cssi/SciSciGPT-SciSciNet huggingface dataset:
Generalized multiple depot traveling salesmen problem-Polyhedral study and exact algorithm

The generalized multiple depot traveling salesmen problem (GMDTSP) is a variant of the multiple depot traveling salesmen problem (MDTSP), where each salesman starts at a distinct depot, the targets are partitioned into clusters and at least one target in each cluster is visited by some salesman. The GMDTSP is an NP-hard problem as it generalizes the MDTSP and has practical applications in design of ring networks, vehicle routing, flexible manufacturing, scheduling and postal routing. We present an integer programming formulation for the GMDTSP and valid inequalities to strengthen the linear programming relaxation. Furthermore, we present a polyhedral analysis of the convex hull of feasible solutions to the GMDTSP and derive facet-defining inequalities that strengthen the linear programming relaxation of the GMDTSP. All these results are then used to develop a branch-and-cut algorithm to obtain optimal solutions to the problem. The performance of the algorithm is evaluated through extensive computational experiments on several benchmark instances. HighlightsThe generalized multiple depot traveling salesmen problem is formulated as a mixed integer linear program.A polyhedral study and an exact algorithm based on the branch-and-cut framework are developed.Performance evaluation through extensive computational experiments on bench- mark instances.
INDIFFERENCE PRICING FOR CONTINGENT CLAIMS: LARGE DEVIATIONS EFFECTS

We study utility indifference prices and optimal purchasing quantities for a nontraded contingent claim in an incomplete semimartingale market with vanishing hedging errors. We make connections with the theory of large deviations. We concentrate on sequences of semicomplete markets where in the nth market, the claim Bn admits the decomposition Bn=Dn+Yn. Here, Dn is replicable by trading in the underlying assets Sn, but Yn is independent of Sn. Under broad conditions, we may assume that Yn vanishes in accordance with a large deviations principle (LDP) as n grows. In this setting, for an exponential investor, we identify the limit of the average indifference price pn(qn), for qn units of Bn, as n→∞. We show that if |qn|→∞, the limiting price typically differs from the price obtained by assuming bounded positions supn|qn|<∞, and the difference is explicitly identifiable using large deviations theory. Furthermore, we show that optimal purchase quantities occur at the large deviations scaling, and hence large positions arise endogenously in this setting.
Automorphisms of perfect power series rings

Abstract Let R be a perfect ring of characteristic p. We show that the group of continuous R-linear automorphisms of the perfect power series ring over R is generated by the automorphisms of the ordinary power series ring together with Frobenius; this answers a question of Jared Weinstein.
AN EXTENSION OF THE MOSER-TARDOS ALGORITHMIC LOCAL LEMMA ∗

A recent theorem of Bissacot et al. [arXiv:0910.1824v2, 2010], proved using results about the cluster expansion in statistical mechanics, extends the Lovasz local lemma by weakening the conditions under which its conclusion holds. In this note, we prove an algorithmic analogue of this result, extending Moser and Tardos's recent algorithmic local lemma [J. ACM, 57 (2010), 11], and providing an alternative proof of the theorem of Bissacot et al. applicable in the Moser--Tardos algorithmic framework.
Prediction Error Reduction Function as a Variable Importance Score

This paper introduces and develops a novel variable importance score function in the context of ensemble learning, and demonstrates its appeal empirically. Our proposed score function is simple and more straightforward than its counterpart proposed in the context of random forest, and by avoiding permutations, it is by design computationally more efficient than the random forest variable importance function. Just like the random forest variable importance function, our score handles both regression and classification seamlessly. One of the distinct advantage of our proposed score is the fact that it offers a natural cut off at zero, with all the positive scores indicating importance and significance, while the negative scores are deemed indications of insignificance. An extra advantage of our proposed score lies in the fact it works very well beyond ensemble of trees and can seamlessly be used with any base learners in the random subspace learning context. Our examples, both simulated and real, demonstrate that our proposed score does compete mostly favorably with the random forest score.
Prediction and Inference with Missing Data in Patient Alert Systems

