cssi/SciSciGPT-SciSciNet huggingface dataset:
Multilayer tensor factorization with applications to recommender systems

Recommender systems have been widely adopted by electronic commerce and entertainment industries for individualized prediction and recommendation, which benefit consumers and improve business intelligence. In this article, we propose an innovative method, namely the recommendation engine of multilayers (REM), for tensor recommender systems. The proposed method utilizes the structure of a tensor response to integrate information from multiple modes, and creates an additional layer of nested latent factors to accommodate between-subjects dependency. One major advantage is that the proposed method is able to address the “cold-start” issue in the absence of information from new customers, new products or new contexts. Specifically, it provides more effective recommendations through sub-group information. To achieve scalable computation, we develop a new algorithm for the proposed method, which incorporates a maximum block improvement strategy into the cyclic blockwise-coordinate-descent algorithm. In theory, we investigate algorithmic properties for convergence from an arbitrary initial point and local convergence, along with the asymptotic consistency of estimated parameters. Finally, the proposed method is applied in simulations and IRI marketing data with 116 million observations of product sales. Numerical studies demonstrate that the proposed method outperforms existing competitors in the literature.
\(U(1)_{\chi}\), Seesaw Dark Matter, and Higgs Decay

It has recently been pointed out that the underlying symmetry of dark matter may well be $U(1)_\chi$ (coming from $SO(10) \to SU(5) \times U(1)_\chi$) with the dark parity of any given particle determined by $(-1)^{Q_\chi + 2j}$, where $Q_\chi$ is its $U(1)_\chi$ charge and $j$ its spin angular momentum. Armed with this new insight, previous simple models of dark matter are reinterpreted, and a novel idea is proposed that light seesaw dark matter exists in analogy to light neutrinos and is produced by the rare decay of the standard-model Higgs boson.
The QuarkNet/Grid Collaborative Learning e-Lab

This paper describes a case study that uses grid computing techniques to support the collaborative learning of high school students investigating cosmic rays. Students gather and upload science data to an e-Lab website. They explore those data using techniques from the GriPhyN collaboration. These techniques include virtual data transformations, workflows, metadata cataloging and indexing, data product provenance and persistence, as well as job planners for execution locally and on the grid. Students use web browsers and a custom interface that extends the GriPhyN Chiron portal to perform all of these tasks. They share results in the form of online posters and ask each other questions in this asynchronous environment. Students can discover and extend the research of other students, modeling the processes of modern large-scale scientific collaborations. Also, the e-Lab provides tools for teachers to guide student work throughout an investigation.http://quarknet.uchicago.edu/elab/cosmic
A generative model for deep convolutional learning

A generative model is developed for deep (multi-layered) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up (pretraining) and top-down (refinement) probabilistic learning. Experimental results demonstrate powerful capabilities of the model to learn multi-layer features from images, and excellent classification results are obtained on the MNIST and Caltech 101 datasets.
On-Board Visual Tracking with Unmanned Aircraft System (UAS)

This paper presents the development of a real time tracking algorithm that runs on a 1.2 GHz PC/104 computer onboard a small UAV. The algorithm uses zero mean normalized cross correlation to detect and locate an object in the image. A Kalman filter is used to make the tracking algorithm computationally efficient. Object position in an image frame is predicted using the motion model and a search window centered at the predicted position is generated. Object position is updated with the measurement from object detection. The detected position is sent to the motion controller to move the gimbal so that the object stays at the center of the image frame. Detection and tracking is autonomously carried out on the payload computer and the system is able to work in two different methods. The first method starts detecting and tracking using a stored image patch. The second method allows the operator on the ground to select the interest object for the UAV(Unmanned Aerial Vehicle) to track. The system is capable of re-detecting an object, in the event of tracking failure. Performance of the tracking system was verified both in the lab and on the field by mounting the payload on a vehicle and simulating a flight. Tests show that the system can detect and track a diverse set of objects in real time. Flight testing of the system will be conducted at the next available opportunity.
Corticospinal Tract (CST) Reconstruction Based on Fiber Orientation Distributions (FODs) Tractography.

The Corticospinal Tract (CST) is a part of pyramidal tract (PT), and it can innervate the voluntary movement of skeletal muscle through spinal interneurons (the 4th layer of the Rexed gray board layers), and anterior horn motorneurons (which control trunk and proximal limb muscles). Spinal cord injury (SCI) is a highly disabling disease often caused by traffic accidents. The recovery of CST and the functional reconstruction of spinal anterior horn motor neurons play an essential role in the treatment of SCI. However, the localization and reconstruction of CST are still challenging issues; the accuracy of the geometric reconstruction can directly affect the results of the surgery. The main contribution of this paper is the reconstruction of the CST based on the fiber orientation distributions (FODs) tractography. Differing from tensor-based tractography in which the primary direction is a determined orientation, the direction of FODs tractography is determined by the probability. The spherical harmonics (SPHARM) can be used to approximate the efficiency of FODs tractography. We manually delineate the three ROIs (the posterior limb of the internal capsule, the cerebral peduncle, and the anterior pontine area) by the ITK-SNAP software, and use the pipeline software to reconstruct both the left and right sides of the CST fibers. Our results demonstrate that FOD-based tractography can show more and correct anatomical CST fiber bundles.
FRINGE PAIRS IN GENERALIZED MSTD SETS

