cssi/SciSciGPT-SciSciNet huggingface dataset:
Protecting Real-Time GPU Kernels on Integrated CPU-GPU SoC Platforms

Integrated CPU-GPU architecture provides excellent acceleration capabilities for data parallel applications on embedded platforms while meeting the size, weight and power (SWaP) requirements. However, sharing of main memory between CPU applications and GPU kernels can severely affect the execution of GPU kernels and diminish the performance gain provided by GPU. For example, in the NVIDIA Jetson TX2 platform, an integrated CPU-GPU architecture, we observed that, in the worst case, the GPU kernels can suffer as much as 3X slowdown in the presence of co-running memory intensive CPU applications. In this paper, we propose a software mechanism, which we call BWLOCK++, to protect the performance of GPU kernels from co-scheduled memory intensive CPU applications.
Multiple pattern matching: A Markov chain approach

RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches in genomewide searches, and for predicting whether a given function has evolved many times in different species or arose from a single common ancestor. In this manuscript, we review in an integrated and self-contained manner some basic concepts of automata theory, generating functions and transfer matrix methods that are relevant to pattern analysis in biological sequences. We formalize, in a general framework, the concept of Markov chain embedding to analyze patterns in random strings produced by a memoryless source. This conceptualization, together with the capability of automata to recognize complicated patterns, allows a systematic analysis of problems related to the occurrence and frequency of patterns in random strings. The applications we present focus on the concept of synchronization of automata, as well as automata used to search for a finite number of keywords (including sets of patterns generated according to base pairing rules) in a general text.
A new generating function for calculating the Igusa local zeta function

Abstract A new method is devised for calculating the Igusa local zeta function Z f of a polynomial f ( x 1 , … , x n ) over a p-adic field. This involves a new kind of generating function G f that is the projective limit of a family of generating functions, and contains more data than Z f . This G f resides in an algebra whose structure is naturally compatible with operations on the underlying polynomials, facilitating calculation of local zeta functions. This new technique is used to expand significantly the set of quadratic polynomials whose local zeta functions have been calculated explicitly. Local zeta functions for arbitrary quadratic polynomials over p-adic fields with p odd are presented, as well as for polynomials over unramified 2-adic fields of the form Q + L where Q is a quadratic form and L is a linear form such that Q and L have disjoint variables. For a quadratic form over an arbitrary p-adic field with odd p, this new technique makes clear precisely which of the three candidate poles are actual poles.
Entropy growth in the early universe and confirmation of initial big bang conditions (Why the quark-gluon model is not the best analogy)

Andrew Beckwith abeckwith@uh.edu, beckwith@aibep.org PACs: 98.80.Cq, 95.35.+d, 95.30.Sf, 65.40.gd, 11.25.Uv Abstract This paper shows how increased entropy values from an initially low big bang level can be measured experimentally by counting relic gravitons. Furthermore the physical mechanism of this entropy increase is explained via analogies with early-universe phase transitions. The role of Jack Ng’s (2007, 2008a, 2008b) revised infinite quantum statistics in the physics of gravitational wave detection is acknowledged. Ng’s infinite quantum statistics can be used to show that gravitons N S Δ ≈ Δ is a starting point to the increasing
Fundamental Limits of Database Alignment

We consider the problem of aligning a pair of databases with correlated entries. We introduce a new measure of correlation in a joint distribution that we call cycle mutual information. This measure has operational significance: it determines whether exact recovery of the correspondence between database entries is possible for any algorithm. Additionally, there is an efficient algorithm for database alignment that achieves this information theoretic threshold.
Finite-Sample Risk Bounds for Maximum Likelihood Estimation With Arbitrary Penalties

The minimum description length two-part coding index of resolvability provides a finite-sample upper bound on the statistical risk of penalized likelihood estimators over countable models. However, the bound does not apply to unpenalized maximum likelihood estimation or procedures with exceedingly small penalties. In this paper, we point out a more general inequality that holds for arbitrary penalties. In addition, this approach makes it possible to derive exact risk bounds of order $1/n$ for iid parametric models, which improves on the order $(\log n)/n$ resolvability bounds. We conclude by discussing implications for adaptive estimation.
Obstructions to Compatible Splittings

Suppose one has a map of split short exact sequences in a category of modules, or more generally, in any abelian category. Do the short exact sequences split compatibly, i.e., does there exist a splitting of each short exact sequence which commutes with the map of short exact sequences? The answer is sometimes “yes” and sometimes “no”. We define and prove basic properties of a group of obstructions to the existence of compatible splittings.
Learning the Reward Function for a Misspecified Model

In model-based reinforcement learning it is typical to decouple the problems of learning the dynamics model and learning the reward function. However, when the dynamics model is flawed, it may generate erroneous states that would never occur in the true environment. It is not clear a priori what value the reward function should assign to such states. This paper presents a novel error bound that accounts for the reward model's behavior in states sampled from the model. This bound is used to extend the existing Hallucinated DAgger-MC algorithm, which offers theoretical performance guarantees in deterministic MDPs that do not assume a perfect model can be learned. Empirically, this approach to reward learning can yield dramatic improvements in control performance when the dynamics model is flawed.
The Hardness of Approximation of Euclidean k-Means

