cssi/SciSciGPT-SciSciNet huggingface dataset:
Learning in Structured MDPs with Convex Cost Functions: Improved Regret Bounds for Inventory Management

We consider a stochastic inventory control problem under censored demands, lost sales, and positive lead times. This is a fundamental problem in inventory management, with significant literature establishing near-optimality of a simple class of policies called "base-stock policies" for the underlying Markov Decision Process (MDP), as well as convexity of long run average-cost under those policies. We consider the relatively less studied problem of designing a learning algorithm for this problem when the underlying demand distribution is unknown. The goal is to bound regret of the algorithm when compared to the best base-stock policy. We utilize the convexity properties and a newly derived bound on bias of base-stock policies to establish a connection to stochastic convex bandit optimization. Our main contribution is a learning algorithm with a regret bound of ~O (L√T+D) for the inventory control problem. Here L is the fixed and known lead time, and D is an unknown parameter of the demand distribution described roughly as the number of time steps needed to generate enough demand for depleting one unit of inventory. Notably, even though the state space of the underlying MDP is continuous and L-dimensional, our regret bounds depend linearly on L. Our results significantly improve the previously best known regret bounds for this problem where the dependence on L was exponential and many further assumptions on demand distribution were required. The techniques presented here may be of independent interest for other settings that involve large structured MDPs but with convex cost functions.
Believer-Skeptic Meets Actor-Critic: Rethinking the Role of Basal Ganglia Pathways during Decision-Making and Reinforcement Learning

The flexibility of behavioral control is a testament to the brain's capacity for dynamically resolving uncertainty during goal-directed actions. This ability to select actions and learn from immediate feedback is driven by the dynamics of basal ganglia (BG) pathways. A growing body of empirical evidence conflicts with the traditional view that these pathways act as independent levers for facilitating (i.e., direct pathway) or suppressing (i.e., indirect pathway) motor output, suggesting instead that they engage in a dynamic competition during action decisions that computationally captures action uncertainty. Here we discuss the utility of encoding action uncertainty as a dynamic competition between opposing control pathways and provide evidence that this simple mechanism may have powerful implications for bridging neurocomputational theories of decision making and reinforcement learning.
New perovskite oxide CaCu3Cr2Ru2O12 : Comparison with structural, magnetic, and transport properties of the CaCu3B2B'2O12 perovskite family

A new member of the CaCu 3 B 2 B' 2 O 12 perovskite family, CaCu 3 Cr 2 Ru 2 O 12 , has been synthesized at 12 GPa and 1150 °C. Rietveld refinement using powder X-ray diffraction data reveals that this oxide crystallizes in space group Im3 where cations are disordered over the octahedral B site. Measurements of magnetic susceptibility exhibit a temperature independent Pauli paramagnetic behavior. There is no indication of magnetic ordering, in contrast to the ferrimagnetic behavior associated with the superexchange between Cu(II) and Cr(III) in CaCu 3 Cr 2 Sb 2 O 12 . Although itinerant electron behavior is similar to that observed for the isostructural CaCu 3 Ga 2 Ru 2 O 12 , Cu(II)-O-Ru(V) ↔ Cu(III)-O-Ru(IV) charge transfer is not expected. Rather, a delocalization mechanism involving both CrO 6 and RuO 6 octahedral sublattices is proposed, as is typical for double perovskites. The pure paramagnetic behaviors of CaCu 3 Ga 2 B' 2 O 12 (B' = Nb, Sb, and Ta) perovskites, which contrast with the antiferromagnetic CaCu 3 Ti 4 O 12 , indicate that the electronic coupling within the A sublattice is strongly influenced by the electronic structure of the B sublattice.
Video from Stills: Lensless Imaging with Rolling Shutter

Because image sensor chips have a finite bandwidth with which to read out pixels, recording video typically requires a trade-off between frame rate and pixel count. Compressed sensing techniques can circumvent this trade-off by assuming that the image is compressible. Here, we propose using multiplexing optics to spatially compress the scene, enabling information about the whole scene to be sampled from a row of sensor pixels, which can be read off quickly via a rolling shutter CMOS sensor. Conveniently, such multiplexing can be achieved with a simple lensless, diffuser-based imaging system. Using sparse recovery methods, we are able to recover 140 video frames at over 4,500 frames per second, all from a single captured image with a rolling shutter sensor. Our proof-of-concept system uses easily-fabricated diffusers paired with an off-the-shelf sensor. The resulting prototype enables compressive encoding of high frame rate video into a single rolling shutter exposure, and exceeds the sampling-limited performance of an equivalent global shutter system for sufficiently sparse objects.
Kinesin-5 Promotes Microtubule Nucleation and Assembly by Stabilizing a Lattice-Competent Conformation of Tubulin