A More Sums Than Differences (MSTD) set is a set A for which |A + A| > |A − A|. Martin and O’Bryant proved that the proportion of MSTD sets in {0, 1,…,n} is bounded below by a positive number as n goes to infinity. Iyer, Lazarev, Miller and Zhang introduced the notion of a generalized MSTD set, a set A for which |sA − dA| > |σA − δA| for a prescribed s + d = σ + δ. We offer efficient constructions of k-generational MSTD sets, sets A where A,A + A,…,kA are all MSTD. We also offer an alternative proof that the proportion of sets A for which |sA − dA|−|σA − δA| = x is positive, for any x ∈ ℤ. We prove that for any &#x1d716; > 0, Pr(1 − &#x1d716; <log |sA − dA|/log |σA − δA| < 1 + &#x1d716;) goes to 1 as the size of A goes to infinity and we give a set A which has the current highest value of log |A + A|/log |A − A|. We also study decompositions of intervals {0, 1,…,n} into MSTD sets and prove that a positive proportion of decompositions into two sets have the property that both sets are MSTD.
SpecWatch: A framework for adversarial spectrum monitoring with unknown statistics

Abstract In cognitive radio networks (CRNs), dynamic spectrum access has been proposed to improve the spectrum utilization, but it also generates spectrum misuse problems. One common solution to these problems is to deploy monitors to detect misbehaviors on certain channel. However, in multi-channel CRNs, it is very costly to deploy monitors on every channel. With a limited number of monitors, we have to decide which channels to monitor. In addition, we need to determine how long to monitor each channel and in which order to monitor, because switching channels incurs costs. Moreover, the information about the misuse behavior is not available a priori. To answer those questions, we model the spectrum monitoring problem as a combinatorial adversarial multi-armed bandit problem with switching costs (MAB-SC), propose an effective framework, and design two online algorithms, SpecWatch-II and SpecWatch-III, based on the same framework. To evaluate the algorithms, we use weak regret, i.e., the performance difference between the solution of our algorithm and optimal (fixed) solution in hindsight, as the metric. We prove that the expected weak regret of SpecWatch-II is O(T2/3), where T is the time horizon. Whereas, the actual weak regret of SpecWatch-III is O(T2/3) with probability 1 − δ , for any δ ∈ (0, 1). Both algorithms guarantee the upper bounds matching the lower bound of the general adversarial MAB-SC problem. Therefore, they are all asymptotically optimal.
SOME RESULTS CONCERNING THE p-ROYDEN AND p-HARMONIC BOUNDARIES OF A GRAPH OF BOUNDED DEGREE

Let p be a real number greater than one and let i be a connected graph of bounded degree. We show that the p-Royden boundary of i with the p-harmonic boundary removed is an Fae-set. We also characterize the p-harmonic boundary of i in terms of the intersection of the extreme points of a certain subset of one-sided infinite paths in i.
Bisecting binomial coefficients

Abstract In this paper, we deal with the problem of bisecting binomial coefficients. We find many (previously unknown) infinite classes of integers which admit nontrivial bisections, and a class with only trivial bisections. As a byproduct of this last construction, we show conjectures Q 2 and Q 4 of Cusick and Li (2005). We next find several bounds for the number of nontrivial bisections and further compute (using a supercomputer) the exact number of such bisections for n ≤ 51 .
On the Location of the Minimizer of the Sum of Two Strongly Convex Functions

The problem of finding the minimizer of a sum of convex functions is central to the field of distributed optimization. Thus, it is of interest to understand how that minimizer is related to the properties of the individual functions in the sum. In this paper, we provide an upper bound on the region containing the minimizer of the sum of two strongly convex functions. We consider two scenarios with different constraints on the upper bound of the gradients of the functions. In the first scenario, the gradient constraint is imposed on the location of the potential minimizer, while in the second scenario, the gradient constraint is imposed on a given convex set in which the minimizers of two original functions are embedded. We characterize the boundaries of the regions containing the minimizer in both scenarios.
$\ell^{2}$-torsion of free-by-cyclic groups

We provide an upper bound on the $\ell^{2}$-torsion of a free-by-cyclic group, $-\rho^{(2)}(\mathbb{F} \rtimes_{\Phi} \mathbb{Z})$, in terms of a relative train-track representative for $\Phi \in \mathrm{Aut}(\mathbb{F})$. Our result shares features with a theorem of Luck-Schick computing the $\ell^{2}$-torsion of the fundamental group of a 3-manifold that fibers over the circle in that it shows that the $\ell^{2}$-torsion is determined by the exponential dynamics of the monodromy. In light of the result of Luck-Schick, a special case of our bound is analogous to the bound on the volume of a 3-manifold that fibers over the circle with pseudo-Anosov monodromy by the normalized entropy recently demonstrated by Kojima-McShane.
When is a group action determined by its orbit structure

