cssi/SciSciGPT-SciSciNet huggingface dataset:
A Step-Indexing Approach to Partial Functions

We describe an ACL2 package for defining partial recursive functions that also supports efficient execution. While packages for defining partial recursive functions already exist for other theorem provers, they often require inductive definitions or recursion operators which are not available in ACL2 and they provide little, if any, support for executing the resulting definitions. We use stepindexing as the underlying implementation technology, enabling the definitions to be carried out in first order logic. We also show how recent enhancements to ACL2’s guard feature can be used to enable the efficient execution of partial recursive functions.
Decomposition of Nonlinear Dynamical Systems Using Koopman Gramians

In this paper we propose a new Koopman operator approach to the decomposition of nonlinear dynamical systems using Koopman Gramians. We introduce the notion of an input-Koopman operator, and show how input-Koopman operators can be used to cast a nonlinear system into the classical state-space form, and identify conditions under which input and state observable functions are well separated. We then extend an existing method of dynamic mode decomposition for learning Koopman operators from data known as deep dynamic mode decomposition to systems with controls or disturbances. We illustrate the accuracy of the method in learning an input-state separable Koopman operator for an example system, even when the underlying system exhibits mixed state-input terms. We next introduce a nonlinear decomposition algorithm, based on Koopman Gramians, that maximizes internal subsystem observability and disturbance rejection from unwanted noise from other subsystems. We derive a relaxation based on Koopman Gramians and multi-way partitioning for the resulting NP-hard decomposition problem. We lastly illustrate the proposed algorithm with the swing dynamics for an IEEE 39-bus system.
Unirationality of Moduli Spaces of Special Cubic Fourfolds and K3 Surfaces

We provide explicit descriptions of the generic members of Hassett’s divisors \(\mathcal{C}_{d}\) for relevant 18 ≤ d ≤ 38 and for d = 44, which furthermore gives unirationality of these \(\mathcal{C}_{d}\). It follows as a corollary that the moduli space \(\mathcal{N}_{d}\) of polarized K3 surfaces of degree d is unirational for d = 14, 26, 38. The case d = 26 is entirely new, while the other two cases have been previously proven by Mukai. We also explain the construction of what we conjecture to be a new family of hyperkahler manifolds which are not birational to any moduli space of (twisted) sheaves on a K3 surface.
DELTACON: A principled massive-graph similarity function

How much did a network change since yesterday? How different is the wiring between Bob’s brain (a left-handed male) and Alice’s brain (a right-handed female)? Graph similarity with known node correspondence, i.e. the detection of changes in the connectivity of graphs, arises in numerous settings. In this work, we formally state the axioms and desired properties of the graph similarity functions, and evaluate when state-of-the-art methods fail to detect crucial connectivity changes in graphs. We propose DELTACON, a principled, intuitive, and scalable algorithm that assesses the similarity between two graphs on the same nodes (e.g. employees of a company, customers of a mobile carrier). Experiments on various synthetic and real graphs showcase the advantages of our method over existing similarity measures. Finally, we employ DELTACON to real applications: (a) we classify people to groups of high and low creativity based on their brain connectivity graphs, and (b) do temporal anomaly detection in the who-emails-whom Enron graph.
Arbitrary spin Galilean oscillator

Abstract The so-called Dirac oscillator was proposed as a modification of the free Dirac equation which reproduces many of the properties of the simple harmonic oscillator but accompanied by a strong spin–orbit coupling term. It is shown here using the formalism of totally symmetric multispinors that the Dirac oscillator can be made to accommodate spin by incorporating it into the framework of Galilean relativity. This is done explicitly for spin zero and spin one as special cases of the arbitrary spin result. For the general case it is shown that the coefficient of the spin–orbit term has a 1 / S behavior.
Efficient functional ANOVA through wavelet-domain Markov groves

We introduce a wavelet-domain method for functional analysis of variance (fANOVA). It is based on a Bayesian hierarchical model that employs a graphical hyperprior in the form of a Markov grove (MG...
The Hopf algebra of odd symmetric functions

Abstract We consider a q -analogue of the standard bilinear form on the commutative ring of symmetric functions. The q = − 1 case leads to a Z -graded Hopf superalgebra which we call the algebra of odd symmetric functions. In the odd setting, we describe counterparts of the elementary and complete symmetric functions, power sums, Schur functions, and combinatorial interpretations of associated change of basis relations.
A family of non-split topologically slice links with arbitrarily large smooth slice genus

We construct an infinite family of topologically slice 2--component boundary links $\ell_i$, none of which is smoothly concordant to a split link, such that $g_4(\ell_i)=i$.
Partial rigidity of CR embeddings of real hypersurfaces into hyperquadrics with small signature difference