The Euclidean k-means problem is a classical problem that has been extensively studied in the theoretical computer science, machine learning and the computational geometry communities. In this problem, we are given a set of n points in Euclidean space R^d, and the goal is to choose k center points in R^d so that the sum of squared distances of each point to its nearest center is minimized. The best approximation algorithms for this problem include a polynomial time constant factor approximation for general k and a (1+c)-approximation which runs in time poly(n) exp(k/c). At the other extreme, the only known computational complexity result for this problem is NP-hardness [Aloise et al.'09]. The main difficulty in obtaining hardness results stems from the Euclidean nature of the problem, and the fact that any point in R^d can be a potential center. This gap in understanding left open the intriguing possibility that the problem might admit a PTAS for all k, d. In this paper we provide the first hardness of approximation for the Euclidean k-means problem. Concretely, we show that there exists a constant c > 0 such that it is NP-hard to approximate the k-means objective to within a factor of (1+c). We show this via an efficient reduction from the vertex cover problem on triangle-free graphs: given a triangle-free graph, the goal is to choose the fewest number of vertices which are incident on all the edges. Additionally, we give a proof that the current best hardness results for vertex cover can be carried over to triangle-free graphs. To show this we transform G, a known hard vertex cover instance, by taking a graph product with a suitably chosen graph H, and showing that the size of the (normalized) maximum independent set is almost exactly preserved in the product graph using a spectral analysis, which might be of independent interest.
Reachability preservers: new extremal bounds and approximation algorithms

In this paper we prove new results about the extremal structure of paths in directed graphs. Say we are given a directed graph G = (V, E) on n nodes, a set of sources S ⊆ V of size |S| = n1/3, and a subset P ⊆ S × V of pairs (s, t) where s ∈ S, of size O(n2/3), such that for all pairs (s, t) ∈ P, there is a path from s to t. Our goal is to remove as many edges from G as possible while maintaining the reachability of all pairs in P. How many edges will we have to keep? Can you always go down to n1+o(1) edges? Or maybe for some nasty graphs G you cannot even go below the simple bound of O(n4/3) edges? Embarrassingly, in a world where graph reachability is ubiquitous in countless scientific fields, the current bounds on the answer to this question are far from tight. In this paper, we make polynomial progress in both the upper and lower bounds for these Reachability Preservers over bounds that were implicit in the literature. We show that in the above scenario, O(n) edges will always be sufficient, and in general one is even guaranteed a subgraph on [EQUATION] edges that preserves the reachability of all pairs in P. We complement this with a lower bound graph construction, establishing that the above result fully characterizes the settings in which we are guaranteed a preserver of size O(n). Moreover, we design an efficient algorithm that can always compute a preserver of existentially optimal size. The second contribution of this paper is a new connection between extremal graph sparsification results and classical Steiner Network Design problems. Surprisingly, prior to this work, the osmosis of techniques between these two fields had been superficial. This allows us to improve the state of the art approximation algorithms for the most basic Steiner-type problem in directed graphs from the O(n0.6+e) of Chlamatac, Dinitz, Kortsarz, and Laekhanukit (SODA'17) to O(n0.577+e).
Homological Invariants of FI-modules and FI_G-modules

Abstract We explore a theory of depth for finitely presented FI G -modules. Using this theory, we prove results about the regularity, and provide novel bounds on stable ranges of FI-modules, making effective a theorem of Nagpal and thereby refining the stable range in results of Church, Ellenberg, and Farb.
On the combined effect of directional antennas and imperfect spectrum sensing upon ergodic capacity of cognitive radio systems

We consider a cognitive radio system, consisting of a primary transmitter (PU tx ), a primary receiver (PU rx ), a secondary transmitter (SU tx ), and a secondary receiver (SU rx ). The secondary users (SUs) are equipped with steerable directional antennas. We assume the SUs and primary users (PUs) coexist. We find the ergodic capacity of channel between SU tx and SU rx , and study how spectrum sensing errors affect the capacity. In our system, the SUtx first senses the spectrum and then transmits data at two power levels, according to the result of sensing. The optimal SUtx transmit power levels and the optimal directions of SUtx transmit antenna and SUrx receive antenna are obtained by maximizing the ergodic capacity, subject to average transmit power and average interference power constraints. To study the effect of fading channel, we considered three scenarios: 1) when SU tx knows fading channels between SU tx and PU rx , PU tx and SU rx , SU tx and SU rx , 2) when SU tx knows only the channel between SU tx and SU rx , and statistics of the other two channels, and, 3) when SU tx only knows the statistics of these three fading channels. For each scenario, we explore the optimal SUtx transmit power levels and the optimal directions of SUtx and SUrx antennas.
Online Learning to Rank with Feedback at the Top