We present a simple approach to questions of topological orbit equivalence for actions of countable groups. For example, for any action of a countable group ΓΓ on a topological manifold where the fixed sets for any element are contained in codimension two submanifolds, every orbit equivalence is equivariant. Even in the presence of larger fixed sets, for actions preserving rigid geometric structures our results force sufficiently smooth orbit equivalences to be equivariant. For instance, if a countable group Γ acts on $$ \mathbb{T}^{n} $$ and the action is C 1 orbit equivalent to the standard action of $$ SL_n(\mathbb{Z}) $$ on $$ \mathbb{T}^{n} $$ , then Γ is isomorphic to $$ SL_n(\mathbb{Z}) $$ and the actions are isomorphic. (The same result holds if we replace $$ SL_n(\mathbb{Z}) $$ by a finite index subgroup.) We also show that preserving a geometric structure is an invariant of smooth orbit equivalence and give an application of our ideas to the theory of hyperbolic groups. In the course of proving our theorems, we generalize a theorem of Sierpinski which says that a connected Hausdorff compact topological space is not the disjoint union of countably many closed sets. We prove a stronger statement that allows “small” intersections provided the space is locally connected. This implies that for any continuous action of a countable group Γ on a connected, locally connected, locally compact, Hausdorff topological space, where the fixed set of every element is “small”, every orbit equivalence is equivariant.
Lozenge tilings of doubly-intruded hexagons

Abstract Motivated in part by Propp's intruded Aztec diamond regions, we consider hexagonal regions out of which two horizontal chains of triangular holes (called ferns) are removed, so that the chains are at the same height, and are attached to the boundary. By contrast with the intruded Aztec diamonds (whose numbers of domino tilings contain some large prime factors in their factorization), the number of lozenge tilings of our doubly-intruded hexagons turns out to be given by simple product formulas in which all factors are linear in the parameters. We present in fact q-versions of these formulas, which enumerate the corresponding plane-partitions-like structures by their volume. We also pose some natural statistical mechanics questions suggested by our set-up, which should be possible to tackle using our formulas.
Algorithms and Training for Weighted Multiset Automata and Regular Expressions

Multiset automata are a class of automata for which the symbols can be read in any order and obtain the same result. We investigate weighted multiset automata and show how to construct them from weighted regular expressions. We present training methods to learn the weights for weighted regular expressions and for general multiset automata from data. Finally, we examine situations in which inside weights can be computed more efficiently.
Joint Dictionaries for Zero-Shot Learning

A classic approach toward zero-shot learning (ZSL) is to map the input domain to a set of semantically meaningful attributes that could be used later on to classify unseen classes of data (e.g. visual data). In this paper, we propose to learn a visual feature dictionary that has semantically meaningful atoms. Such a dictionary is learned via joint dictionary learning for the visual domain and the attribute domain, while enforcing the same sparse coding for both dictionaries. Our novel attribute aware formulation provides an algorithmic solution to the domain shift/hubness problem in ZSL. Upon learning the joint dictionaries, images from unseen classes can be mapped into the attribute space by finding the attribute aware joint sparse representation using solely the visual data. We demonstrate that our approach provides superior or comparable performance to that of the state of the art on benchmark datasets.
A multiple timescales approach to bridging spiking- and population-level dynamics

A rigorous bridge between spiking-level and macroscopic quantities is an on-going and well-developed story for asynchronously firing neurons, but focus has shifted to include neural populations exhibiting varying synchronous dynamics. Recent literature has used the Ott-Antonsen ansatz (2008) to great effect, allowing a rigorous derivation of an order parameter for large oscillator populations. The ansatz has been successfully applied using several models including networks of Kuramoto oscillators, theta models, and integrate-and-fire neurons, along with many types of network topologies. In the present study, we take a converse approach: given the mean field dynamics of slow synapses, we predict the synchronization properties of finite neural populations. The slow synapse assumption is amenable to averaging theory and the method of multiple timescales. Our proposed theory applies to two heterogeneous populations of N excitatory n-dimensional and N inhibitory m-dimensional oscillators with homogeneous synaptic weights. We then demonstrate our theory using two examples. In the first example, we take a network of excitatory and inhibitory theta neurons and consider the case with and without heterogeneous inputs. In the second example, we use Traub models with calcium for the excitatory neurons and Wang-Buzsaki models for the inhibitory neurons. We accurately predict phase drift and phase locking in each example even when the slow synapses exhibit non-trivial mean-field dynamics.
Human-level intelligence or animal-like abilities?