We study the rigidity of holomorphic mappings from a neighborhood of a Levi-nondegenerate CR hypersurface $M$ with signature $l$ into a hyperquadric $Q_{l'}^{N} \subseteq \mathbb{CP}^{N+1}$ of larger dimension and signature. We show that if the CR complexity of $M$ is not too large then the image of $M$ under any such mapping is contained in a complex plane with dimension independent of $N$. This result follows from two theorems, the first demonstrating that for sufficiently degenerate mappings, the image of $M$ is contained in a plane, and the second relating the degeneracy of mappings into different quadrics.
Two-Player Games for Efficient Non-Convex Constrained Optimization

In recent years, constrained optimization has become increasingly relevant to the machine learning community, with applications including Neyman-Pearson classification, robust optimization, and fair machine learning. A natural approach to constrained optimization is to optimize the Lagrangian, but this is not guaranteed to work in the non-convex setting, and, if using a first-order method, cannot cope with non-differentiable constraints (e.g. constraints on rates or proportions). The Lagrangian can be interpreted as a two-player game played between a player who seeks to optimize over the model parameters, and a player who wishes to maximize over the Lagrange multipliers. We propose a non-zero-sum variant of the Lagrangian formulation that can cope with non-differentiable--even discontinuous--constraints, which we call the "proxy-Lagrangian". The first player minimizes external regret in terms of easy-to-optimize "proxy constraints", while the second player enforces the original constraints by minimizing swap regret. For this new formulation, as for the Lagrangian in the non-convex setting, the result is a stochastic classifier. For both the proxy-Lagrangian and Lagrangian formulations, however, we prove that this classifier, instead of having unbounded size, can be taken to be a distribution over no more than m+1 models (where m is the number of constraints). This is a significant improvement in practical terms.
Optimal stretching for lattice points and eigenvalues

We aim to maximize the number of first-quadrant lattice points in a convex domain with respect to reciprocal stretching in the coordinate directions. The optimal domain is shown to be asymptotically balanced, meaning that the stretch factor approaches $1$ as the “radius” approaches infinity. In particular, the result implies that among all $p$-ellipses (or Lame curves), the $p$-circle encloses the most first-quadrant lattice points as the radius approaches infinity, for $1\lt p \lt \infty$. The case $p=2$ corresponds to minimization of high eigenvalues of the Dirichlet Laplacian on rectangles, and so our work generalizes a result of Antunes and Freitas. Similarly, we generalize a Neumann eigenvalue maximization result of van den Berg, Bucur and Gittins. Further, Ariturk and Laugesen recently handled $0 \lt p \lt 1$ by building on our results here. The case $p=1$ remains open, and is closely related to minimizing energy levels of harmonic oscillators: which right triangles in the first quadrant with two sides along the axes will enclose the most lattice points, as the area tends to infinity?
HNN decompositions of the Lodha–Moore groups, and topological applications

The Lodha–Moore groups provide the first known examples of type F∞ groups that are non-amenable and contain no non-abelian free subgroups. These groups are related to Thompson’s group F in certain ways, for instance they contain it as a subgroup in a natural way. We exhibit decompositions of four Lodha–Moore groups, G, Gy, yG and yGy, into ascending HNN extensions of isomorphic copies of each other, both in ways reminiscent to such decompositions for F and also in quite different ways. This allows us to prove two new topological results about the Lodha–Moore groups. First, we prove that they all have trivial homotopy groups at infinity; in particular they are the first examples of groups satisfying all four parts of Geoghegan’s 1979 conjecture about F. Second, we compute the Bieri–Neumann–Strebel invariant Σ1 for the Lodha–Moore groups, and get some partial results for the Bieri–Neumann–Strebel–Renz invariants Σm, including a full computation of Σ2.
Look-ahead before you leap: end-to-end active recognition by forecasting the effect of motion

Visual recognition systems mounted on autonomous moving agents face the challenge of unconstrained data, but simultaneously have the opportunity to improve their performance by moving to acquire new views of test data. In this work, we first show how a recurrent neural network-based system may be trained to perform end-to-end learning of motion policies suited for this “active recognition” setting. Further, we hypothesize that active vision requires an agent to have the capacity to reason about the effects of its motions on its view of the world. To verify this hypothesis, we attempt to induce this capacity in our active recognition pipeline, by simultaneously learning to forecast the effects of the agent’s motions on its internal representation of the environment conditional on all past views. Results across two challenging datasets confirm both that our end-to-end system successfully learns meaningful policies for active category recognition, and that “learning to look ahead” further boosts recognition performance.
A Construction of Cospectral Graphs for the Normalized Laplacian

We give a method to construct cospectral graphs for the normalized Laplacian by a local modification in some graphs with special structure. Namely, under some simple assumptions, we can replace a small bipartite graph with a cospectral mate without changing the spectrum of the entire graph. We also consider a related result for swapping out biregular bipartite graphs for the matrix $A+tD$. We produce (exponentially) large families of non-bipartite, non-regular graphs which are mutually cospectral, and also give an example of a graph which is cospectral with its complement but is not self-complementary.
On the Distribution of Hecke Eigenvalues for Cuspidal Automorphic Representations for GL(2)