We consider an online learning to rank setting in which, at each round, an oblivious adversary generates a list of m documents, pertaining to a query, and the learner ranks the documents according to assigned scores. The adversary then generates a relevance vector and the learner updates its ranker according to the feedback received. We consider the setting where the feedback is restricted to be the relevance levels of only the top k documents in the ranked list, for k ≪ m. However, the performance of learner is judged based on the unrevealed full relevance vectors, using an appropriate learning to rank loss function. We develop efficient algorithms for well known losses in the pointwise, pairwise and listwise families. We also prove that no online algorithm can have sublinear regret, with top 1 feedback, for any loss that is calibrated with respect to NDCG. We apply our algorithms on benchmark datasets demonstrating efficient online learning of a ranking function from highly restricted feedback.
Global Well-Posedness for the Massive Maxwell–Klein–Gordon Equation with Small Critical Sobolev Data

In this paper we prove global well-posedness and modified scattering for the massive Maxwell–Klein–Gordon equation in the Coulomb gauge on $$\mathbb {R}^{1+d}$$ $$(d \ge 4)$$ for data with small critical Sobolev norm. This extends to the general case $$ m^2 > 0 $$ the results of Krieger–Sterbenz–Tataru ( $$d=4,5 $$ ) and Rodnianski–Tao ( $$ d \ge 6 $$ ), who considered the case $$ m=0$$ . We proceed by generalizing the global parametrix construction for the covariant wave operator and the functional framework from the massless case to the Klein–Gordon setting. The equation exhibits a trilinear cancelation structure identified by Machedon–Sterbenz. To treat it one needs sharp $$L^{2}$$ null form bounds, which we prove by estimating renormalized solutions in null frames spaces similar to the ones considered by Bejenaru–Herr. To overcome logarithmic divergences we rely on an embedding property of $$ \Box ^{-1} $$ in conjunction with endpoint Strichartz estimates in Lorentz spaces.
The optimal mechanism in differential privacy

Differential privacy is a framework to quantify to what extent individual privacy in a statistical database is preserved while releasing useful aggregate information about the database. This dissertation studies the fundamental trade-off between privacy and utility in differential privacy in the most basic problem settings. We first derive the optimal (epsilon)-differentially private mechanism for single real-valued query function under a very general utility-maximization (or cost-minimization) framework. The class of noise probability distributions in the optimal mechanism has staircase-shaped probability density functions which are symmetric (around the origin), monotonically decreasing and geometrically decaying. The staircase mechanism can be viewed as a geometric mixture of uniform probability distributions, providing a simple algorithmic description for the mechanism. Furthermore, the staircase mechanism naturally generalizes to discrete query output settings as well as more abstract settings. We explicitly derive the parameter of the optimal staircase mechanism for ell_1 and ell_2 cost functions. Comparing the optimal performances with those of the usual Laplacian mechanism, we show that in the high privacy regime (epsilon is small), the Laplacian mechanism is asymptotically optimal as epsilon to 0; in the low privacy regime (epsilon is large), the minimum magnitude and second moment of noise are Theta(Delta e^{-epsilon/2) and Theta(Delta^2 e^{-{2\epsilon}/{3}) as epsilon to +infinity, respectively, while the corresponding figures when using the Laplacian mechanism are {Delta}/{epsilon} and {2\Delta^2}/{\epsilon^2}, where Delta is the sensitivity of the query function. We conclude that the gains of the staircase mechanism are more pronounced in the low privacy regime. We also show the optimality of the staircase mechanism for epsilon- differentially privacy in the multiple dimensional setting where the query output has multiple components, e.g., histogram query function. We prove that when the dimension is two, for the ell^1 cost function, the noise probability distribution in the optimal mechanism has a multiple dimensional staircase-shaped probability density function. We explicitly derive the parameter of the optimal two-dimensional staircase mechanism, and study the asymptotical performance of optimal mechanism in the high and low privacy regimes. Comparing the optimal performances with those of the usual Laplacian mechanism, we show that in the high privacy regime (epsilon is small), the Laplacian mechanism is asymptotically optimal as epsilon to 0; in the low privacy regime (epsilon is large), the optimal cost is Theta(e^{-{epsilon}/{3}), while the cost of the Laplacian mechanism is {2\Delta}/{\epsilon}. We conclude that the gains of the staircase mechanism are more pronounced in the low privacy regime. Lastly, we study the optimal mechanisms in (epsilon, delta)-differential privacy for integer-valued query functions under a utility-maximization/cost-minimization framework. We show that the…
Excess of genomic defects in a woolly mammoth on Wrangel island