The vision systems of the eagle and the snake outperform everything that we can make in the laboratory, but snakes and eagles cannot build an eyeglass or a telescope or a microscope. (Judea Pearl)
Saturating Auto-Encoders

Abstract: We introduce a simple new regularizer for auto-encoders whose hidden-unit activation functions contain at least one zero-gradient (saturated) region. This regularizer explicitly encourages activations in the saturated region(s) of the corresponding activation function. We call these Saturating Auto-Encoders (SATAE). We show that the saturation regularizer explicitly limits the SATAE's ability to reconstruct inputs which are not near the data manifold. Furthermore, we show that a wide variety of features can be learned when different activation functions are used. Finally, connections are established with the Contractive and Sparse Auto-Encoders.
Cylindrical contact homology for dynamically convex contact forms in three dimensions

We show that for dynamically convex contact forms in three dimensions, the cylindrical contact homology differential d can be defined by directly counting holomorphic cylinders for a generic almost complex structure, without any abstract perturbation of the Cauchy-Riemann equation. We also prove that d^2 = 0. Invariance of cylindrical contact homology in this case can be proved using S^1-dependent almost complex structures, similarly to work of Bourgeois-Oancea; this will be explained in another paper.
Approximations of convex bodies by measure-generated sets

Given a Borel measure $$\mu $$ on $$\mathbb {R}^{n}$$ , we define a convex set by $$\begin{aligned} \mathrm{M}\left( \mu \right) =\bigcup _{\begin{array}{c} 0\le f\le 1,\\ \int _{\mathbb {R}^{n}}f\,\mathrm{d}\mu =1 \end{array} }\left\{ \int _{\mathbb {R}^{n}}yf\left( y\right) \,\mathrm{d}\mu \left( y\right) \right\} , \end{aligned}$$ where the union is taken over $$\mu $$ -measurable functions $$f:\mathbb {R}^{n}\rightarrow \left[ 0,1\right] $$ such that $$\int _{\mathbb {R}^{n}}f\,\mathrm{d}\mu =1$$ and $$\int _{\mathbb {R}^{n}}yf\left( y\right) \,\mathrm{d}\mu \left( y\right) $$ exists. We study the properties of these measure-generated sets, and use them to investigate natural variations of problems of approximation of general convex bodies by polytopes with as few vertices as possible. In particular, we study an extension of the vertex index which was introduced by Bezdek and Litvak. As an application, we prove that for any non-degenerate probability measure $$\mu $$ , one has the lower bound $$\begin{aligned} \int _{\mathbb {R}^{n}}\left\| x\right\| _{Z_{1}\left( \mu \right) }\,\mathrm{d}\mu \left( x\right) \ge c\sqrt{n}, \end{aligned}$$ where $$Z_{1}\left( \mu \right) $$ is the $$L_{1}$$ -centroid body of $$\mu $$ .
Base size sets and determining sets

Abstract The determining number or fixing number of a graph Γ is the smallest size of a subset of vertices S of Γ such that any automorphism of Γ that stabilizes S stabilizes all of Γ . The determining set D ( G ) of a finite group G is the set of all determining numbers of all finite graphs for which G is the automorphism group. Similarly, the base size of a permutation representation ρ : G → Sym ( S ) of a group G is the smallest size of a subset B of S such that its pointwise stabilizer in G is trivial. The base size set B ( G ) of a finite group G is the set of all base sizes of all faithful representations of G on finite sets. In this paper we compare the sets D ( G ) and B ( G ) . We show that for finite abelian groups, B ( G ) = D ( G ) = { 1 , 2 , … , k } , where k is the number of elementary divisors of G . We characterize B ( G ) and D ( G ) for dihedral groups of the form D p k and D 2 p k for an odd prime p and prove B ( G ) ≠ D ( G ) for dihedral groups of the form D p q where p and q are distinct odd primes.
Brauer characters and normal Sylow p-subgroups

Abstract In this paper, we study some variations of the well-known Ito–Michler theorem for p-Brauer characters using various inequalities involving the p-Brauer character degrees of finite groups. Several new criteria for the existence of a normal Sylow p-subgroup of finite groups are obtained using the p-parts and p ′ -parts of the p-Brauer character degrees.
A Resolution of the Paradox of Enrichment

The paradox of enrichment was observed by Rosenzweig [1971] in a class of predator–prey models. Two of the parameters in the models are crucial for the paradox. These two parameters are the prey's carrying capacity and prey's half-saturation for predation. Intuitively, increasing the carrying capacity due to enrichment of the prey's environment should lead to a more stable predator–prey system. Analytically, it turns out that increasing the carrying capacity always leads to an unstable predator–prey system that is susceptible to extinction from environmental random perturbations. This is the so-called paradox of enrichment. Our resolution here rests upon a closer investigation on a dimensionless number H formed from the carrying capacity and the prey's half-saturation. By recasting the models into dimensionless forms, the models are in fact governed by a few dimensionless numbers including H. The effects of the two parameters: carrying capacity and half-saturation are incorporated into the number H. In fact, increasing the carrying capacity is equivalent (i.e. has the same effect on H) to decreasing the half-saturation which implies more aggressive predation. Since there is no paradox between more aggressive predation and instability of the predator–prey system, the paradox of enrichment is resolved. The so-called instability of the predator–prey system is characterized by the existence of a stable limit cycle in the phase plane, which gets closer and closer to the predator axis and prey axis. Due to random environmental perturbations, this can lead to extinction. We also further explore spatially dependent models for which the phase space is infinite-dimensional. The spatially independent limit cycle which is generated by a Hopf bifurcation from an unstable steady state, is linearly stable in the infinite-dimensional phase space. Numerical simulations indicate that the basin of attraction of the limit cycle is riddled. This shows that spatial perturbations can sometimes (neither always nor never) remove the paradox of enrichment near the limit cycle!
Learning the Problem-Optimum Map: Analysis and Application to Global Optimization in Robotics