Given a self-dual cuspidal automorphic representation for GL(2) over a number field, we establish the existence of an infinite number of Hecke eigenvalues that are greater than an explicit positive constant, and an infinite number of Hecke eigenvalues that are less than an explicit negative constant. This provides an answer to a question of Serre. We also consider analogous problems for cuspidal automorphic representations that are not self-dual.
Non-Abelian Lefschetz hyperplane theorems

Suppose X is a smooth projective algebraic variety over C, and D ⊂ X is an ample divisor. There are many classical theorems relating properties of X with those of D. For example: • The natural restriction map H(X,Z/`Z) → H(D,Z/`Z) is an isomorphism if i < dim(D) and an injection if i = dim(D) (where here H can be taken to mean e.g. singular or etale cohomology); • The natural restriction map Pic(X)→ Pic(D) is an isomorphism if dim(X) ≥ 4; • The natural map π 1 (D)→ π 1 (X) is an isomorphism if dim(X) ≥ 3. I’d like to reinterpret these theorems in a way which is, hopefully, suggestive: • The restriction map Hom(X,K(Z/`Z, i)) → Hom(D,K(Z/`Z, i)) is an inclusion on π0 and a weak equivalence on each connected component (for i = dim(D))—here Hom can be taken to mean the space of continuous maps, or one can make sense of this in algebraic geometry by taking K(Z/`Z, i) to be a simplicial scheme; • The restriction map Hom(X,BGm)→ Hom(D,BGm) is an equivalence of stacks if dim(X) ≥ 4; • The restriction map Hom(X,BG) → Hom(D,BG) is an equivalence of stacks for all finite etale group schemes G if dim(X) ≥ 3 (that is, the fact that the fundamental groups are isomorphic follows is equivalent to the categories of finite Galois etale covers—classified by BG—are the same).
Limitations of Design-based Causal Inference and A/B Testing under Arbitrary and Network Interference

Randomized experiments on a network often involve interference between connected units, namely, a situation in which an individual’s treatment can affect the response of another individual. Current...
Frequentism and Bayesianism: A Python-driven Primer

This paper presents a brief, semi-technical comparison of the es- sential features of the frequentist and Bayesian approaches to statistical infer- ence, with several illustrative examples implemented in Python. The differences between frequentism and Bayesianism fundamentally stem from differing defini- tions of probability, a philosophical divide which leads to distinct approaches to the solution of statistical problems as well as contrasting ways of asking and answering questions about unknown parameters. After an example-driven discussion of these differences, we briefly compare several leading Python sta- tistical packages which implement frequentist inference using classical methods and Bayesian inference using Markov Chain Monte Carlo. 1
Scaling the Kalman Filter for Large-Scale Traffic Estimation

This work introduces a scalable filtering algorithm for multiagent traffic estimation. Large-scale networks are spatially partitioned into overlapping road sections. The traffic dynamics of each section is given by the switching mode model using a conservation principle, and the traffic state in each section is estimated by a local agent. In the proposed filter, a consensus term is applied to promote interagent agreement on overlapping sections. The new filter, termed as (spatially) distributed local Kalman consensus filter (DLKCF), is shown to maintain globally asymptotically stable mean error dynamics when all sections switch among observable modes. When a section is unobservable, we show that the mean estimate of each state variable in the section is ultimately bounded, which is achieved by exploring the interaction between the properties of the traffic model and the measurement feedback of the filter. Based on the above results, the boundedness of the mean estimation error of the DLKCF under switching sequences with observable and unobservable modes is established to address the overall performance of the filter. Numerical experiments show the ability of the DLKCF to promote consensus, increase estimation accuracy compared to a local filter, and reduce the computational load compared to a centralized approach.
WNOS: An Optimization-based Wireless Network Operating System

This article investigates the basic design principles for a new Wireless Network Operating System (WNOS), a radically different approach to software-defined networking (SDN) for infrastructure-less wireless networks. Departing from well-understood approaches inspired by OpenFlow, WNOS provides the network designer with an abstraction hiding (i) the lower-level details of the wireless protocol stack and (ii) the distributed nature of the network operations. Based on this abstract representation, the WNOS takes network control programs written on a centralized, high-level view of the network and automatically generates distributed cross-layer control programs based on distributed optimization theory that are executed by each individual node on an abstract representation of the radio hardware. We first discuss the main architectural principles of WNOS. Then, we discuss a new approach to automatically generate solution algorithms for each of the resulting subproblems in an automated fashion. Finally, we illustrate a prototype implementation of WNOS on software-defined radio devices and test its effectiveness by considering specific cross-layer control problems. Experimental results indicate that, based on the automatically generated distributed control programs, WNOS achieves 18%, 56% and 80.4% utility gain in networks with low, medium and high levels of interference; maybe more importantly, we illustrate how the global network behavior can be controlled by modifying a few lines of code on a centralized abstraction.
Stochastic optimization and control framework for 5G network slicing with effective isolation