Summary Besides sliding apart antiparallel microtubules during spindle elongation, the mitotic kinesin-5, Eg5, promotes microtubule polymerization, emphasizing its importance in mitotic spindle length control. Here, we characterize the Eg5 microtubule polymerase mechanism by assessing motor-induced changes in the longitudinal and lateral tubulin-tubulin bonds that form the microtubule lattice. Isolated Eg5 motor domains promote microtubule nucleation, growth, and stability; thus, crosslinking tubulin by pairs of motor heads is not necessary for polymerase activity. Eg5 binds preferentially to microtubules over free tubulin, which contrasts with microtubule-depolymerizing kinesins that preferentially bind free tubulin over microtubules. Colchicine-like inhibitors that stabilize the bent conformation of tubulin allosterically inhibit Eg5 binding, consistent with a model in which Eg5 induces a curved-to-straight transition in tubulin. Domain swap experiments establish that the family-specific loop11-helix 4 junction, which resides near the nucleotide-sensing switch-II domain, is necessary and sufficient for the polymerase activity of Eg5. Thus, we propose a microtubule polymerase mechanism in which Eg5 at the plus-end promotes a curved-to-straight transition in tubulin that enhances lateral bond formation and thereby promotes microtubule growth and stability. One implication is that regulation of Eg5 motile properties by regulatory proteins or small molecule inhibitors could also have effects on intracellular microtubule dynamics.
Market monitoring and influence: evidence from deposit pricing and liability composition from 1986 to 2013

Abstract We examine the monitoring and ex-post influence of depositors on risk-taking of U.S. bank holding companies (BHCs) from September 1986 to December 2013. As the basis for our empirical analysis, we develop a theoretical model which shows that under risky lending and deposit insurance, a bank’s liability and asset choices are interrelated through its probability of insolvency. Our empirical results are as follows. First, for the sub-sample of the ten largest (Top10) BHCs, deposit risk pricing only exists over some sub-periods prior to the 2007 financial crisis. However, interest rates on insured deposits and uninsured deposits for the Non-Top10 BHCs increase with bank risk over the whole sample period. Moreover, the growth rates of insured and uninsured deposits tend to decrease as bank risk increases for Non-Top10 BHCs over the entire sample period, but only in some sub-periods for the Top10 institutions. Second, although Top10 BHCs do not increase the insured deposits-to-liabilities ratio to weaken market discipline over the entire sample period, all other institutions engage in such regulatory arbitrage in some sub-periods. Third, higher risk premium embedded in current deposit interest rates is more likely to reduce future insolvency risk of troubled BHCs. This suggests that depositors monitor the riskiness of BHCs while also exerting strong ex-post influence on risk-taking of problem institutions. Fourth, in the post-Dodd-Frank Act/Basel III period, the interest rates, the shares, and the growth rate of insured deposits for the Top10 BHCs are significantly negatively related to bank insolvency risk. This could be due to strengthened regulatory oversight on the largest high-risk institutions and is consistent with a substitution relationship between depositor discipline and regulatory oversight.
Human papillomavirus, radiation dose and survival of patients with anal cancer

Purpose: To determine if anal cancer patients with HPV positive disease have different overall survival (OS) compared to those with HPV negative disease, and to elucidate differences in the associa...
Optimal R&D Subsidies with Heterogeneous Firms in a Dynamic Setting

When observably heterogeneous firms engage in R&D and policy can be conditioned on the heterogeneity, what is the optimal policy? This paper starts with a static duopoly model of R&D competition with uncertainty and finds it welfare enhancing to subsidize the larger firms with no subsidies for the smaller firm, extending existing results. This result follows because the policymaker’s goal is to minimize the average cost of production. Our paper demonstrates that these results are not robust to a dynamic setting. The optimal policy depends on the equilibrium type of competition that emerges without intervention—an insight that cannot be found in a static setting. In a dynamic setting, the degree of competition becomes an endogenous variable. Interestingly, although the optimal policy in some cases provides a slightly larger subsidy for the larger firm, it is the smaller firm that benefits most in terms of firm value.
The effect of procedural injustice during emergency 911 calls: a factorial vignette-based study

This study tests the effects of procedurally unfair treatment by 911 dispatchers on behavioral intentions to cooperate with criminal justice professionals. A factorial vignette design and a university-based sample (N = 488) were used. This study used two different vignettes, each of which involved a different type of emergency (i.e., a burglary incident and a traffic accident) and two experimental manipulations (i.e., procedural injustice and seriousness). Participants who received the injustice stimuli reported they would be less likely call 911 in the future to report a similar incident, less likely to cooperate with the 911 operator if asked additional questions, and less willing to cooperate with the police once they arrived on the scene. In relative terms, the seriousness of the incident (e.g., amount of property stolen) mattered far less. This study demonstrates that procedural injustice during 911 calls not only adversely affects dispatchers, but also the police when they arrive on the scene.
Gale duality and Koszul duality

Abstract Given a hyperplane arrangement in an affine space equipped with a linear functional, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul dual to each other, and that the roles of the two algebras are reversed by Gale duality. We also study the centers and representation categories of our algebras, which are in many ways analogous to integral blocks of category O .
Recovering Best Statistical Guarantees via the Empirical Divergence-Based Distributionally Robust Optimization