This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for real-time applications in robotics, since it can produce near globally optimal solutions orders of magnitude faster than standard methods. This paper establishes theoretical conditions on how many and where samples are needed over the space of problems to achieve a given approximation quality. The framework is applied to solve globally optimal collision-free inverse kinematics problems, wherein large solution databases are used to produce near-optimal solutions in a submillisecond time on a standard PC.
Crosstalk based Fine-Grained Reconfiguration Techniques for Polymorphic Circuits

Truly polymorphic circuits, whose functionality/circuit behavior can be altered using a control variable, can provide tremendous benefits in multi-functional system design and resource sharing. For secure and fault tolerant hardware designs these can be crucial as well. Polymorphic circuits work in literature so far either rely on environmental parameters such as temperature, variation etc. or on special devices such as ambipolar FET, configurable magnetic devices, etc., that often result in inefficiencies in performance and/or realization. In this paper, we introduce a novel polymorphic circuit design approach where deterministic interference between nano-metal lines is leveraged for logic computing and configuration. For computing, the proposed approach relies on nano-metal lines, their interference and commonly used FETs. For polymorphism, it requires only an extra metal line that carries the control signal. In this paper, we show a wide range of crosstalk polymorphic logic gates and their evaluation results. We also show an example of a large circuit that performs both the functionalities of multiplier and sorter depending on the configuration signal. A comparison is made with respect to other existing approaches in literature, and transistor count is benchmarked. For crosstalk-polymorphic circuits, the transistor count reduction range from 25% to 83% with respect to various other approaches. For example, polymorphic AOI21-OA21 cell show 83%, 85% and 50% transistor count reduction, and Multiplier-Sorter circuit show 40%, 36% and 28% transistor count reduction with respect to CMOS, genetically evolved, and ambipolar transistor based polymorphic circuits, respectively.
Note on asymptotically conical expanding Ricci solitons

We show that at the level of formal expansions, any compact Riemannian manifold is the sphere at infinity of an asymptotically conical gradient expanding Ricci soliton.
A solution to the reversible embedding problem for finite Markov chains

The embedding problem for Markov chains is a famous problem in probability theory and only partial results are available up till now. In this paper, we propose a variant of the embedding problem called the reversible embedding problem which has a deep physical and biochemical background and provide a complete solution to this new problem. We prove that the reversible embedding of a stochastic matrix, if it exists, must be unique. Moreover, we obtain the sufficient and necessary conditions for the existence of the reversible embedding and provide an effective method to compute the reversible embedding. Some examples are also given to illustrate the main results of this paper.
Learning continuous time bayesian networks

Continuous time Bayesian networks (CTBN) describe structured stochastic processes with finitely many states that evolve nver continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which represents a finite state continuous time Markov process whose transition model is a function of its parents. We address the problem of leaning parameters and structure of a CTBN from fully observed data. We define a conjugate prior for CTBNs and show how it can be used both for Bayesian parameter estimation and as the basis of a Bayesian score for structure learning. Because acyclicity is not a constraint in CTBNs, we can show that the structure leaning problem is significantly easier, both in theory and in practice, than structure leaning for dynamic Bayesian networks (DBNs). Furthermore, as CTBNs can tailor the parameters and dependency structure to the different time granularities of the evolution of different variables, they can provide a better fit to continuous-time processes than DBNs with a fixed time granularity.
Integrating Abstractions to Enhance the Execution of Distributed Applications

One of the factors that limits the scale, performance, and sophistication of distributed applications is the difficulty of concurrently executing them on multiple distributed computing resources. In part, this is due to a poor understanding of the general properties and performance of the coupling between applications and dynamic resources. This paper addresses this issue by integrating abstractions representing distributed applications, resources, and execution processes into a pilot-based middleware. The middleware provides a platform that can specify distributed applications, execute them on multiple resource and for different configurations, and is instrumented to support investigative analysis. We analyzed the execution of distributed applications using experiments that measure the benefits of using multiple resources, the late-binding of scheduling decisions, and the use of backfill scheduling.
Large scale distributed neural network training through online distillation