Network slicing is an emerging technique for providing resources to diverse wireless services with heterogeneous quality-of-service needs. However, beyond satisfying end-to-end requirements of network users, network slicing needs to also provide isolation between slices so as to prevent one slice's faults and congestion from affecting other slices. In this paper, the problem of network slicing is studied in the context of a wireless system having a time-varying number of users that require two types of slices: reliable low latency (RLL) and self-managed (capacity limited) slices. To address this problem, a novel control framework for stochastic optimization is proposed based on the Lyapunov drift-plus-penalty method. This new framework enables the system to minimize power, maintain slice isolation, and provide reliable and low latency end-to-end communication for RLL slices. Simulation results show that the proposed approach can maintain the system's reliability while providing effective slice isolation in the event of sudden changes in the network environment.
Exchangeable Pairs, Switchings, and Random Regular Graphs

We consider the distribution of cycle counts in a random regular graph, which is closely linked to the graph's spectral properties. We broaden the asymptotic regime in which the cycle counts are known to be approximately Poisson, and we give an explicit bound in total variation distance for the approximation. Using this result, we calculate limiting distributions of linear eigenvalue statistics for random regular graphs. Previous results on the distribution of cycle counts by McKay, Wormald, and Wysocka (2004) used the method of switchings, a combinatorial technique for asymptotic enumeration. Our proof uses Stein's method of exchangeable pairs and demonstrates an interesting connection between the two techniques.
On the Global Regularity for a Wave-Klein—Gordon Coupled System

In this paper we consider a coupled Wave-Klein—Gordon system in 3D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by Wang and LeFloch—Ma as a simplified model for the global nonlinear stability of the Minkowski space-time for self-gravitating massive fields.
OverFeat: Integrated Recognition, Localization and Detection using Convolutional Networks

Abstract: We present an integrated framework for using Convolutional Networks for classification, localization and detection. We show how a multiscale and sliding window approach can be efficiently implemented within a ConvNet. We also introduce a novel deep learning approach to localization by learning to predict object boundaries. Bounding boxes are then accumulated rather than suppressed in order to increase detection confidence. We show that different tasks can be learned simultaneously using a single shared network. This integrated framework is the winner of the localization task of the ImageNet Large Scale Visual Recognition Challenge 2013 (ILSVRC2013) and obtained very competitive results for the detection and classifications tasks. In post-competition work, we establish a new state of the art for the detection task. Finally, we release a feature extractor from our best model called OverFeat.
Hox genes limit germ cell formation in the short germ insect Gryllus bimaculatus

Hox genes are conserved transcription factor-encoding genes that specify the identity of body regions in bilaterally symmetrical animals. In the cricket Gryllus bimaculatus, a member of the hemimetabolous insect group Orthoptera, the induction of a subset of mesodermal cells to form the primordial germ cells (PGCs) is restricted to the second through the fourth abdominal segments (A2 to A4). In numerous insect species, the Hox genes Sex-combs reduced (Scr), Antennapedia (Antp), Ultrabithorax (Ubx), and abdominal-A (abd-A) jointly regulate the identities of middle and posterior body segments, suggesting that these genes may restrict PGC formation to specific abdominal segments in G. bimaculatus Here we show that reducing transcript levels of some or all of these Hox genes results in supernumerary and/or ectopic PGCs, either individually or in segment-specific combinations, suggesting that the role of these Hox genes is to limit PGC development with respect to their number, segmental location, or both. These data provide evidence of a role for this ancient group of genes in PGC development.
Higher Genus Doubly Periodic Minimal Surfaces

ABSTRACTWe construct Weierstrass data for higher genus embedded doubly periodic minimal surfaces and present numerical evidence that the associated period problem can be solved. In the orthogonal ends case, there previously was only one known surface for each genus g. We illustrate multiple new examples for each genus g ⩾ 3. In the parallel ends case, the known examples limit as a foliation of parallel planes with nodes. We construct a new example for each genus g ⩾ 3 that limit as g − 1 singly periodic Scherk surfaces glued between two doubly periodic Scherk surfaces and also as a singly periodic surface with four vertical and 2g horizontal Scherk ends.
Proper Policies in Infinite-State Stochastic Shortest Path Problems

We consider stochastic shortest path problems with infinite state and control spaces, a nonnegative cost per stage, and a termination state. We extend the notion of a proper policy, a policy that terminates within a finite expected number of steps, from the context of finite state space to the context of infinite state space. We consider the optimal cost function $J^*$ , and the optimal cost function $\hat{J}$ over just the proper policies. We show that $J^*$ and $\hat{J}$ are the smallest and largest solutions of Bellman's equation, respectively, within a suitable class of Lyapounov-like functions. If the cost per stage is bounded, these functions are those that are bounded over the effective domain of $\hat{J}$ . The standard value iteration algorithm may be attracted to either $J^*$ or $\hat{J}$ , depending on the initial condition.
Learning latent variable structured prediction models with Gaussian perturbations