Distributionally robust optimization (DRO), a recent methodology to handle stochastic optimization problems in the presence of data, is based on robustifications of stochastic constraints that are ...
Weak positivity for Hodge modules

We prove the weak positivity of the kernels of Kodaira-Spencertype maps for pure Hodge module extensions of generically defined variations of Hodge structure.
Water purification by shock electrodialysis: Deionization, filtration, separation, and disinfection

Abstract The development of energy and infrastructure efficient water purification systems is among the most critical engineering challenges facing our society. Water purification is often a multi-step process involving filtration, desalination, and disinfection of a feedstream. Shock electrodialysis (shock ED) is a newly developed technique for water desalination, leveraging the formation of ion concentration polarization (ICP) zones and deionization shock waves in microscale pores near to an ion selective element. While shock ED has been demonstrated as an effective water desalination tool, we here present evidence of other simultaneous functionalities. We show that shock ED can thoroughly filter micron-scale particles and aggregates of nanoparticles present in the feedwater. We also demonstrate that shock ED can enable disinfection of feedwaters, as approximately 99% of viable bacteria (here Escherichia coli ) in the inflow were killed or removed by our prototype. Shock ED also separates positive from negative particles, contrary to claims that ICP acts as a virtual barrier for all charged particles. By combining these functionalities (filtration, separation and disinfection) with deionization, shock ED has the potential to enable highly compact and efficient water purification systems.
Always Lurking: Understanding and Mitigating Bias in Online Human Trafficking Detection

Web-based human trafficking activity has increased in recent years but it remains sparsely dispersed among escort advertisements and difficult to identify due to its often-latent nature. The use of intelligent systems to detect trafficking can thus have a direct impact on investigative resource allocation and decision-making, and, more broadly, help curb a widespread social problem. Trafficking detection involves assigning a normalized score to a set of escort advertisements crawled from the Web -- a higher score indicates a greater risk of trafficking-related (involuntary) activities. In this paper, we define and study the problem of trafficking detection and present a trafficking detection pipeline architecture developed over three years of research within the DARPA Memex program. Drawing on multi-institutional data, systems, and experiences collected during this time, we also conduct post hoc bias analyses and present a bias mitigation plan. Our findings show that, while automatic trafficking detection is an important application of AI for social good, it also provides cautionary lessons for deploying predictive machine learning algorithms without appropriate de-biasing. This ultimately led to integration of an interpretable solution into a search system that contains over 100 million advertisements and is used by over 200 law enforcement agencies to investigate leads.
Relative decidability and definability in henselian valued fields

Let (K, v) be a henselian valued field of characteristic 0. Then K admits a definable partition on each piece of which the leading term of a polynomial in one variable can be computed as a definable function of the leading term of a linear map. The main step in obtaining this partition is an answer to the question, given a polynomial f(x) ∈ K[x], what is v(f(x))?Two applications are given: first, a constructive quantifier elimination relative to the leading terms, suggesting a relative decision procedure; second, a presentation of every definable subset of K as the pullback of a definable set in the leading terms subjected to a linear translation.
Predicting First Impressions with Deep Learning

Describable visual facial attributes are now commonplace in human biometrics and affective computing, with existing algorithms even reaching a sufficient point of maturityfor placement into commercial products. These algorithms model objective facets of facial appearance, such as hair and eye color, expression, and aspects of the geometry of the face. A natural extension, which has not been studied to any great extent thus far, is the ability to model subjective attributes that are assigned to a face based purely on visual judgements. For instance, with just a glance, our first impression of a face may lead us to believe that a person is smart, worthy of our trust, and perhaps even our admiration - regardless of the underlying truth behind such attributes. Psychologists believe that these judgements are based on a variety of factors such as emotional states, personality traits, and other physiognomic cues. But work in this direction leads to an interesting question: how do we create models for problems where there is no ground truth, only measurable behavior? In this paper, we introduce a convolutional neural network-based regression framework that allows us to train predictive models of crowd behavior for social attribute assignment. Over images from the AFLW face database, these models demonstrate strong correlations with human crowd ratings.
Bayesian Poisson tucker decomposition for learning the structure of international relations

We introduce Bayesian Poisson Tucker decomposition (BPTD) for modeling country-country interaction event data. These data consist of interaction events of the form "country i took action a toward country j at time t." BPTD discovers overlapping country-community memberships, including the number of latent communities. In addition, it discovers directed community-community interaction networks that are specific to "topics" of action types and temporal "regimes." We show that BPTD yields an efficient MCMC inference algorithm and achieves better predictive performance than related models. We also demonstrate that it discovers interpretable latent structure that agrees with our knowledge of international relations.
WEAK DISTRIBUTIVITY IMPLYING DISTRIBUTIVITY