Techniques such as ensembling and distillation promise model quality improvements when paired with almost any base model. However, due to increased test-time cost (for ensembles) and increased complexity of the training pipeline (for distillation), these techniques are challenging to use in industrial settings. In this paper we explore a variant of distillation which is relatively straightforward to use as it does not require a complicated multi-stage setup or many new hyperparameters. Our first claim is that online distillation enables us to use extra parallelism to fit very large datasets about twice as fast. Crucially, we can still speed up training even after we have already reached the point at which additional parallelism provides no benefit for synchronous or asynchronous stochastic gradient descent. Two neural networks trained on disjoint subsets of the data can share knowledge by encouraging each model to agree with the predictions the other model would have made. These predictions can come from a stale version of the other model so they can be safely computed using weights that only rarely get transmitted. Our second claim is that online distillation is a cost-effective way to make the exact predictions of a model dramatically more reproducible. We support our claims using experiments on the Criteo Display Ad Challenge dataset, ImageNet, and the largest to-date dataset used for neural language modeling, containing $6\times 10^{11}$ tokens and based on the Common Crawl repository of web data.
At a Glance: Pixel Approximate Entropy as a Measure of Line Chart Complexity

When inspecting information visualizations under time critical settings, such as emergency response or monitoring the heart rate in a surgery room, the user only has a small amount of time to view the visualization “at a glance”. In these settings, it is important to provide a quantitative measure of the visualization to understand whether or not the visualization is too “complex” to accurately judge at a glance. This paper proposes Pixel Approximate Entropy (PAE), which adapts the approximate entropy statistical measure commonly used to quantify regularity and unpredictability in time-series data, as a measure of visual complexity for line charts. We show that PAE is correlated with user-perceived chart complexity, and that increased chart PAE correlates with reduced judgement accuracy. ‘We also find that the correlation between PAE values and participants’ judgment increases when the user has less time to examine the line charts.
Polarizable Molecular Simulations Reveal How Silicon-Containing Functional Groups Govern the Desalination Mechanism in Nanoporous Graphene

We report a molecular dynamics (MD) simulation study of reverse osmosis desalination using nanoporous monolayer graphene passivated by SiH2 and Si(OH)2 functional groups. A highly accurate and detailed polarizable molecular mechanics force field model was developed for simulating graphene nanopores of various sizes and geometries. The simulated water fluxes and ion rejection percentages are explained using detailed atomistic mechanisms derived from analysis of the simulation trajectories. Our main findings are as follows: (1) The Si(OH)2 pores possess superior ion rejection rates due to selective electrostatic repulsion of Cl– ions, but Na+ ions are attracted to the pore and block water transfer. (2) By contrast, the SiH2 pores operate via a steric mechanism that excludes ions based on the size and flexibility of their hydration layers. (3) In the absence of ions, water flux is directly proportional to the solvent accessible area within the pore; however, simulated fluxes are lower than those inferred fro...
On the energy landscape of spherical spin glasses

Abstract We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebraic relation that characterizes one-step replica symmetric breaking Parisi measures. For these measures, we show that any two nonparallel spin configurations around the maximum energy are asymptotically orthogonal to each other. In sharp contrast, we study models with full replica symmetry breaking and show that all possible values of the asymptotic distance are attained near the maximum energy.
A resolution of singularities for Drinfeld’s compactification by stable maps

Drinfeld's relative compactification plays a basic role in the theory of automorphic sheaves, and its singularities encode representation-theoretic information in the form of intersection cohomology. We introduce a resolution of singularities consisting of stable maps from nodal deformations of the curve into twisted flag varieties. As an application, we prove that the twisted intersection cohomology sheaf on Drinfeld's compactification is universally locally acyclic over the moduli stack of G-bundles at points sufficiently antidominant relative to their defect.
Accelerating Stochastic Gradient Descent for Least Squares Regression

There is widespread sentiment that it is not possible to effectively utilize fast gradient methods (e.g. Nesterov's acceleration, conjugate gradient, heavy ball) for the purposes of stochastic optimization due to their instability and error accumulation, a notion made precise in d'Aspremont 2008 and Devolder, Glineur, and Nesterov 2014. This work considers these issues for the special case of stochastic approximation for the least squares regression problem, and our main result refutes the conventional wisdom by showing that acceleration can be made robust to statistical errors. In particular, this work introduces an accelerated stochastic gradient method that provably achieves the minimax optimal statistical risk faster than stochastic gradient descent. Critical to the analysis is a sharp characterization of accelerated stochastic gradient descent as a stochastic process. We hope this characterization gives insights towards the broader question of designing simple and effective accelerated stochastic methods for more general convex and non-convex optimization problems.
Bikei Invariants and Gauss Diagrams for Virtual Knotted Surfaces

Marked vertex diagrams provide a combinatorial way to represent knotted surfaces in ℝ4; including virtual crossings allows for a theory of virtual knotted surfaces and virtual cobordisms. Biquandle counting invariants are defined only for marked vertex diagrams representing knotted orientable surfaces; we extend these invariants to all virtual marked vertex diagrams by considering colorings by involutory biquandles, also known as bikei. We introduce a way of representing marked vertex diagrams with Gauss diagrams and use these to characterize orientability.
Smoothed projections and mixed boundary conditions