Woolly mammoths (Mammuthus primigenius) populated Siberia, Beringia, and North America during the Pleistocene and early Holocene. Recent breakthroughs in ancient DNA sequencing have allowed for complete genome sequencing for two specimens of woolly mammoths (Palkopoulou et al. 2015). One mammoth specimen is from a mainland population 45,000 years ago when mammoths were plentiful. The second, a 4300 yr old specimen, is derived from an isolated population on Wrangel island where mammoths subsisted with small effective population size more than 43-fold lower than previous populations. These extreme differences in effective population size offer a rare opportunity to test nearly neutral models of genome architecture evolution within a single species. Using these previously published mammoth sequences, we identify deletions, retrogenes, and non-functionalizing point mutations. In the Wrangel island mammoth, we identify a greater number of deletions, a larger proportion of deletions affecting gene sequences, a greater number of candidate retrogenes, and an increased number of premature stop codons. This accumulation of detrimental mutations is consistent with genomic meltdown in response to low effective population sizes in the dwindling mammoth population on Wrangel island. In addition, we observe high rates of loss of olfactory receptors and urinary proteins, either because these loci are non-essential or because they were favored by divergent selective pressures in island environments. Finally, at the locus of FOXQ1 we observe two independent loss-of-function mutations, which would confer a satin coat phenotype in this island woolly mammoth.
Strongly uplifting cardinals and the boldface resurrection axioms

We introduce the strongly uplifting cardinals, which are equivalently characterized, we prove, as the superstrongly unfoldable cardinals and also as the almost-hugely unfoldable cardinals, and we show that their existence is equiconsistent over ZFC with natural instances of the boldface resurrection axiom, such as the boldface resurrection axiom for proper forcing.
Evidential reasoning in parallel hierarchical vision programs

This paper presents an efficient adaptation and application of the Dempster-Shafer theory of evidence, one that can be used effectively in a massively parallel hierarchical program for visual pattern perception. It describes the techniques used, and shows in an extended example how they serve to improve the program's performance as it applies a multiple-level set of processes.
Matrix Completion from $O(n)$ Samples in Linear Time.

We consider the problem of reconstructing a rank-$k$ $n \times n$ matrix $M$ from a sampling of its entries. Under a certain incoherence assumption on $M$ and for the case when both the rank and the condition number of $M$ are bounded, it was shown in \cite{CandesRecht2009, CandesTao2010, keshavan2010, Recht2011, Jain2012, Hardt2014} that $M$ can be recovered exactly or approximately (depending on some trade-off between accuracy and computational complexity) using $O(n \, \text{poly}(\log n))$ samples in super-linear time $O(n^{a} \, \text{poly}(\log n))$ for some constant $a \geq 1$. In this paper, we propose a new matrix completion algorithm using a novel sampling scheme based on a union of independent sparse random regular bipartite graphs. We show that under the same conditions w.h.p. our algorithm recovers an $\epsilon$-approximation of $M$ in terms of the Frobenius norm using $O(n \log^2(1/\epsilon))$ samples and in linear time $O(n \log^2(1/\epsilon))$. This provides the best known bounds both on the sample complexity and computational complexity for reconstructing (approximately) an unknown low-rank matrix. The novelty of our algorithm is two new steps of thresholding singular values and rescaling singular vectors in the application of the "vanilla" alternating minimization algorithm. The structure of sparse random regular graphs is used heavily for controlling the impact of these regularization steps.
Notes on computational-to-statistical gaps: predictions using statistical physics

In these notes we describe heuristics to predict computational-to-statistical gaps in certain statistical problems. These are regimes in which the underlying statistical problem is information-theoretically possible although no efficient algorithm exists, rendering the problem essentially unsolvable for large instances. The methods we describe here are based on mature, albeit non-rigorous, tools from statistical physics. These notes are based on a lecture series given by the authors at the Courant Institute of Mathematical Sciences in New York City, on May 16th, 2017.
Minimizing Polarization and Disagreement in Social Networks

The rise of social media and online social networks has been a disruptive force in society. Opinions are increasingly shaped by interactions on online social media, and social phenomena including disagreement and polarization are now tightly woven into everyday life. In this work we initiate the study of the following question: \beginquotation \noindent Given n agents, each with its own initial opinion that reflects its core value on a topic, and an opinion dynamics model, what is the structure of a social network that minimizes \em disagreementand \em controversy simultaneously? \endquotation \noindent This question is central to recommender systems: should a recommender system prefer a link suggestion between two online users with similar mindsets in order to keep disagreement low, or between two users with different opinions in order to expose each to the others viewpoint of the world, and decrease overall levels of polarization and controversy? Such decisions have an important global effect on society \citewilliams2007social. Our contributions include a mathematical formalization of this question as an optimization problem and an exact, time-efficient algorithm. We also prove that there always exists a graph with $O(n/e^2)$ edges that is a $(1+e)$ approximation to the optimum. Our formulation is an instance of optimization over \em graph topologies, see also \citeboyd2004fastest,daitch2009fitting,sun2006fastest. Furthermore, for a given graph, we show how to optimize the same objective over the agents» innate opinions in polynomial time. Finally, we perform an empirical study of our proposed methods on synthetic and real-world data that verify their value as mining tools to better understand the trade-off between of disagreement and polarization. We find that there is a lot of space to reduce both controversy and disagreement in real-world networks; for instance, on a Reddit network where users exchange comments on politics, our methods achieve a reduction in controversy and disagreement of the order $6.2 \times 10^4$.
E2F1 Drives Breast Cancer Metastasis by Regulating the Target Gene FGF13 and Altering Cell Migration