The standard margin-based structured prediction commonly uses a maximum loss over all possible structured outputs. The large-margin formulation including latent variables not only results in a non-convex formulation but also increases the search space by a factor of the size of the latent space. Recent work has proposed the use of the maximum loss over random structured outputs sampled independently from some proposal distribution, with theoretical guarantees. We extend this work by including latent variables. We study a new family of loss functions under Gaussian perturbations and analyze the effect of the latent space on the generalization bounds. We show that the non-convexity of learning with latent variables originates naturally, as it relates to a tight upper bound of the Gibbs decoder distortion with respect to the latent space. Finally, we provide a formulation using random samples and relaxations that produces a tighter upper bound of the Gibbs decoder distortion up to a statistical accuracy, which enables a polynomial time evaluation of the objective function. We illustrate the method with synthetic experiments and a computer vision application.
Exact bounds on the free energy in QCD

We consider the free energy W [J] = Wk(H) of QCD coupled to an external source Jb μ(x) = Hb μ cos(k · x), where Hb μ is, by analogy with spin models, an external “magnetic” field with a color index that is modulated by a plane wave. We report an optimal bound on Wk(H) and an exact asymptotic expression for Wk(H) at large H. They imply confinement of color in the sense that the free energy per unit volume Wk(H)/V and the average magnetization m(k,H) = 1 V ∂Wk(H) ∂H vanish in the limit of constant external field k→ 0. Recent lattice data indicate a gluon propagator
Exposing Deep Fakes Using Inconsistent Head Poses

In this paper, we propose a new method to expose AI-generated fake face images or videos (commonly known as the Deep Fakes). Our method is based on the observations that Deep Fakes are created by splicing synthesized face region into the original image, and in doing so, introducing errors that can be revealed when 3D head poses are estimated from the face images. We perform experiments to demonstrate this phenomenon and further develop a classification method based on this cue. Using features based on this cue, an SVM classifier is evaluated using a set of real face images and Deep Fakes.
Leveraging Coding Techniques for Speeding up Distributed Computing

Large scale clusters running MapReduce, Spark etc. routinely process data that are on the orders of petabytes or more. The philosophy in these methods is to split the overall job into smaller tasks that are executed on different servers; this is called the map phase. This is followed by a data shuffling phase where appropriate data is exchanged between the servers. The final reduce phase, completes the computation. Prior work has explored a mechanism for reducing the overall execution time by operating on a computation vs. communication tradeoff. Specifically, the idea is to run redundant copies of map tasks that are placed on judiciously chosen servers. The shuffle phase exploits the location of the nodes and utilizes coded transmission. The main drawback of this approach is that it requires the original job to be split into a number of map tasks that grows exponentially in the system parameters. This is problematic, as we demonstrate that splitting jobs too finely can in fact adversely affect the overall execution time. In this work we show that one can simultaneously obtain low communication loads while ensuring that jobs do not need to be split too finely. Our approach uncovers a deep relationship between this problem and a class of combinatorial structures called resolvable designs. We present experimental results obtained on Amazon EC2 clusters for a widely known distributed algorithm, namely TeraSort. We obtain over 4.69x improvement in speedup over the baseline approach and more than 2.6x over current state of the art.
Robust Control for Renewable-Integrated Power Networks Considering Input Bound Constraints and Worst Case Uncertainty Measure

Uncertainty from renewable energy and loads is one of the major challenges for stable grid operation. Various approaches have been explored to remedy these uncertainties. In this paper, we design centralized or decentralized state-feedback controllers for generators while considering worst case uncertainty. Specifically, this paper introduces the notion of $\mathcal {L}_{\infty }$ robust control and stability for uncertain power networks. An uncertain and nonlinear differential algebraic equation model of the network is presented. The model includes unknown disturbances from renewables and loads. Given an operating point, the linearized state-space presentation is given. Then, the notion of $\mathcal {L}_{\infty }$ robust control and stability is discussed, resulting in a nonconvex optimization routine that yields a state feedback gain mitigating the impact of disturbances. The developed routine includes explicit input-bound constraints on generators’ inputs and a measure of the worst case disturbance. The feedback control architecture can be centralized, distributed, or decentralized. Algorithms based on successive convex approximations are then given to address the nonconvexity. Case studies are presented showcasing the performance of the $\mathcal {L}_{\infty }$ controllers in comparison with automatic generation control and $\mathcal {H}_{\infty }$ control methods.
Robust Machine Comprehension Models via Adversarial Training

It is shown that many published models for the Stanford Question Answering Dataset (Rajpurkar et al., 2016) lack robustness, suffering an over 50% decrease in F1 score during adversarial evaluation based on the AddSent (Jia and Liang, 2017) algorithm. It has also been shown that retraining models on data generated by AddSent has limited effect on their robustness. We propose a novel alternative adversary-generation algorithm, AddSentDiverse, that significantly increases the variance within the adversarial training data by providing effective examples that punish the model for making certain superficial assumptions. Further, in order to improve robustness to AddSent’s semantic perturbations (e.g., antonyms), we jointly improve the model’s semantic-relationship learning capabilities in addition to our AddSentDiverse-based adversarial training data augmentation. With these additions, we show that we can make a state-of-the-art model significantly more robust, achieving a 36.5% increase in F1 score under many different types of adversarial evaluation while maintaining performance on the regular SQuAD task.
Why approximate when you can get the exact? Optimal targeted viral marketing at scale