Let $B$ be a complete Boolean algebra. We show that if λ is an infinite cardinal and $B$ is weakly ( λ ω , ω )-distributive, then $B$ is ( λ , 2)-distributive. Using a similar argument, we show that if κ is a weakly compact cardinal such that $B$ is weakly (2 κ , κ )-distributive and $B$ is ( α , 2)-distributive for each α κ , then $B$ is ( κ, 2)-distributive.
The Data Acquisition System for LZ

The Data Acquisition System of the LZ experiment, the 10-tonne dark matter detector to be installed at the Sanford Underground Research Facility (SURF), will collect signals from 788 photomultiplier tubes (PMTs). Because the signals from the time projection chamber PMTs will be passed through dual-gain amplifiers, the DAQ system will collect waveforms from a total of 1276 channels, using custom built, 32-channel, FPGA-based digital signal processors. The appropriately conditioned signals will be digitized at 100 MHz with 14-bit resolution. Based on actual measurements with a small-scale prototype system, the LZ DAQ is expected to be able to handle a maximum data rate of 1,500 MB/s. During calibrations, it is estimated that only 33% of the system resources are utilized. The digital filters that are used for event selection operate with an aggregate throughput in excess of 595,000 MB/s. Event selection decisions are based on, for example, the amount of scintillation (S1) and photoluminescence S2 light, S1 and S2 hit-patterns, and total energy deposition.
A matrix analysis approach to discrete comparison principles for nonmonotone PDE

We present a linear algebra approach to establishing a discrete comparison principle for a nonmonotone class of quasilinear elliptic partial differential equations. In the absence of a lower order term, local conditions on the mesh are required to establish the comparison principle and uniqueness of the piecewise linear finite element solution. We consider the assembled matrix corresponding to the linearized problem satisfied by the difference of two solutions to the nonlinear problem. Monotonicity of the assembled matrix establishes a maximum principle for the linear problem and a comparison principle for the nonlinear problem. The matrix analysis approach to the discrete comparison principle yields sharper constants and more relaxed mesh conditions than does the argument by contradiction used in previous work.
Noncommutative topology and Jordan operator algebras

Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with $a^2 \in A$ for all $a \in A$. We study noncommutative topology, noncommutative peak sets and peak interpolation, and hereditary subalgebras of Jordan operator algebras. We show that Jordan operator algebras present perhaps the most general setting for a `full' noncommutative topology in the C*-algebraic sense of Akemann, L. G. Brown, Pedersen, etc, and as modified for not necessarily selfadjoint algebras by the authors with Read, Hay and other coauthors. Our breakthrough relies in part on establishing several strong variants of C*-algebraic results of Brown relating to hereditary subalgebras, proximinality, deeper facts about $L+L^*$ for a left ideal $L$ in a C*-algebra, noncommutative Urysohn lemmas, etc. We also prove several other approximation results in $C^*$-algebras and various subspaces of $C^*$-algebras, related to open and closed projections, and technical $C^*$-algebraic results of Brown.
ML(n)BiCGStab: Reformulation, Analysis and Implementation

With the aid of index functions, we re-derive the ML(n)BiCGStab algorithm in [39] more systematically. There are n ways to define the ML(n)BiCGStab residual vector. Each definition leads to a different ML(n)BiCGStab algorithm. We demonstrate this by presenting a second algorithm which requires less storage. In theory, this second algorithm serves as a bridge that connects the Lanczos-based BiCGStab and the Arnoldi-based FOM while ML(n)BiCG is a bridge connecting BiCG and FOM. We also analyze the breakdown situation from the probabilistic point of view and summarize some useful properties of ML(n)BiCGStab. Implementation issues are also addressed.
Discriminative Features via Generalized Eigenvectors

Representing examples in a way that is compatible with the underlying classifier can greatly enhance the performance of a learning system. In this paper we investigate scalable techniques for inducing discriminative features by taking advantage of simple second order structure in the data. We focus on multiclass classification and show that features extracted from the generalized eigenvectors of the class conditional second moments lead to classifiers with excellent empirical performance. Moreover, these features have attractive theoretical properties, such as inducing representations that are invariant to linear transformations of the input. We evaluate classifiers built from these features on three different tasks, obtaining state of the art results.
Remarks on the Fourier coefficients of modular forms

Abstract We consider a variant of a question of N. Koblitz. For an elliptic curve E / Q which is not Q -isogenous to an elliptic curve with torsion, Koblitz has conjectured that there exists infinitely many primes p such that N p ( E ) = # E ( F p ) = p + 1 − a p ( E ) is also a prime. We consider a variant of this question. For a newform f, without CM, of weight k ⩾ 4 , on Γ 0 ( M ) with trivial Nebentypus χ 0 and with integer Fourier coefficients, let N p ( f ) = χ 0 ( p ) p k − 1 + 1 − a p ( f ) (here a p ( f ) is the p-th-Fourier coefficient of f). We show under GRH and Artinʼs Holomorphy Conjecture that there are infinitely many p such that N p ( f ) has at most [ 5 k + 1 + log ( k ) ] distinct prime factors. We give examples of about hundred forms to which our theorem applies. We also show, on GRH, that the number of distinct prime factors of N p ( f ) is of normal order log ( log ( p ) ) and that the distribution of these values is asymptotically a Gaussian distribution (“Erdős–Kac type theorem”).
SHADHO: Massively Scalable Hardware-Aware Distributed Hyperparameter Optimization