In prior work we demonstrated that loss of E2F transcription factors inhibits metastasis. Here we address the mechanisms for this phenotype and identify the E2F regulated genes that coordinate tumor cell metastasis. Transcriptomic profiling of E2F1 knockout tumors identified a role for E2F1 as a master regulator of a suite of pro-metastatic genes, but also uncovered E2F1 target genes with an unknown role in pulmonary metastasis. High expression of one of these genes, Fgf13, is associated with early human breast cancer metastasis in a clinical dataset. Together these data led to the hypothesis that Fgf13 is critical for breast cancer metastasis, and that upregulation of Fgf13 may partially explain how E2F1 promotes breast cancer metastasis. To test this hypothesis we ablated Fgf13 via CRISPR. Deletion of Fgf13 in a MMTV-PyMT breast cancer cell line reduces colonization of the lungs in a tail vein injection. In addition, loss of Fgf13 reduced in vitro cell migration, suggesting that Fgf13 may be critical for tumor cells to escape the primary tumor and to colonize the distal sites. The significance of this work is twofold: we have both uncovered genomic features by which E2F1 regulates metastasis and we have identified new pro-metastatic functions for the E2F1 target gene Fgf13.
Model-assisted design of experiments in the presence of network-correlated outcomes

SummaryIn this paper we consider how to assign treatment in a randomized experiment in which the correlation among the outcomes is informed by a network available pre-intervention. Working within the potential outcome causal framework, we develop a class of models that posit such a correlation structure among the outcomes. We use these models to develop restricted randomization strategies for allocating treatment optimally, by minimizing the mean squared error of the estimated average treatment effect. Analytical decompositions of the mean squared error, due both to the model and to the randomization distribution, provide insights into aspects of the optimal designs. In particular, the analysis suggests new notions of balance based on specific network quantities, in addition to classical covariate balance. The resulting balanced optimal restricted randomization strategies are still design-unbiased when the model used to derive them does not hold. We illustrate how the proposed treatment allocation strategies improve on allocations that ignore the network structure.
INSPECTRE: Privately Estimating the Unseen

We develop differentially private methods for estimating various distributional properties. Given a sample from a discrete distribution $p$, some functional $f$, and accuracy and privacy parameters $\alpha$ and $\varepsilon$, the goal is to estimate $f(p)$ up to accuracy $\alpha$, while maintaining $\varepsilon$-differential privacy of the sample. We prove almost-tight bounds on the sample size required for this problem for several functionals of interest, including support size, support coverage, and entropy. We show that the cost of privacy is negligible in a variety of settings, both theoretically and experimentally. Our methods are based on a sensitivity analysis of several state-of-the-art methods for estimating these properties with sublinear sample complexities.
Crystal structure on rigged configurations and the filling map

In this paper, we extend work of the first author on a crystal structure on rigged configurations of simply-laced type to all non-exceptional affine types using the technology of virtual rigged configurations and crystals. Under the bijection between rigged configurations and tensor products of Kirillov--Reshetikhin crystals specialized to a single tensor factor, we obtain a new tableaux model for Kirillov--Reshetikhin crystals. This is related to the model in terms of Kashiwara--Nakashima tableaux via a filling map, generalizing the recently discovered filling map in type $D_n^{(1)}$.
Syzygies on Tutte polynomials of freedom matroids

It follows from a theorem of Derksen [J. Algebraic Combin., 30 (2009) 43–86] that the Tutte polynomial of a rank-r matroid on an n-set is “naturally” a linear combination of Tutte polynomials of rank-r size-n freedom matroids. However, the Tutte polynomials of rank-r size-n freedom matroids are not linearly independent. We construct two natural bases for these polynomials and as a corollary, we prove that the Tutte polynomials of rank-r matroids of size-n span a subspace of dimension $${r(n-r)+1}$$ . We also find a generating set for the linear relations between Tutte polynomials of freedom matroids. This generating set is indexed by a pair of intervals, one of size 2 and one of size 4, in the weak order of freedom matroids. This weak order is a distributive lattice and a sublattice of Young’s partition lattice.
Individualized treatment effects with censored data via fully nonparametric Bayesian accelerated failure time models