One of the most central problems in viral marketing is Influence Maximization (IM), which finds a set of k seed users who can influence the maximum number of users in online social networks. Unfortunately, all existing algorithms to IM, including the state of the art SSA and IMM, have an approximation ratio of (1 − 1/e − e). Recently, a generalization of IM, Cost-aware Target Viral Marketing (CTVM), asks for the most cost-effective users to influence the most relevant users, has been introduced. The current best algorithm for CTVM has an approximation ratio of (1 − 1/√e − e). In this paper, we study the CTVM problem, aiming to optimally solve the problem. We first highlight that using a traditional two stage stochastic programming to exactly solve CTVM is not possible because of scalability. We then propose an almost exact algorithm TIPTOP, which has an approximation ratio of (1 — e). This result significantly improves the current best solutions to both IM and CTVM. At the heart of TIPTOP lies an innovative technique that reduces the number of samples as much as possible. This allows us to exactly solve CTVM on a much smaller space of generated samples using Integer Programming. While obtaining an almost exact solution, TIPTOP is very scalable, running on billion-scale networks such as Twitter under three hours. Furthermore, TIPTOP lends a tool for researchers to benchmark their solutions against the optimal one in large-scale networks, which is currently not available.
Wide Aperture Exoplanet Telescope: a low-cost flat configuration for a 100+ meter ground based telescope

The Wide Aperture Exoplanet Telescope (WAET) is a ground-based optical telescope layout in which one dimension of a filled aperture can be made very large (beyond 100 m) at low cost and complexity. With an unusual beam path but otherwise conventional optics, we obtain a fully steerable telescope on a low-rise mount with a fixed-gravity vector on key components. Numerous design considerations and scaling laws suggest that WAET can be far less expensive than other giant segmented mirror telescopes.
A note on the cone conjecture for K3 surfaces in positive characteristic

We prove that, for a K3 surface in characteristic p > 2, the automorphism group acts on the nef cone with a rational polyhedral fundamental domain and on the nodal classes with finitely many orbits. As a consequence, for any non-negative integer g, there are only finitely many linear systems of irreducible curves on the surface of arithmetic genus g, up to the action of the automorphism group.
Visually-Aware Fashion Recommendation and Design with Generative Image Models

Building effective recommender systems for domains like fashion is challenging due to the high level of subjectivity and the semantic complexity of the features involved (i.e., fashion styles). Recent work has shown that approaches to 'visual' recommendation (e.g. clothing, art, etc.) can be made more accurate by incorporating visual signals directly into the recommendation objective, using 'off-the-shelf' feature representations derived from deep networks. Here, we seek to extend this contribution by showing that recommendation performance can be significantly improved by learning 'fashion aware' image representations directly, i.e., by training the image representation (from the pixel level) and the recommender system jointly; this contribution is related to recent work using Siamese CNNs, though we are able to show improvements over state-of-the-art recommendation techniques such as BPR and variants that make use of pretrained visual features. Furthermore, we show that our model can be used generatively, i.e., given a user and a product category, we can generate new images (i.e., clothing items) that are most consistent with their personal taste. This represents a first step towards building systems that go beyond recommending existing items from a product corpus, but which can be used to suggest styles and aid the design of new products.
Unsupervised body part regression via spatially self-ordering convolutional neural networks

Automatic body part recognition for CT slices can benefit various medical image applications. Recent deep learning methods demonstrate promising performance, with the requirement of large amounts of labeled images for training. The intrinsic structural or superior-inferior slice ordering information in CT volumes is not fully exploited. In this paper, we propose a convolutional neural network (CNN) based unsupervised body part regression (UBR) algorithm to address this problem. A novel unsupervised learning method and two inter-sample CNN loss functions are presented. Distinct from previous work, UBR builds a coordinate system for the human body and outputs a continuous score for each axial slice, representing the normalized position of the body part in the slice. The training process of UBR resembles a self-organization process: slice scores are learned from inter-slice relationships. The training samples are unlabeled CT volumes that are abundant, thus no extra annotation effort is needed. UBR is simple, fast, and accurate. Quantitative and qualitative experiments validate its effectiveness. In addition, we show two applications of UBR in network initialization and anomaly detection.
Optimizing Signalized Intersections Performance Under Conventional and Automated Vehicles Traffic