Mixed boundary conditions are introduced to finite element exterior calculus. We construct smoothed projections from Sobolev de Rham complexes onto finite element de Rham complexes which commute with the exterior derivative, preserve homogeneous boundary conditions along a fixed boundary part, and satisfy uniform bounds for shape-regular families of triangulations and bounded polynomial degree. The existence of such projections implies stability and quasi-optimal convergence of mixed finite element methods for the Hodge Laplace equation with mixed boundary conditions. In addition, we prove the density of smooth differential forms in Sobolev spaces of differential forms over weakly Lipschitz domains with partial boundary conditions.
Explicit integration of extremely stiff reaction networks: partial equilibrium methods

In two preceding papers (Guidry et al 2013 Comput. Sci. Disc. 6 015001 and Guidry and Harris 2013 Comput. Sci. Disc. 6 015002), we have shown that when reaction networks are well removed from equilibrium, explicit asymptotic and quasi-steady-state approximations can give algebraically stabilized integration schemes that rival standard implicit methods in accuracy and speed for extremely stiff systems. However, we also showed that these explicit methods remain accurate but are no longer competitive in speed as the network approaches equilibrium. In this paper, we analyze this failure and show that it is associated with the presence of fast equilibration timescales that neither asymptotic nor quasi-steady-state approximations are able to remove efficiently from the numerical integration. Based on this understanding, we develop a partial equilibrium method to deal effectively with the approach to equilibrium and show that explicit asymptotic methods, combined with the new partial equilibrium methods, give an integration scheme that can plausibly deal with the stiffest networks, even in the approach to equilibrium, with accuracy and speed competitive with that of implicit methods. Thus we demonstrate that such explicit methods may offer alternatives to implicit integration of even extremely stiff systems and that these methods may permit integration of much larger networks than have been possible before in a number of fields.
Quasi-Monte Carlo tractability of high dimensional integration over products of simplices

Quasi-Monte Carlo (QMC) methods for high dimensional integrals over unit cubes and products of spheres are well-studied in the literature. We study QMC tractability of integrals of functions defined over the product of m copies of the simplex T d ? R d . The domain is a tensor product of m reproducing kernel Hilbert spaces defined by 'weights' γ m , j , for j = 1 , 2 , ? , m . Similar to the results on the unit cube in m dimensions, and the product of m copies of the d -dimensional sphere, we prove that strong polynomial tractability holds iff lim sup m ? ∞ ? j = 1 m γ m , j < ∞ and polynomial tractability holds iff lim sup m ? ∞ ? j = 1 m γ m , j log ( m + 1 ) < ∞ . We also show that weak tractability holds iff lim m ? ∞ ? j = 1 m γ m , j m = 0 . The proofs employ Sobolev space techniques and weighted reproducing kernel Hilbert space techniques for the simplex and products of simplices as domain. Properties of orthogonal polynomials on a simplex are also used extensively.
Characteristic Variety of the Gauss-Manin Differential Equations of a Generic Parallelly Translated Arrangement

We consider a weighted family of \(n\) generic parallelly translated hyperplanes in \(\mathbb{C}^k\) and describe the characteristic variety of the Gauss–Manin differential equations for associated hypergeometric integrals. The characteristic variety is given as the zero set of Laurent polynomials, whose coefficients are determined by weights and the Plucker coordinates of the associated point in the Grassmannian Gr\((k,n)\). The Laurent polynomials are in involution.
Predicting Performance on MOOC Assessments Using Multi-Regression Models.

The past few years has seen the rapid growth of data min- ing approaches for the analysis of data obtained from Mas- sive Open Online Courses (MOOCs). The objectives of this study are to develop approaches to predict the scores a stu- dent may achieve on a given grade-related assessment based on information, considered as prior performance or prior ac- tivity in the course. We develop a personalized linear mul- tiple regression (PLMR) model to predict the grade for a student, prior to attempting the assessment activity. The developed model is real-time and tracks the participation of a student within a MOOC (via click-stream server logs) and predicts the performance of a student on the next as- sessment within the course offering. We perform a com- prehensive set of experiments on data obtained from three openEdX MOOCs via a Stanford University initiative. Our experimental results show the promise of the proposed ap- proach in comparison to baseline approaches and also helps in identification of key features that are associated with the study habits and learning behaviors of students.
Unit Groups of Representation Rings and their Ghost Rings as Inflation Functors

Abstract The theory of biset functors developed by Serge Bouc has been instrumental in the study of the unit group of the Burnside ring of a finite group, in particular for the case of p-groups. The ghost ring of the Burnside ring defines an inflation functor, and becomes a useful tool in studying the Burnside ring functor itself. We are interested in studying the unit group of another representation ring: the trivial source ring of a finite group. In this article, we show how the unit groups of the trivial source ring and its associated ghost ring define inflation functors. Since the trivial source ring is often seen as connecting the Burnside ring to the character ring and Brauer character ring of a finite group, we study all these representation rings at the same time. We point out that restricting all of these representation rings' unit groups to their torsion subgroups also give inflation functors, which we can completely determine in the case of the character ring and Brauer character ring.
A Large-Scale Study on Regularization and Normalization in GANs