Individuals often respond differently to identical treatments, and characterizing such variability in treatment response is an important aim in the practice of personalized medicine. In this article, we describe a nonparametric accelerated failure time model that can be used to analyze heterogeneous treatment effects (HTE) when patient outcomes are time-to-event. By utilizing Bayesian additive regression trees and a mean-constrained Dirichlet process mixture model, our approach offers a flexible model for the regression function while placing few restrictions on the baseline hazard. Our nonparametric method leads to natural estimates of individual treatment effect and has the flexibility to address many major goals of HTE assessment. Moreover, our method requires little user input in terms of model specification for treatment covariate interactions or for tuning parameter selection. Our procedure shows strong predictive performance while also exhibiting good frequentist properties in terms of parameter coverage and mitigation of spurious findings of HTE. We illustrate the merits of our proposed approach with a detailed analysis of two large clinical trials (N = 6769) for the prevention and treatment of congestive heart failure using an angiotensin-converting enzyme inhibitor. The analysis revealed considerable evidence for the presence of HTE in both trials as demonstrated by substantial estimated variation in treatment effect and by high proportions of patients exhibiting strong evidence of having treatment effects which differ from the overall treatment effect.
The Archimedean Projection Property

AbstractLet H be a hypersurface in R n and let π be an orthogonal projection in R n restrictedto H. We say that H satisﬁes the Archimedean projection property correspondingto π if there exists a constant C such that Vol(π −1 (U)) = C·Vol(U) for every mea-surable U in the range of π. It is well-known that the (n−1)-dimensional sphere, asa hypersurface in R n , satisﬁes the Archimedean projection property correspondingto any codimension 2 orthogonal projection in R n , the range of any such projectionbeing an (n − 2)-dimensional ball. Here we construct new hypersurfaces that sat-isfy Archimedean projection properties. Our construction works for any projectioncodimension k, 2 ≤ k ≤ n− 1, and it allows us to specify a wide variety of desiredprojection ranges Ω n−k ⊂ R n−k . Letting Ω n−k be an (n − k)-dimensional ball foreach k, it produces a new family of smooth, compact hypersurfaces in R n satisfyingcodimension k Archimedean projection properties that includes, in the special casek = 2, the (n−1)-dimensional spheres.
Directed-polymer systems explored via their quantum analogs: General polymer interactions and their consequences

The impact of polymer-polymer interactions of various types on the thermodynamics, structure, and accommodation of topological constraints is addressed for systems comprising many directed polymers in two spatial dimensions. The approach is predicated on the well-known equivalence between the classical equilibrium statistical mechanics of directed polymers in two spatial dimensions and the imaginary-time quantum dynamics of particles in one spatial dimension, originally exploited by P.-G. de Gennes [P.-G. de Gennes, J. Chem. Phys. 48, 2257 (1968)]. Known results concerning two exactly solvable microscopic models of quantum particles moving in one spatial dimension---the Lieb-Liniger model of contact interactions and the Calogero-Sutherland model of long-range interactions---are used to shed light on the behavior of the corresponding polymeric systems. In addition, the technique of bosonization is used to reveal how generic polymer interactions give rise to an emergent polymer fluid that has universal collective excitations. Additionally, the response of the system to topological constraints such as pins though which polymers cannot pass is explored. Immediately on the compressed side of a pin there is a divergent pile-up in polymer density, while on the other side there is a gap of finite area in which polymer density is negligible. Comparison of this response to that of a system of simply noncrossing (i.e., noncrossing but otherwise noninteracting) directed polymers, explored in a companion paper, reveals that generic interactions leave the structure quantitatively unchanged on the line transverse to the pin, and leave it qualitatively unchanged throughout the two dimensions of the system's extent. Furthermore, the free-energy cost associated with a pin that partitions a system having generic interactions is found to be proportional to the pin-partitioning cost for a system of simply noncrossing polymers.
On Virasoro Constraints for Orbifold Gromov–Witten Theory

Virasoro constraints for orbifold Gromov-Witten theory are described. These constraints are applied to the degree zero, genus zero orbifold Gromov-Witten potentials of the weighted projective stacks , , and to obtain formulas of descendant cyclic Hurwitz-Hodge integrals.
Parallel Closed-Loop Connected Vehicle Simulator for Large-Scale Transportation Network Management: Challenges, Issues, and Solution Approaches

The augmented scale and complexity of urban transportation networks have significantly increased the execution time and resource requirements of vehicular network simulations, exceeding the capabilities of sequential simulators. The need for a parallel and distributed simulation environment is inevitable from a smart city perspective, especially when the entire city-wide information system is expected to be integrated with numerous services and ITS applications. In this paper, we present a conceptual model of an Integrated Distributed Connected Vehicle Simulator (IDCVS) that can emulate real-time traffic in a large metro area by incorporating hardware-in-the-loop simulation together with the closed-loop coupling of SUMO and OMNET++. We also discuss the challenges, issues, and solution approaches for implementing such a parallel closed-loop transportation network simulator by addressing transportation network partitioning problems, synchronization, and scalability issues. One unique feature of the envisioned integrated simulation tool is that it utilizes the vehicle traces collected through multiple roadway sensors? DSRC onboard unit, magnetometer, loop detector, and video detector. Another major feature of the proposed model is the incorporation of hybrid parallelism in both transportation and communication simulation platforms. We identify the challenges and issues involved in IDCVS to incorporate this multi-level parallelism. We also discuss the approaches for integrating hardware-in-the-loop simulation, addressing the steps involved in preprocessing sensor data, filtering, and extrapolating missing data, managing large real-time traffic data, and handling different data formats.
Neural Module Networks

