cube diagram. We show that a property of a cube diagram is a link invariant if and only if the property is invariant under five cube diagram moves. A knot homology is constructed from cube diagrams and shown to be equivalent to knot Floer homology.
Identifying and reducing gender bias in word-level language models

Many text corpora exhibit socially problematic biases, which can be propagated or amplified in the models trained on such data. For example, doctor cooccurs more frequently with male pronouns than female pronouns. In this study we (i) propose a metric to measure gender bias; (ii) measure bias in a text corpus and the text generated from a recurrent neural network language model trained on the text corpus; (iii) propose a regularization loss term for the language model that minimizes the projection of encoder-trained embeddings onto an embedding subspace that encodes gender; (iv) finally, evaluate efficacy of our proposed method on reducing gender bias. We find this regularization method to be effective in reducing gender bias up to an optimal weight assigned to the loss term, beyond which the model becomes unstable as the perplexity increases. We replicate this study on three training corpora—Penn Treebank, WikiText-2, and CNN/Daily Mail—resulting in similar conclusions.
Uniqueness of unconditional bases in $c_0$-products

We give counterexamples to a conjecture of Bourgain, Casazza, Lindenstrauss and Tzafriri that if X has a unique unconditional basis (up to permutation) then so does c_0(X). In particular, we show that for Tsirelson's space T, every unconditional basis of c_0(T) must be equivalent to a subsequence of the canonical basis but c_0(T) still fails to have a unique unconditional basis. We also give some positive results including a simpler proof that c_0(l_1)has a unique unconditional basis.
Efficient generalized Golub–Kahan based methods for dynamic inverse problems

We consider efficient methods for computing solutions to and estimating uncertainties in dynamic inverse problems, where the parameters of interest may change during the measurement procedure. Compared to static inverse problems, incorporating prior information in both space and time in a Bayesian framework can become computationally intensive, in part, due to the large number of unknown parameters. In these problems, explicit computation of the square root and/or inverse of the prior covariance matrix is not possible. In this work, we develop efficient, iterative, matrix-free methods based on the generalized Golub-Kahan bidiagonalization that allow automatic regularization parameter and variance estimation. We demonstrate that these methods can be more flexible than standard methods and develop efficient implementations that can exploit structure in the prior, as well as possible structure in the forward model. Numerical examples from photoacoustic tomography, deblurring, and passive seismic tomography demonstrate the range of applicability and effectiveness of the described approaches. Specifically, in passive seismic tomography, we demonstrate our approach on both synthetic and real data. To demonstrate the scalability of our algorithm, we solve a dynamic inverse problem with approximately $43,000$ measurements and $7.8$ million unknowns in under $40$ seconds on a standard desktop.
Variational Inference for Gaussian Process Models with Linear Complexity

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data, standard strategies for sparsifying the model can prevent the approximation of complex functions. In this work, we propose a novel variational Gaussian process model that decouples the representation of mean and covariance functions in reproducing kernel Hilbert space. We show that this new parametrization generalizes previous models. Furthermore, it yields a variational inference problem that can be solved by stochastic gradient ascent with time and space complexity that is only linear in the number of mean function parameters, regardless of the choice of kernels, likelihoods, and inducing points. This strategy makes the adoption of large-scale expressive Gaussian process models possible. We run several experiments on regression tasks and show that this decoupled approach greatly outperforms previous sparse variational Gaussian process inference procedures.
Solvable base change and Rankin-Selberg convolutions

Let π and π′ be unitary automorphic cuspidal representations of GLn(AE) and GLm(AF), and let E and F be solvable Galois extensions of Q of degrees l and l′, respectively. Using the fact that the automorphic induction and base change maps exist for E and F, and assuming an invariance condition under the actions of the Galois groups, we attach to the pair (π, π′) a Rankin-Selberg L-function L(s, π ×E,F xxxxxx) for which we prove a prime number theorem. This gives a method for comparing two representations that could be defined over completely different extensions, and the main results give a measure of how many cuspidal components the two representations π and π′ have in common when automorphically induced down to the rational numbers. The proof uses the structure of the Galois group of the composite extension EF and the character groups attached to the fields via class field theory. The second main theorem also gives an indication of when the base change of π up to the composite extension EF remains cuspidal.
Characterizing Scalability Issues in Spreadsheet Software using Online Forums