Computer vision is experiencing an AI renaissance, in which machine learning models are expediting important breakthroughs in academic research and commercial applications. Effectively training these models, however, is not trivial due in part to hyperparameters: user-configured values that control a model's ability to learn from data. Existing hyperparameter optimization methods are highly parallel but make no effort to balance the search across heterogeneous hardware or to prioritize searching high-impact spaces. In this paper, we introduce a framework for massively Scalable Hardware-Aware Distributed Hyperparameter Optimization (SHADHO). Our framework calculates the relative complexity of each search space and monitors performance on the learning task over all trials. These metrics are then used as heuristics to assign hyperparameters to distributed workers based on their hardware. We first demonstrate that our framework achieves double the throughput of a standard distributed hyperparameter optimization framework by optimizing SVM for MNIST using 150 distributed workers. We then conduct model search with SHADHO over the course of one week using 74 GPUs across two compute clusters to optimize U-Net for a cell segmentation task, discovering 515 models that achieve a lower validation loss than standard U-Net.
A Policy Search Method For Temporal Logic Specified Reinforcement Learning Tasks

Reward engineering is an important aspect of reinforcement learning. Whether or not the users' intentions can be correctly encapsulated in the reward function can significantly impact the learning outcome. Current methods rely on manually crafted reward functions that often requires parameter tuning to obtain the desired behavior. This operation can be expensive when exploration requires systems to interact with the physical world. In this paper, we explore the use of temporal logic (TL) to specify tasks in reinforcement learning. TL formula can be translated to a real-valued function that measures its level of satisfaction against a trajectory. We take advantage of this function and propose temporal logic policy search (TLPS), a model-free learning technique that finds a policy that satisfies the TL specification. A set of simulated experiments are conducted to evaluate the proposed approach.
The Singularities of the parameter surface of a minimal elliptic threefold

Let f : X -> S be any elliptic fibration. If X has dimension 3 and is not uniruled, then X has a minimal model (with terminal singularities) [Mori]. In earlier work we have shown that there exists a birationally equivalent elliptic fibration p: Y -> T such that Y is minimal and a multiple of K_Y can be expressed as the pullback of a divisor from T. Moreover T has at worst quotient singularities; it is not difficult to find examples where T is actually singular. In this paper we describe the singularities of this parameter surface T in the case of no multiple fibers. Although T is not uniquely determined by the birational equivalence class of the fibration, any two such T are related by a particular kind of birational map.
Efficiently finding simple schedules in Gaussian half-duplex relay line networks

The problem of operating a Gaussian Half-Duplex (HD) relay network optimally is challenging due to the exponential number of listen/transmit network states that need to be considered. Recent results have shown that, for the class of Gaussian HD networks with N relays, there always exists a simple schedule, i.e., with at most N+1 active states, that is sufficient for approximate (i.e., up to a constant gap) capacity characterization. This paper investigates how to efficiently find such a simple schedule over line networks. Towards this end, a polynomial-time algorithm is designed and proved to output a simple schedule that achieves the approximate capacity. The key ingredient of the algorithm is to leverage similarities between network states in HD and edge coloring in a graph. It is also shown that the algorithm allows to derive a closed-form expression for the approximate capacity of the Gaussian line network that can be evaluated distributively and in linear time.
Ehrhart quasi-period collapse in rational polygons

Abstract In 1976, P. R. Scott characterized the Ehrhart polynomials of convex integral polygons. We study the same question for Ehrhart polynomials and quasi-polynomials of non -integral convex polygons. Turning to the case in which the Ehrhart quasi-polynomial has nontrivial quasi-period, we determine the possible minimal periods of the coefficient functions of the Ehrhart quasi-polynomial of a rational polygon.
Core partitions into distinct parts and an analog of Euler's theorem

A special case of an elegant result due to Anderson proves that the number of ( s , s + 1 ) -core partitions is finite and is given by the Catalan number C s . Amdeberhan recently conjectured that the number of ( s , s + 1 ) -core partitions into distinct parts equals the Fibonacci number F s + 1 . We prove this conjecture by enumerating, more generally, ( s , d s - 1 ) -core partitions into distinct parts (the special case d = 1 was independently also proved by Xiong). We do this by relating them to certain tuples of nested twin-free sets.As a by-product of our results, we obtain a bijection between partitions into distinct parts and partitions into odd parts, which preserves the perimeter (that is, the largest part plus the number of parts minus 1 ). This simple but curious analog of Euler's theorem appears to be missing from the literature on partitions.
Universality of phase diagrams in QCD and QCD-like theories