Visual question answering is fundamentally compositional in nature—a question like where is the dog? shares substructure with questions like what color is the dog? and where is the cat? This paper seeks to simultaneously exploit the representational capacity of deep networks and the compositional linguistic structure of questions. We describe a procedure for constructing and learning neural module networks, which compose collections of jointly-trained neural "modules" into deep networks for question answering. Our approach decomposes questions into their linguistic substructures, and uses these structures to dynamically instantiate modular networks (with reusable components for recognizing dogs, classifying colors, etc.). The resulting compound networks are jointly trained. We evaluate our approach on two challenging datasets for visual question answering, achieving state-of-the-art results on both the VQA natural image dataset and a new dataset of complex questions about abstract shapes.
The Variational Homoencoder: Learning to learn high capacity generative models from few examples

Hierarchical Bayesian methods can unify many related tasks (e.g. k-shot classification, conditional and unconditional generation) as inference within a single generative model. However, when this generative model is expressed as a powerful neural network such as a PixelCNN, we show that existing learning techniques typically fail to effectively use latent variables. To address this, we develop a modification of the Variational Autoencoder in which encoded observations are decoded to new elements from the same class. This technique, which we call a Variational Homoencoder (VHE), produces a hierarchical latent variable model which better utilises latent variables. We use the VHE framework to learn a hierarchical PixelCNN on the Omniglot dataset, which outperforms all existing models on test set likelihood and achieves strong performance on one-shot generation and classification tasks. We additionally validate the VHE on natural images from the YouTube Faces database. Finally, we develop extensions of the model that apply to richer dataset structures such as factorial and hierarchical categories.
Roots in Operator and Banach Algebras

We show that several known facts concerning roots of matrices generalize to operator algebras and Banach algebras. We show for example that the so-called Newton, binomial, Visser, and Halley iterative methods converge to the root in Banach and operator algebras under various mild hypotheses. We also show that the ‘sign’ and ‘geometric mean’ of matrices generalize to Banach and operator algebras, and we investigate their properties. We also establish some other facts about roots in this setting.
Scattering of electromagnetic waves by many thin cylinders

Abstract Electromagnetic wave scattering by many parallel to z -axis, thin, perfectly conducting, circular infinite cylinders is studied asymptotically as a → 0. Let D m be the cross-section of the m th cylinder, a be its radius, and x ˆ m = ( x m 1 , x m 2 ) be its center, 1 ⩽ m ⩽ M , M = M ( a ). It is assumed that the points x ˆ m are distributed so that N ( Δ ) = ln 1 a ∫ Δ N ( x ) d x [ 1 + o ( 1 ) ] , where N ( Δ ) is the number of points x ˆ m in an arbitrary open subset Δ of the plane xoy . The function N ( x ) ⩾ 0 is a given continuous function. An equation for the self-consistent (efficient) field is derived as a → 0. The cylinders are assumed perfectly conducting. A formula is derived for the effective refraction coefficient in the medium in which many cylinders are distributed. These cylinders may model nanowires embedded in the medium. Our result shows how these cylinders influence the refraction coefficient of the medium.
Why Is My Classifier Discriminatory

Recent attempts to achieve fairness in predictive models focus on the balance between fairness and accuracy. In sensitive applications such as healthcare or criminal justice, this trade-off is often undesirable as any increase in prediction error could have devastating consequences. In this work, we argue that the fairness of predictions should be evaluated in context of the data, and that unfairness induced by inadequate samples sizes or unmeasured predictive variables should be addressed through data collection, rather than by constraining the model. We decompose cost-based metrics of discrimination into bias, variance, and noise, and propose actions aimed at estimating and reducing each term. Finally, we perform case-studies on prediction of income, mortality, and review ratings, confirming the value of this analysis. We find that data collection is often a means to reduce discrimination without sacrificing accuracy.
The equality case of the Penrose inequality for asymptotically flat graphs

We prove the equality case of the Penrose inequality in all dimensions for asymptotically flat hypersurfaces. It was re- cently proven by G. Lam (19) that the Penrose inequality holds for asymptotically flat graphical hypersurfaces in Euclidean space with non-negative scalar curvature and with a minimal boundary. Our main theorem states that if the equality holds, then the hy- persurface is a Schwarzschild solution. As part of our proof, we show that asymptotically flat graphical hypersurfaces with a min- imal boundary and non-negative scalar curvature must be mean convex, using the argument that we developed in (15). This en- ables us to obtain the ellipticity for the linearized scalar curvature operator and to establish the strong maximum principles for the scalar curvature equation.
Decoding the encoding of functional brain networks: An fMRI classification comparison of non-negative matrix factorization (NMF), independent component analysis (ICA), and sparse coding algorithms.