In traditional usability studies, researchers talk to users of tools to understand their needs and challenges. Insights gained via such interviews offer context, detail, and background. Due to costs in time and money, we are beginning to see a new form of tool interrogation that prioritizes scale, cost, and breadth by utilizing existing data from online forums. In this case study, we set out to apply this method of using online forum data to a specific issue---challenges that users face with Excel spreadsheets. Spreadsheets are a versatile and powerful processing tool if used properly. However, with versatility and power come errors, from both users and the software, which make using spreadsheets less effective. By scraping posts from the website Reddit, we collected a dataset of questions and complaints about Excel. Specifically, we explored and characterized the issues users were facing with spreadsheet software in general, and in particular, as resulting from a large amount of data in their spreadsheets. We discuss the implications of our findings on the design of next-generation spreadsheet software.
Selective but not Ramsey

Abstract We give a partial answer to the following question of Dobrinen: For a given topological Ramsey space R , are the notions of selective for R and Ramsey for R equivalent? Every topological Ramsey space R has an associated notion of Ramsey ultrafilter for R and selective ultrafilter for R (see [1] ). If R is taken to be the Ellentuck space then the two concepts reduce to the familiar notions of Ramsey and selective ultrafilters on ω ; so by a well-known result of Kunen the two are equivalent. We give the first example of an ultrafilter on a topological Ramsey space that is selective but not Ramsey for the space. We show that for the topological Ramsey space R 1 from [2] , the notions of selective for R 1 and Ramsey for R 1 are not equivalent. In particular, we prove that forcing with a closely related topological Ramsey space using almost-reduction, adjoins an ultrafilter that is selective but not Ramsey for R 1 .
A two-weight inequality for essentially well localized operators with general measures

Abstract We develop a new formulation of well localized operators as well as a new proof for the necessary and sufficient conditions to characterize their boundedness between L 2 ( R n , u ) and L 2 ( R n , v ) for general Radon measures u and v.
Stack and register complexity of radix conversions

Abstract We investigate the question of computational resources (such as stacks and counters) necessary to perform radix conversions. To this end it is shown that no PDA can compute the significand of the best n-digit floating point approximation of a power of an incommensurable radix. This extends the results of W. Clinger. We also prove that a two counter machine with input is capable of such conversions. On the other hand we note a curious asymmetry with respect to the order in which the digits are input by showing that a two counter machine can decode its input online if the digits are presented in the most-to-least significant order while no such machine can decode its input in this manner if the digits are presented in the least-to-most significant order. Some structural results about two counter machines (with input) are also established.
A Linear/Producer/Consumer Model of Classical Linear Logic

This paper defines a new proof- and category-theoretic framework for classical linear logic that separates reasoning into one linear regime and two persistent regimes corresponding to ! and ?. The resulting linear/producer/consumer (LPC) logic puts the three classes of propositions on the same semantic footing, following Benton’s linear/non-linear formulation of intuitionistic linear logic. Semantically, LPC corresponds to a system of three categories connected by adjunctions reflecting the linear/producer/consumer structure. The paper’s metatheoretic results include admissibility theorems for the cut and duality rules, and a translation of the LPC logic into category theory. The work also presents several concrete instances of the LPC model.
Symmetries of embedded complete bipartite graphs

We characterize which automorphisms of an arbitrary complete bipartite graph Kn;m can be induced by a homeomorphism of some embedding of the graph in S 3 . 1. Introduction. Knowing the symmetries of a molecule helps to pre- dict its chemical behavior. Chemists use the point group as a way to rep- resent the rigid symmetries of a molecule. However, molecules which are large enough to be exible (such as long polymers) or have pieces which
Voltage Multistability and Pulse Emergency Control for Distribution System With Power Flow Reversal

High levels of penetration of distributed generation and aggressive reactive power compensation may result in the reversal of power flows in future distribution grids. The voltage stability of these operating conditions may be very different from the more traditional power consumption regime. This paper focuses on the demonstration of multistability phenomenon in radial distribution systems with reversed power flow where multiple stable equilibria coexist for the given set of parameters. The system may experience transitions between different equilibria after being subjected to disturbances such as short-term losses of distributed generation or transient faults. Convergence to an undesirable equilibrium places the system in an emergency or in extremis state. Traditional emergency control schemes are not capable of restoring the system if it gets entrapped in one of the low voltage equilibria. Moreover, undervoltage load shedding may have a reverse action on the system and can induce voltage collapse. We propose a novel pulse emergency control strategy that restores the system to the normal state without any interruption of power delivery. The results are validated with dynamic simulations of IEEE 13-bus feeder performed with SystemModeler software. The dynamic models can also be used for characterization of the solution branches via a novel approach, so-called the admittance homotopy power flow method.
Complexity and scaling in quantum quench in 1 + 1 dimensional fermionic field theories