We show the universality of phase diagrams in QCD and QCD-like theories through the large-Nc equivalence. The whole phase diagrams are identical between QCD at finite isospin chemical potential and SO(2Nc) and Sp(2Nc) gauge theories at finite baryon chemical potential. In the chiral limit, they are also identical to that of QCD at finite chiral chemical potential. Outside the pion or diquark condensed phase in these theories, the universality of phase diagrams is applicable to QCD at finite baryon chemical potential. We further argue that the universality may work approximately even for Nc = 3. Our result makes it possible to study QCD at finite baryon chemical potential and high temperature, especially the chiral phase transition, using sign-free theories on the lattice.
Rational Dynamical Systems

Abstract We introduce the notion of a rational dynamical system extending the classical notion of a topological dynamical system and we prove (multiple) recurrence results for such systems via a partition theorem for the rational numbers proved by Farmaki and Koutsogiannis (2010) in [3] . In particular, we extend classical recurrence results developed by Furstenberg and Weiss. Also, we give some applications of these topological recurrence results to topology, to combinatorics, to Diophantine approximations and to number theory.
A Buffer-Stock Model for the Government: Balancing Stability and Sustainability

A fiscal reaction function to debt and the cycle is built on a buffer-stock model for the government. This model inspired by the buffer-stock model of the consumer (Deaton 1991; Carroll 1997) includes a debt limit instead of the Intertemporal Budget Constraint (IBC). The IBC is weak (Bohn, 2007), a debt limit is more realistic as it reflects the risk of losing market access. This risk increases the welfare cost of fiscal stimulus at high debt. As a result, the higher the debt, the less governments should smooth the cycle. A larger reaction of interest rates to debt and higher hysteresis magnify this interaction between the debt level and the appropriate reaction to shocks. With very persistent shocks, the appropriate reaction to negative shocks in highly indebted countries can even be procyclical.
Estimating Unknown Sparsity in Compressed Sensing

In the theory of compressed sensing (CS), the sparsity ||x||0 of the unknown signal x ∈ Rp is commonly assumed to be a known parameter. However, it is typically unknown in practice. Due to the fact that many aspects of CS depend on knowing ||x||0, it is important to estimate this parameter in a data-driven way. A second practical concern is that ||x||0 is a highly unstable function of x. In particular, for real signals with entries not exactly equal to 0, the value ||x||0 = p is not a useful description of the effective number of coordinates. In this paper, we propose to estimate a stable measure of sparsity s(x) := ||x||12/||x||22, which is a sharp lower bound on ||x||0. Our estimation procedure uses only a small number of linear measurements, does not rely on any sparsity assumptions, and requires very little computation. A confidence interval for s(x) is provided, and its width is shown to have no dependence on the signal dimension p. Moreover, this result extends naturally to the matrix recovery setting, where a soft version of matrix rank can be estimated with analogous guarantees. Finally, we show that the use of randomized measurements is essential to estimating s(x). This is accomplished by proving that the minimax risk for estimating s(x) with deterministic measurements is large when n ≪ p.
VoxML: A Visualization Modeling Language

We present the specification for a modeling language, VoxML, which encodes semantic knowledge of real-world objects represented as three-dimensional models, and of events and attributes related to and enacted over these objects.VoxML is intended to overcome the limitations of existing 3D visual markup languages by allowing for the encoding of a broad range of semantic knowledge that can be exploited by a variety of systems and platforms, leading to multimodal simulations of real-world scenarios using conceptual objects that represent their semantic values
Isomorphy Classes of Finite Order Automorphisms of SL(2, k)

ABSTRACTIn this paper, we consider the order m k-automorphisms of SL(2,k). We first characterize the forms that order m k-automorphisms of SL(2,k) take and then we find simple conditions on matrices A and B, involving eigenvalues and the field that the entries of A and B lie in, that are equivalent to isomorphy between the order m k-automorphisms InnA and InnB. We examine the number of isomorphy classes and conclude with examples for selected fields.
Nitrate removal from water using electrostatic regeneration of functionalized adsorbent

Abstract Nitrate is an important pollutant in drinking water worldwide, and a number of methods exist for its removal from water including ion exchange and reverse osmosis. However, these approaches suffer from a variety of disadvantages including requirements for supply and disposal of brine used for regeneration in ion exchange and low water recovery ratio for reverse osmosis. Here, we demonstrate the use of high surface area activated carbon electrodes functionalized with moieties having high affinity for adsorption of nitrate from aqueous solution, such as those used in ion exchange. Adsorption of surfactant molecules having a quaternary amine ionic group to the activated carbon surfaces provides functionalization of the surfaces without complex chemistries. The functionalized electrodes have adsorption capacities of about 80 mg NO3− per gram of activated carbon material. Unlike a traditional ion exchanger, the functionalized surfaces can be repeatedly regenerated by the application of an electrostatic potential which displaces the bound NO3− while leaving an excess of electronic charge on the electrode. The cell is completed by a counter electrode passing current via Faradaic reactions during regeneration. The proposed system is a hybrid form of capacitive deionization, wherein one electrode is strongly capacitive and the counter electrode is dominated by Faradaic reactions. Up to approximately 40% of the initial capacity of the electrode is accessible following electrical regeneration.
K-Semistability for irregular Sasakian manifolds