Abstract Background Brain networks in fMRI are typically identified using spatial independent component analysis (ICA), yet other mathematical constraints provide alternate biologically-plausible frameworks for generating brain networks. Non-negative matrix factorization (NMF) would suppress negative BOLD signal by enforcing positivity. Spatial sparse coding algorithms (L1 Regularized Learning and K-SVD) would impose local specialization and a discouragement of multitasking, where the total observed activity in a single voxel originates from a restricted number of possible brain networks. New method The assumptions of independence, positivity, and sparsity to encode task-related brain networks are compared; the resulting brain networks within scan for different constraints are used as basis functions to encode observed functional activity. These encodings are then decoded using machine learning, by using the time series weights to predict within scan whether a subject is viewing a video, listening to an audio cue, or at rest, in 304 fMRI scans from 51 subjects. Results and comparison with existing method The sparse coding algorithm of L1 Regularized Learning outperformed 4 variations of ICA (p Conclusion The success of sparse coding algorithms suggests that algorithms which enforce sparsity, discourage multitasking, and promote local specialization may capture better the underlying source processes than those which allow inexhaustible local processes such as ICA. Negative BOLD signal may capture task-related activations.
Optimization-Based Calibration of Simulation Input Models

Studies on simulation input uncertainty are often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we non...
Yang–Mills for Probabilists

The rigorous construction of quantum Yang–Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang–Mills theories is the first step towards this goal. This article presents a formulation of some of the core aspects this problem as problems in probability theory. The presentation begins with an introduction to the basic setup of Euclidean Yang–Mills theories and lattice gauge theories. This is followed by a discussion of what is meant by a continuum limit of lattice gauge theories from the point of view of theoretical physicists. Some of the main issues are then posed as problems in probability. The article ends with a brief review of the mathematical literature.
A Spatiotemporal Ventricular Myocyte Model Incorporating Mitochondrial Calcium Cycling.

Abstract Intracellular calcium (Ca2+) cycling dynamics in cardiac myocytes are spatiotemporally generated by stochastic events arising from a spatially distributed network of coupled Ca2+ release units that interact with an intertwined mitochondrial network. In this study, we developed a spatiotemporal ventricular myocyte model that integrates mitochondria-related Ca2+ cycling components into our previously developed ventricular myocyte model consisting of a three-dimensional Ca2+ release unit network. Mathematical formulations of mitochondrial membrane potential, mitochondrial Ca2+ cycling, mitochondrial permeability transition pore stochastic opening and closing, intracellular reactive oxygen species signaling, and oxidized Ca2+/calmodulin-dependent protein kinase II signaling were incorporated into the model. We then used the model to simulate the effects of mitochondrial depolarization on mitochondrial Ca2+ cycling, Ca2+ spark frequency, and Ca2+ amplitude, which agree well with experimental data. We also simulated the effects of the strength of mitochondrial Ca2+ uniporters and their spatial localization on intracellular Ca2+ cycling properties, which substantially affected diastolic and systolic Ca2+ levels in the mitochondria but exhibited only a small effect on sarcoplasmic reticulum and cytosolic Ca2+ levels under normal conditions. We show that mitochondrial depolarization can cause Ca2+ waves and Ca2+ alternans, which agrees with previous experimental observations. We propose that this new, to our knowledge, spatiotemporal ventricular myocyte model, incorporating properties of mitochondrial Ca2+ cycling and reactive-oxygen-species-dependent signaling, will be useful for investigating the effects of mitochondria on intracellular Ca2+ cycling and action potential dynamics in ventricular myocytes.
Beyond the Coulson–Fischer point: characterizing single excitation CI and TDDFT for excited states in single bond dissociations

Linear response time dependent density functional theory (TDDFT), which builds upon configuration interaction singles (CIS) and TD-Hartree-Fock (TDHF), is the most widely used class of excited state quantum chemistry methods and is often employed to study photochemical processes. This paper studies the behavior of the resulting excited state potential energy surfaces beyond the Coulson-Fischer (CF) point in single bond dissociations, when the optimal reference determinant is spin-polarized. Many excited states exhibit sharp kinks at the CF point, and connect to different dissociation limits via a zone of unphysical concave curvature. In particular, the unrestricted MS = 0 lowest triplet T1 state changes character, and does not dissociate into ground state fragments. The unrestricted MS = ±1 T1 CIS states better approximate the physical dissociation limit, but their degeneracy is broken beyond the CF point for most single bond dissociations. On the other hand, the MS = ±1 T1 TDHF states reach the asymptote too soon, by merging with the ground state from the CF point onwards. Use of local exchange-correlation functionals causes MS = ±1 T1 TDDFT states to resemble their unphysical MS = 0 counterpart. The 2 orbital, 2-electron model system of minimal basis H2 is analytically treated to understand the origin of these issues, revealing that the lack of double excitations is at the root of these remarkable observations. The behavior of excited state surfaces is also numerically examined for species like H2, NH3, C2H6 and LiH in extended basis sets.