We consider the scaling behavior of circuit complexity under quantum quench in an a relativistic fermion field theory on a one dimensional spatial lattice. This is done by finding an exactly solvable quench protocol which asymptotes to massive phases at early and late times and crosses a critical point in between. We find a variety of scaling behavior as a function of the quench rate, starting with a saturation for quenches at the lattice scale, a “fast quench scaling” at intermediate rate and a Kibble Zurek scaling at slow rates.
Micromachined Force Scale for Optical Power Measurement by Radiation Pressure Sensing

We introduce a micromachined force scale for laser power measurement by means of radiation pressure sensing. With this technique, the measured laser light is not absorbed and can be utilized while being measured. We employ silicon micromachining technology to construct a miniature force scale, opening the potential to its use for fast in-line laser process monitoring. Here, we describe the mechanical sensing principle and conversion to an electrical signal. We further outline an electrostatic force substitution process for nulling of the radiation pressure force on the sensor mirror. Finally, we look at the performance of a proof-of-concept device in open-loop operation (without the nulling electrostatic force) subjected to a modulated laser at 250 W and find its response time is less than 20 ms with noise floor dominated by electronics at 2.5 W/ $\surd $ Hz.
Spaces of conics on low degree complete intersections

Let X be a smooth complete intersection. Suppose p and q are general points of X, we consider conics in X passing through p and q. We show the moduli space of these conics is a smooth complete intersection. The main ingredients of the proof are a criterion for characterizing when a smooth projective variety is a complete intersection, the Grothendieck-Riemann-Roch theorem and the geometry of the spaces of conics.
Neural Semantic Encoders

We present a memory augmented neural network for natural language understanding: Neural Semantic Encoders. NSE is equipped with a novel memory update rule and has a variable sized encoding memory that evolves over time and maintains the understanding of input sequences through read, compose and write operations. NSE can also access 1 multiple and shared memories. In this paper, we demonstrated the effectiveness and the flexibility of NSE on five different natural language tasks: natural language inference, question answering, sentence classification, document sentiment analysis and machine translation where NSE achieved state-of-the-art performance when evaluated on publically available benchmarks. For example, our shared-memory model showed an encouraging result on neural machine translation, improving an attention-based baseline by approximately 1.0 BLEU.
An Improved Bound on (A+A)/(A+A)

We show that, for a finite set $A$ of real numbers, the size of the set $$\frac{A+A}{A+A} = \left\{ \frac{a+b}{c+d} : a,b,c,d \in A, c+d \neq 0 \right \}$$ is bounded from below by $$\left|\frac{A+A}{A+A} \right| \gg \frac{|A|^{2+1/4}}{|A / A|^{1/8} \log |A|}.$$ This improves a result of Roche-Newton (2016).
Supersymmetric Dark Matter after Run I at the LHC: From a TeV to a PeV

The absence of low energy supersymmetry in run I data at the LHC has pushed the nominal scale for supersymmetry beyond a TeV. While this is consistent with the discovery of the Higgs boson at ≈ 125 GeV, simple models with scalar and gaugino mass universality are being pushed into corners of parameter space. Some possibilities within the constrained minimal supersymmetric extension of the standard model (with four parameters) are discussed along with a one parameter extension in which the Higgs soft masses are non-universal. Also discussed are 2-, 3-, and 4-parameter versions of pure gravity mediated models with a wino, Higgsino, or bino LSP respectively.
Controller Synthesis for Mode-Target Games