We introduce a notion of K-semistability for Sasakian manifolds. This extends to the irregular case of the orbifold K-semistability of Ross–Thomas. Our main result is that a Sasakian manifold with constant scalar curvature is necessarily K-semistable. As an application, we show how one can recover the volume minimization results of Martelli–Sparks–Yau, and the Lichnerowicz obstruction of Gauntlett–Martelli–Sparks–Yau from this point of view.
AMON: An Open Source Architecture for Online Monitoring, Statistical Analysis, and Forensics of Multi-Gigabit Streams

The Internet, as a global system of interconnected networks, carries an extensive array of information resources and services. Key requirements include good quality-of-service and protection of the infrastructure from nefarious activity [e.g., distributed denial of service (DDoS) attacks]. Network monitoring is essential to network engineering, capacity planning, and prevention/mitigation of threats. We develop an open-source architecture, All-packet MONitor (AMON), for online monitoring and analysis of multi-gigabit network streams. It leverages the high-performance packet monitor PF_RING and is readily deployable on commodity hardware. AMON examines all packets, partitions traffic into sub-streams by using rapid hashing and computes certain real-time data products. The resulting data structures provide views of the intensity and connectivity structure of network traffic at the time-scale of routing. The proposed integrated framework includes modules for the identification of heavy-hitters as well as for visualization and statistical detection at the time-of-onset of high-impact events such as DDoS. This allows operators to quickly visualize and diagnose attacks, and limit offline and time-consuming post-mortem analysis. We demonstrate our system in the context of real-world attack incidents, and validate it against state-of-the-art alternatives. AMON has been deployed and is currently processing multi-gigabit live Internet traffic at Merit Network. It is extensible and allows the addition of further statistical and filtering modules for real-time forensics.
Probabilistic Community Detection With Unknown Number of Communities

A fundamental problem in network analysis is clustering the nodes into groups which share a similar connectivity pattern. Existing algorithms for community detection assume the knowledge of the num...
Predicting Foreground Object Ambiguity and Efficiently Crowdsourcing the Segmentation(s)

We propose the ambiguity problem for the foreground object segmentation task and motivate the importance of estimating and accounting for this ambiguity when designing vision systems. Specifically, we distinguish between images which lead multiple annotators to segment different foreground objects (ambiguous) versus minor inter-annotator differences of the same object. Taking images from eight widely used datasets, we crowdsource labeling the images as “ambiguous” or “not ambiguous” to segment in order to construct a new dataset we call STATIC. Using STATIC, we develop a system that automatically predicts which images are ambiguous. Experiments demonstrate the advantage of our prediction system over existing saliency-based methods on images from vision benchmarks and images taken by blind people who are trying to recognize objects in their environment. Finally, we introduce a crowdsourcing system to achieve cost savings for collecting the diversity of all valid “ground truth” foreground object segmentations by collecting extra segmentations only when ambiguity is expected. Experiments show our system eliminates up to 47% of human effort compared to existing crowdsourcing methods with no loss in capturing the diversity of ground truths.
On the conditional distribution of a multivariate Normal given a transformation - the linear case.

Abstract We show that the orthogonal projection operator onto the range of the adjoint T ⁎ of a linear operator T can be represented as UT, where U is an invertible linear operator. Given a Normal random vector Y and a linear operator T, we use this representation to obtain a linear operator T ˆ such that T ˆ Y is independent of TY and Y − T ˆ Y is an affine function of TY. We then use this decomposition to prove that the conditional distribution of a Normal random vector Y given T Y , where T is a linear transformation, is again a multivariate Normal distribution. This result is equivalent to the well-known result that given a k-dimensional component of a n-dimensional Normal random vector, where k n , the conditional distribution of the remaining ( n − k ) -dimensional component is a ( n − k ) -dimensional multivariate Normal distribution, and sets the stage for approximating the conditional distribution of Y given g ( Y ) , where g is a continuously differentiable vector field.
Equilibrium Computation and Robust Optimization in Zero Sum Games with Submodular Structure

We define a class of zero-sum games with combinatorial structure, where the best response problem of one player is to maximize a submodular function. For example, this class includes security games played on networks, as well as the problem of robustly optimizing a submodular function over the worst case from a set of scenarios. The challenge in computing equilibria is that both players' strategy spaces can be exponentially large. Accordingly, previous algorithms have worst-case exponential runtime and indeed fail to scale up on practical instances. We provide a pseudopolynomial-time algorithm which obtains a guaranteed (1 - 1/e)^2-approximate mixed strategy for the maximizing player. Our algorithm only requires access to a weakened version of a best response oracle for the minimizing player which runs in polynomial time. Experimental results for network security games and a robust budget allocation problem confirm that our algorithm delivers near-optimal solutions and scales to much larger instances than was previously possible.
Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian

Abstract In this paper, we prove the upper and lower bounds for normal derivatives of spectral clusters u = χ λ s f of Dirichlet Laplacian Δ M , c s λ ‖ u ‖ L 2 ( M ) ⩽ ‖ ∂ ν u ‖ L 2 ( ∂ M ) ⩽ C s λ ‖ u ‖ L 2 ( M ) where the upper bound is true for any Riemannian manifold, and the lower bound is true for some small 0 s s M , where s M depends on the manifold only, provided that M has no trapped geodesics (see Theorem 1.3 for a precise statement), which generalizes the early results for single eigenfunctions by Hassell and Tao in 2002.
Fractal powers in Serrin's swirling vortex solutions

We consider a modification of the fluid flow model for a tornado-like swirling vortex developed by J. Serrin, where velocity decreases as the reciprocal of the distance from the vortex axis. Recent studies, based on radar data of selected severe weather events, indicate that the angular momentum in a tornado may not be constant with the radius, and thus suggest a different scaling of the velocity/radial distance dependence. Motivated by this suggestion, we consider Serrin's approach with the assumption that the velocity decreases as the reciprocal of the distance from the vortex axis to the power $b$ with a general $b>0$. This leads to a boundary-value problem for a system of nonlinear differential equations. We analyze this problem for particular cases, both with nonzero and zero viscosity, discuss the question of existence of solutions, and use numerical techniques to describe those solutions that we cannot obtain analytically.
An Extended Frank--Wolfe Method with “In-Face” Directions, and Its Application to Low-Rank Matrix Completion

Motivated principally by the low-rank matrix completion problem, we present an extension of the Frank--Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. This is accomplished by a new approach to generating “in-face” directions at each iteration, as well as through new choice rules for selecting between in-face and “regular” Frank--Wolfe steps. Our framework for generating in-face directions generalizes the notion of away steps introduced by Wolfe. In particular, the in-face directions always keep the next iterate within the minimal face containing the current iterate. We present computational guarantees for the new method that trade off efficiency in computing near-optimal solutions with upper bounds on the dimension of minimal faces of iterates. We apply the new method to the matrix completion problem, where low-dimensional faces correspond to low-rank matrices. We present computational results that demonstrate the effectiveness of our methodo...
The Rise of Social Botnets: Attacks and Countermeasures

Online social networks (OSNs) are increasingly threatened by social bot s which are software-controlled OSN accounts that mimic human users with malicious intentions. A social botnet refers to a group of social bots under the control of a single botmaster , which collaborate to conduct malicious behavior while mimicking the interactions among normal OSN users to reduce their individual risk of being detected. We demonstrate the effectiveness and advantages of exploiting a social botnet for spam distribution and digital-influence manipulation through real experiments on Twitter and also trace-driven simulations. We also propose the corresponding countermeasures and evaluate their effectiveness. Our results can help understand the potentially detrimental effects of social botnets and help OSNs improve their bot(net) detection systems.
Formal Security Analysis of Neural Networks using Symbolic Intervals

Due to the increasing deployment of Deep Neural Networks (DNNs) in real-world security-critical domains including autonomous vehicles and collision avoidance systems, formally checking security properties of DNNs, especially under different attacker capabilities, is becoming crucial. Most existing security testing techniques for DNNs try to find adversarial examples without providing any formal security guarantees about the non-existence of such adversarial examples. Recently, several projects have used different types of Satisfiability Modulo Theory (SMT) solvers to formally check security properties of DNNs. However, all of these approaches are limited by the high overhead caused by the solver. In this paper, we present a new direction for formally checking security properties of DNNs without using SMT solvers. Instead, we leverage interval arithmetic to compute rigorous bounds on the DNN outputs. Our approach, unlike existing solver-based approaches, is easily parallelizable. We further present symbolic interval analysis along with several other optimizations to minimize overestimations of output bounds. We design, implement, and evaluate our approach as part of ReluVal, a system for formally checking security properties of Relu-based DNNs. Our extensive empirical results show that ReluVal outperforms Reluplex, a state-of-the-art solver-based system, by 200 times on average. On a single 8-core machine without GPUs, within 4 hours, ReluVal is able to verify a security property that Reluplex deemed inconclusive due to timeout after running for more than 5 days. Our experiments demonstrate that symbolic interval analysis is a promising new direction towards rigorously analyzing different security properties of DNNs.
On the uniqueness property of forking in abstract elementary classes

In the setup of abstract elementary classes satisfying a local version of superstability, we prove the uniqueness property for μ-forking, a certain independence notion arising from splitting. This had been a longstanding technical difficulty when constructing forking-like notions in this setup. As an application, we show that the two versions of forking symmetry appearing in the literature (the one defined by Shelah for good frames and the one defined by VanDieren for splitting) are equivalent.