Generative adversarial networks (GANs) are a class of deep generative models which aim to learn a target distribution in an unsupervised fashion. While they were successfully applied to many problems, training a GAN is a notoriously challenging task and requires a significant number of hyperparameter tuning, neural architecture engineering, and a non-trivial amount of "tricks". The success in many practical applications coupled with the lack of a measure to quantify the failure modes of GANs resulted in a plethora of proposed losses, regularization and normalization schemes, as well as neural architectures. In this work we take a sober view of the current state of GANs from a practical perspective. We discuss and evaluate common pitfalls and reproducibility issues, open-source our code on Github, and provide pre-trained models on TensorFlow Hub.
On a class of permutation trinomials in characteristic 2

Recently, Tu, Zeng, Li, and Helleseth considered trinomials of the form $f(X)=X+aX^{q(q-1)+ 1}+bX^{2(q-1)+ 1}\in \mathbb {F}_{q^{2}}[X]$, where q is even and $a,b\in \mathbb {F}_{q^{2}}^{*}$. They found sufficient conditions on a, b for f to be a permutation polynomial (PP) of $\mathbb {F}_{q^{2}}$ and they conjectured that the sufficient conditions are also necessary. The conjecture has been confirmed by Bartoli using the Hasse-Weil bound. In this paper, we give an alternative solution to the question. We also use the Hasse-Weil bound, but in a different way. Moreover, the necessity and sufficiency of the conditions are proved by the same approach.
The Optimal Approximation Factor in Density Estimation.

Consider the following problem: given two arbitrary densities $q_1,q_2$ and a sample-access to an unknown target density $p$, find which of the $q_i$'s is closer to $p$ in total variation. A remarkable result due to Yatracos shows that this problem is tractable in the following sense: there exists an algorithm that uses $O(\epsilon^{-2})$ samples from $p$ and outputs~$q_i$ such that with high probability, $TV(q_i,p) \leq 3\cdot\mathsf{opt} + \epsilon$, where $\mathsf{opt}= \min\{TV(q_1,p),TV(q_2,p)\}$. Moreover, this result extends to any finite class of densities $\mathcal{Q}$: there exists an algorithm that outputs the best density in $\mathcal{Q}$ up to a multiplicative approximation factor of 3. We complement and extend this result by showing that: (i) the factor 3 can not be improved if one restricts the algorithm to output a density from $\mathcal{Q}$, and (ii) if one allows the algorithm to output arbitrary densities (e.g.\ a mixture of densities from $\mathcal{Q}$), then the approximation factor can be reduced to 2, which is optimal. In particular this demonstrates an advantage of improper learning over proper in this setup. We develop two approaches to achieve the optimal approximation factor of 2: an adaptive one and a static one. Both approaches are based on a geometric point of view of the problem and rely on estimating surrogate metrics to the total variation. Our sample complexity bounds exploit techniques from {\it Adaptive Data Analysis}.
The Powell conjecture and reducing sphere complexes

The Powell Conjecture offers a finite generating set for the genus $g$ Goeritz group, the group of automorphisms of $S^3$ that preserve a genus $g$ Heegaard surface $\Sigma_g$, generalizing a classical result of Goeritz in the case $g=2$. We study the relationship between the Powell Conjecture and the reducing sphere complex $\mathcal{R}(\Sigma_g)$, the subcomplex of the curve complex $\mathcal{C}(\Sigma_g)$ spanned by the reducing curves for the Heegaard splitting. We prove that the Powell Conjecture is true if and only if $\mathcal{R}(\Sigma_g)$ is connected. Additionally, we show that reducing curves that meet in at most six points are connected by a path in $\mathcal{R}(\Sigma_g)$; however, we also demonstrate that even among reducing curves meeting in four points, the distance in $\mathcal{R}(\Sigma_g)$ between such curves can be arbitrarily large. We conclude with a discussion of the geometry of $\mathcal{R}(\Sigma_g)$.
Cascaded Projection: End-To-End Network Compression and Acceleration

We propose a data-driven approach for deep convolutional neural network compression that achieves high accuracy with high throughput and low memory requirements. Current network compression methods either find a low-rank factorization of the features that requires more memory or select only a subset of features by pruning entire filter channels. We propose the Cascaded Projection (CaP) compression method that projects the output and input filter channels of successive layers to a unified low dimensional space based on a low-rank projection. We optimize the projection to minimize classification loss and the difference between the next layer's features in the compressed and uncompressed networks. To solve this non-convex optimization problem we propose a new optimization method of a proxy matrix using backpropagation and Stochastic Gradient Descent (SGD) with geometric constraints. Our cascaded projection approach leads to improvements in all critical areas of network compression: high accuracy, low memory consumption, low parameter count and high processing speed. The proposed CaP method demonstrates state of the art results compressing VGG16 and ResNet networks with over 4X reduction in the number of computations and excellent performance in top-5 accuracy on the ImageNet dataset before and after fine-tuning.