Abstract Cyber-Physical Systems (CPS) are notoriously difficult to verify due to the intricate interactions between the cyber and the physical components. To address this difficulty, several researchers have argued that the synthesis paradigm is better suited to ensure the correct operation of CPS than the verification paradigm. The key insight of synthesis is that design should be constrained so that resulting systems are easily verified and, ideally, synthesis algorithms should directly provide a proof of correctness. In this paper we present a Linear Temporal Logic fragment inspired by specifications that frequently occur in control applications where we have a set of modes and corresponding targets to be reached for each mode. The synthesis problem for this fragment is formulated as a mode-target game and we show that these games can be solved in polynomial time by providing two embeddings of mode-target games into Generalized Reactivity(1) (GR(1)) games. While solving GR(1) games requires O(mnN2) symbolic steps when we have m assumptions, n guarantees, and a game graph with N states, mode-target games can be solved in O(nN2) symbolic steps when we have n modes and a game graph with N states. These embeddings, however, do not make full use of the specificity of mode-target games. For this reason we investigate in this paper a solution to mode-target games that does not rely on GR(1) embeddings. The resulting algorithm has the same worst case time complexity and we illustrate through experimental results the extent to which it improves upon the algorithms obtained via GR(1) embeddings. In doing so, we highlight the commonalities between mode-target games and GR(1) games while providing additional insight into the solution of GR(1) games.
GEMFsim: A stochastic simulator for the generalized epidemic modeling framework

Abstract The recently proposed generalized epidemic modeling framework (GEMF) [1] lays the groundwork for systematically constructing a broad spectrum of stochastic spreading processes over complex networks. This article builds an algorithm for exact, continuous-time numerical simulation of GEMF-based processes. Moreover the implementation of this algorithm, GEMFsim, is available in popular scientific programming platforms such as MATLAB, R, Python, and C; GEMFsim facilitates simulating stochastic spreading models that fit in GEMF framework. Using these simulations one can examine the accuracy of mean-field-type approximations that are commonly used for analytical study of spreading processes on complex networks.
Relay Selection for Cooperative NOMA

This letter studies the impact of relay selection (RS) on the performance of cooperative non-orthogonal multiple access (NOMA). In particular, a two-stage RS strategy is proposed, and analytical results are developed to demonstrate that this two-stage strategy can achieve the minimal outage probability among all possible RS schemes, and realize the maximal diversity gain. The provided simulation results show that cooperative NOMA with this two-stage RS scheme outperforms that based on the conventional max–min approach, and can also yield a significant performance gain over orthogonal multiple access.
A Milli-Newton Propulsion System for the Asteroid Mobile Imager and Geologic Observer (AMIGO)

Exploration of small bodies, namely comets and asteroids remain a challenging endeavor due to their low gravity. The risk is so high that missions such as Hayabusa II and OSIRIS-REx will be performing touch and go missions to obtain samples. The next logical step is to perform longer-term mobility on the surface of these asteroid. This can be accomplished by sending small landers of a 1 kg or less with miniature propulsion systems that can just offset the force of asteroid gravity. Such a propulsion system would ideally be used to hop on the surface of the asteroid. Hopping has been found to be most efficient form of mobility on low-gravity. Use of wheels for rolling presents substantial challenges as the wheel can't gain traction to roll. The Asteroid Mobile Imager and Geologic Observer (AMIGO) utilizes 1 kg landers that are stowed in a 1U CubeSat configuration and deployed, releasing an inflatable that is 1-m in diameter. The inflatable is attached to the top of the 1U lander, enabling high speed communications and a means of easily tracking lander from an overhead mothership. Milligravity propulsion is required for the AMIGO landers to perform ballistic hops on the asteroid surface. The propulsion system is used to navigate the lander across the surface of the asteroid under the extremely low gravity while taking care to not exceed escape velocity. Although the concept for AMIGO missions is to use multiple landers, the more surface area evaluated by each lander the better. Without a propulsion system, each AMIGO will have a limited range of observable area. The propulsion system also serves as a rough attitude control system (ACS), as it enables pointing and regulation over where the lander is positioned via an array of MEMS thrusters. Several different techniques have been proposed for hopping nano-landers on low gravity environments including use of reaction wheels, electro-polymers, and rocket thrusters. In this concept, we will be heating sublimate to provide propulsive thrust which is simple and effective. Storing the propulsive gas as a solid provides much better storage density to ensure the longest lifetime possible. The starting point for this propulsion system involves selection of an appropriate, high-performance sublimate that meets the mobility needs of AMIGO. The paper will cover selection of the right sublimate, initial design and prototyping of the thruster using standard off-the-shelf arrays of electro-active MEMs valves. The device will be integrated with the fuel source with thrust profiles measured inside a milli-newton test stand inside a vacuum chamber. MEMS devices are to be used because of the weight and volume saving potential compared to traditional large-sized thrusting mechanisms. Through these efforts we are advancing on a milli-newton thruster that use non-combustibles and can be readily integrated onto nano-landers for asteroid surface exploration.
A Framework for Optimal Matching for Causal Inference