Automated vehicles or AVs (i.e., those that have the ability to operate without a driver and can communicate with the infrastructure) may transform the transportation system. This study integrates AV trajectory planning and signal phase and timing (SPaT) optimization at an isolated intersection. The proposed control algorithm functions under mixed traffic of AVs and conventional vehicles (CNVs) in real-time. The proposed system aims to achieve coordination among incoming vehicles and SPaT through joint optimization. The input to the algorithm includes vehicles arrival data, and the output consists of optimized trajectories and SPaT commands to the AVs and the signal controller, respectively, to be implemented. Comparison of the algorithm to operations with a fully actuated signal control shows 38%–52% reduction in average travel time.
An efficient algorithm for simulating ensembles of parameterized flow problems

Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the individually independent members of the set are subject to different viscosity coefficients, initial conditions, and/or body forces. The proposed scheme applied to the flow ensemble leads to need to solve a single linear system with multiple right-hand sides, and thus is computationally more efficient than solving for all the simulations separately. We show that the scheme is nonlinearly and long-term stable under certain conditions on the time-step size and a parameter deviation ratio. Rigorous numerical error estimate shows the scheme is of first-order accuracy in time and optimally accurate in space. Several numerical experiments are presented to illustrate the theoretical results.
THE NON-COMMUTATIVE A-POLYNOMIAL OF TWIST KNOTS

The purpose of the paper is two-fold: to introduce a multivariable creative telescoping method, and to apply it in a problem of Quantum Topology: namely the computation of the non-commutative A-polynomial of twist knots. Our multivariable creative telescoping method allows us to compute linear recursions for sums of the form given a recursion relation for and the hypergeometric kernel c(n, k). As an application of our method, we explicitly compute the non-commutative A-polynomial for twist knots with -15 and 15 crossings. The non-commutative A-polynomial of a knot encodes the monic, linear, minimal order q-difference equation satisfied by the sequence of colored Jones polynomials of the knot. Its specialization to q = 1 is conjectured to be the better-known A-polynomial of a knot, which encodes important information about the geometry and topology of the knot complement. Unlike the case of the Jones polynomial, which is easily computable for knots with 50 crossings, the A-polynomial is harder to compute and already unknown for some knots with 12 crossings.
Weak atomic convergence of finite voter models toward Fleming–Viot processes

Abstract We consider the empirical measures of multi-type voter models with mutation on large finite sets, and prove their weak atomic convergence in the sense of Ethier and Kurtz (1994) toward a Fleming–Viot process. Convergence in the weak atomic topology is strong enough to answer a line of inquiry raised by Aldous (2013) concerning the distributions of the corresponding entropy processes and diversity processes for types.
Scaling laws and the rate of convergence in thin magnetic films

Abstract We study static 180 degree domain walls in thin infinite magnetic films. We establish the scaling of the minimal energy by Γ -convergence and the energy minimizer profile, which turns out to be the so-called transverse wall as predicted in earlier numerical and experimental work. Surprisingly, the minimal energy decays faster than the area of the film cross section at an infinitesimal cross section diameter. We establish a rate of convergence of the rescaled energies as well.
Closed-Form Detector for Solid Sub-Pixel Targets in Multivariate T-Distributed Background Clutter

The generalized likelihood ratio test (GLRT) is used to derive a detector for solid sub-pixel targets in hyperspectral imagery. A closed-form solution is obtained that optimizes the replacement target model when the background is a fat-tailed elliptically-contoured multivariate t-distribution. This generalizes GLRT-based detectors that have previously been derived for the replacement target model with Gaussian background, and for the additive target model with an elliptically-contoured background. Experiments with simulated hyperspectral data illustrate the performance of this detector in various parameter regimes.
Aspherical 4-manifolds of odd Euler characteristic

An explicit construction of closed, orientable, smooth, aspherical 4-manifolds with any odd Euler characteristic greater than 12 is presented. The manifolds constructed here are all Haken manifolds in the sense of B. Foozwell and H. Rubinstein and can be systematically reduced to balls by suitably cutting them open along essential codimension-one submanifolds. It is easy to construct examples with even Euler characteristic from products of surfaces. And Euler characteristics divisible by 3 are know to arise from complex algebraic geometry considerations. Examples with Euler characteristic 1, 5, 7, or 11 appear to be unknown.
Global properties of nested network model with application to multi-epitope HIV/CTL dynamics

Mathematical modeling and analysis can provide insight on the dynamics of ecosystems which maintain biodiversity in the face of competitive and prey–predator interactions. Of primary interests are the underlying structure and features which stabilize diverse ecological networks. Recently Korytowski and Smith (Theor Ecol 8(1):111–120, 2015) proved that a perfectly nested infection network, along with appropriate life history trade-offs, leads to coexistence and persistence of bacteria-phage communities in a chemostat model. In this article, we generalize their model in order to apply it to the within-host dynamics virus and immune response, in particular HIV and CTL (Cytotoxic T Lymphocyte) cells. Our model can describe sequential viral escape from dominant immune responses and rise in subdominant immune responses, consistent with observed patterns of HIV/CTL evolution. We find a Lyapunov function for the system which leads to rigorous characterization of persistent viral and immune variants, along with informing upon equilibria stability and global dynamics. Results are interpreted in the context of within-host HIV/CTL evolution and numerical simulations are provided.
Approximate Nearest Neighbors in Limited Space

We consider the $(1+\epsilon)$-approximate nearest neighbor search problem: given a set $X$ of $n$ points in a $d$-dimensional space, build a data structure that, given any query point $y$, finds a point $x \in X$ whose distance to $y$ is at most $(1+\epsilon) \min_{x \in X} \|x-y\|$ for an accuracy parameter $\epsilon \in (0,1)$. Our main result is a data structure that occupies only $O(\epsilon^{-2} n \log(n) \log(1/\epsilon))$ bits of space, assuming all point coordinates are integers in the range $\{-n^{O(1)} \ldots n^{O(1)}\}$, i.e., the coordinates have $O(\log n)$ bits of precision. This improves over the best previously known space bound of $O(\epsilon^{-2} n \log(n)^2)$, obtained via the randomized dimensionality reduction method of Johnson and Lindenstrauss (1984). We also consider the more general problem of estimating all distances from a collection of query points to all data points $X$, and provide almost tight upper and lower bounds for the space complexity of this problem.
On the capacity achieving probability measures for molecular receivers

In this paper, diffusion-based molecular communication with ligand receptor receivers is studied. Information messages are assumed to be encoded via variations of the concentration of molecules. The randomness in the ligand reception process induces uncertainty in the communication; limiting the rate of information decoding. We model the ligand receptor receiver by a set of finite-state Markov channels and study the general capacity of such a receiver. Furthermore, the i.i.d. capacity of the receiver is characterized as a lower bound for the general capacity. It is also proved that a finite support probability measure can achieve the i.i.d. capacity of the receiver. Moreover, a bound on the number of points in the support of the probability measure is obtained.
Validation of neural spike sorting algorithms without ground-truth information.

Abstract Background The throughput of electrophysiological recording is growing rapidly, allowing thousands of simultaneous channels, and there is a growing variety of spike sorting algorithms designed to extract neural firing events from such data. This creates an urgent need for standardized, automatic evaluation of the quality of neural units output by such algorithms. New method We introduce a suite of validation metrics that assess the credibility of a given automatic spike sorting algorithm applied to a given dataset. By rerunning the spike sorter two or more times, the metrics measure stability under various perturbations consistent with variations in the data itself, making no assumptions about the internal workings of the algorithm, and minimal assumptions about the noise. Results We illustrate the new metrics on standard sorting algorithms applied to both in vivo and ex vivo recordings, including a time series with overlapping spikes. We compare the metrics to existing quality measures, and to ground-truth accuracy in simulated time series. We provide a software implementation. Comparison with existing methods Metrics have until now relied on ground-truth, simulated data, internal algorithm variables (e.g. cluster separation), or refractory violations. By contrast, by standardizing the interface, our metrics assess the reliability of any automatic algorithm without reference to internal variables (e.g. feature space) or physiological criteria. Conclusions Stability is a prerequisite for reproducibility of results. Such metrics could reduce the significant human labor currently spent on validation, and should form an essential part of large-scale automated spike sorting and systematic benchmarking of algorithms.
Bounds for several-disk packings of hyperbolic surfaces

For any given k ∈ ℕ, this paper gives upper bounds on the radius of a packing of a complete hyperbolic surface of finite area by k equal-radius disks in terms of the surface’s topology. We show tha...
Fiber Bragg Gratings Embedded in 3D-Printed Scaffolds

In recent years there has been considerable interest in utilizing embedded fiber optic based sensors for fabricating smart materials. One of the primary motivations is to provide real-time informat...
Mathematical modeling of perifusion cell culture experiments on GnRH signaling

The effects of pulsatile GnRH stimulation on anterior pituitary cells are studied using perifusion cell cultures, where constantly moving culture medium over the immobilized cells allows intermittent GnRH delivery. The LH content of the outgoing medium serves as a readout of the GnRH signaling pathway activation in the cells. The challenge lies in relating the LH content of the medium leaving the chamber to the cellular processes producing LH secretion. To investigate this relation we developed and analyzed a mathematical model consisting of coupled partial differential equations describing LH secretion in a perifusion cell culture. We match the mathematical model to three different data sets and give cellular mechanisms that explain the data. Our model illustrates the importance of the negative feedback in the signaling pathway and receptor desensitization. We demonstrate that different LH outcomes in oxytocin and GnRH stimulations might originate from different receptor dynamics and concentration. We analyze the model to understand the influence of parameters, like the velocity of the medium flow or the fraction collection time, on the LH outcomes. We show that slow velocities lead to high LH outcomes. Also, we show that fraction collection times, which do not divide the GnRH pulse period evenly, lead to irregularities in the data. We examine the influence of the rate of binding and dissociation of GnRH on the GnRH movement down the chamber. Our model serves as an important tool that can help in the design of perifusion experiments and the interpretation of results.