We propose a novel framework for matching estimators for causal effect from observational data that is based on minimizing the dual norm of estimation error when expressed as an operator. We show that many popular matching estimators can be expressed as optimal in this framework, including nearest-neighbor matching, coarsened exact matching, and mean-matched sampling. This reveals their motivation and aptness as structural priors formulated by embedding the effect in a particular functional space. This also gives rise to a range of new, kernel-based matching estimators that arise when one embeds the effect in a reproducing kernel Hilbert space. Depending on the case, these estimators can be found using either quadratic optimization or integer optimization. We show that estimators based on universal kernels are universally consistent without model specification. In empirical results using both synthetic and real data, the new, kernel-based estimators outperform all standard causal estimators in estimation error.
Spectral radius and Hamiltonicity of graphs with large minimum degree

Let G be a graph of order n and λ(G) the spectral radius of its adjacency matrix. We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in G. One of the main results of the paper is the following theorem
Quantum process in living cells

Coherent quantum effects have been confirmed for several biological processes. These processes exist in the environment of a warm wet cell where decoherence can be a serious concern. Here we propose a mechanism whereby quantum coherence may extend through the water matrix of a cell. The model is based on coherent waves of established ultrafast energy transfers in water. Computations based on the model are found to agree with several experimental results and numerical and descriptive predictions are presented. We compute wave speed, ~156 km/s, and wavelength, ~9.3 nm, and determine that these waves retain local coherence. Close agreements are found for the dipole moment of water dimers, results of microwave radiation on yeast, and the Kleiber law of metabolic rates. The theory requires that a spherical cell must have a minimum diameter of ~20 nm to accommodate a standing energy wave. The quantum properties of the modelsuggest that cellular chemistry favors reactions that support perpetuation of the energy waves.
End-to-end learning of LDA by mirror-descent back propagation over a deep architecture

We develop a fully discriminative learning approach for supervised Latent Dirichlet Allocation (LDA) model using Back Propagation (i.e., BP-sLDA), which maximizes the posterior probability of the prediction variable given the input document. Different from traditional variational learning or Gibbs sampling approaches, the proposed learning method applies (i) the mirror descent algorithm for maximum a posterior inference and (ii) back propagation over a deep architecture together with stochastic gradient/mirror descent for model parameter estimation, leading to scalable and end-to-end discriminative learning of the model. As a byproduct, we also apply this technique to develop a new learning method for the traditional unsupervised LDA model (i.e., BP-LDA). Experimental results on three real-world regression and classification tasks show that the proposed methods significantly outperform the previous supervised topic models, neural networks, and is on par with deep neural networks.
Unicity for representations of the Kauffman bracket skein algebra

This paper resolves the unicity conjecture of Bonahon and Wong for the Kauffman bracket skein algebras of all oriented finite type surfaces at all roots of unity. The proof is a consequence of a general unicity theorem that says that the irreducible representations of a prime affine k-algebra over an algebraically closed field k, that is finitely generated as a module over its center, are generically classified by their central characters. The center of the Kauffman bracket skein algebra of any orientable surface at any root of unity is characterized, and it is proved that the skein algebra is finitely generated as a module over its center. It is shown that for any orientable surface the center of the skein algebra at any root of unity is the coordinate ring of an affine algebraic variety.
Non-reciprocal wave phenomena in energy self-reliant gyric metamaterials

This work presents a mechanism by which non-reciprocal wave transmission is achieved in a class of gyric metamaterial lattices with embedded rotating elements. A modulation of the device's angular momentum is obtained via prescribed rotations of a set of locally housed spinning motors and is then used to induce space-periodic, time-periodic, as well as space-time-periodic variations, which influence wave propagation in distinct ways. Owing to their dependence on gyroscopic effects, such systems are able to break reciprocal wave symmetry without stiffness perturbations rendering them consistently stable as well as energy self-reliant. Dispersion patterns, band gap emergence, as well as non-reciprocal wave transmission in the space-time-periodic gyric metamaterials are predicted both analytically from the gyroscopic system dynamics as well as numerically via time-dependent full wave simulations. In addition to breaking reciprocity, the authors show that the energy content of a frictionless gyric metamaterial is conserved over one temporal modulation cycle enabling it to exhibit a stable response irrespective of the pumping frequency.
Factorization invariants of Puiseux monoids generated by geometric sequences

We study some of the factorization invariants of the class of Puiseux monoids generated by geometric sequences, and we compare and contrast them with the known results for numerical monoids generat...