We describe the Bedside Patient Rescue (BPR) project, the goal of which is risk prediction of adverse events for non-intensive care unit patients using ∼100 variables (vitals, lab results, assessme...
Remarks on non-abelian cohomology of proalgebraic groups

These are detailed notes on a variant of the non-abelian cohomology developed by Minhyong Kim in arXiv:0409456 (published in Invent. Math.) to study rational points of varieties over number fields. The current variant is used in arXiv:1001.5008 to study rational points of the restriction of the universal curve to the generic point of M_{g,n}.
Crossing Patterns in Nonplanar Road Networks

We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross each other. In this paper, we study the sparsity properties of crossing graphs of real-world road networks. We show that, in large road networks (the Urban Road Network Dataset), the crossing graphs have connected components that are primarily trees, and that the remaining non-tree components are typically sparse (technically, that they have bounded degeneracy). We prove theoretically that when an embedded graph has a sparse crossing graph, it has other desirable properties that lead to fast algorithms for shortest paths and other algorithms important in geographic information systems. Notably, these graphs have polynomial expansion, meaning that they and all their subgraphs have small separators.
Submodular meets Structured: Finding Diverse Subsets in Exponentially-Large Structured Item Sets

To cope with the high level of ambiguity faced in domains such as Computer Vision or Natural Language processing, robust prediction methods often search for a diverse set of high-quality candidate solutions or proposals. In structured prediction problems, this becomes a daunting task, as the solution space (image labelings, sentence parses, etc.) is exponentially large. We study greedy algorithms for finding a diverse subset of solutions in structured-output spaces by drawing new connections between submodular functions over combinatorial item sets and High-Order Potentials (HOPs) studied for graphical models. Specifically, we show via examples that when marginal gains of submodular diversity functions allow structured representations, this enables efficient (sub-linear time) approximate maximization by reducing the greedy augmentation step to inference in a factor graph with appropriately constructed HOPs. We discuss benefits, tradeoffs, and show that our constructions lead to significantly better proposals.
Pull-based load distribution among heterogeneous parallel servers: the case of multiple routers

The model is a service system, consisting of several large server pools. A server's processing speed and buffer size (which may be finite or infinite) depend on the pool. The input flow of customers is split equally among a fixed number of routers, which must assign customers to the servers immediately upon arrival. We consider an asymptotic regime in which the total customer arrival rate and pool sizes scale to infinity simultaneously, in proportion to a scaling parameter n, while the number of routers remains fixed. We define and study a multi-router generalization of the pull-based customer assignment (routing) algorithm PULL, introduced in Stolyar (Queueing Syst 80(4): 341---361, 2015) for the single-router model. Under the PULL algorithm, when a server becomes idle it sends a "pull-message" to a randomly uniformly selected router; each router operates independently--it assigns an arriving customer to a server according to a randomly uniformly chosen available (at this router) pull-message, if there is any, or to a randomly uniformly selected server in the entire system otherwise. Under Markov assumptions (Poisson arrival process and independent exponentially distributed service requirements), and under subcritical system load, we prove asymptotic optimality of PULL: as $$n\rightarrow \infty $$nźź, the steady-state probability of an arriving customer experiencing blocking or waiting vanishes. Furthermore, PULL has an extremely low router---server message exchange rate of one message per customer. These results generalize some of the single-router results in Stolyar (2015).
CoVeR: Learning Covariate-Specific Vector Representations with Tensor Decompositions

Word embedding is a useful approach to capture co-occurrence structures in large text corpora. However, in addition to the text data itself, we often have additional covariates associated with individual corpus documents---e.g. the demographic of the author, time and venue of publication---and we would like the embedding to naturally capture this information. We propose CoVeR, a new tensor decomposition model for vector embeddings with covariates. CoVeR jointly learns a \emph{base} embedding for all the words as well as a weighted diagonal matrix to model how each covariate affects the base embedding. To obtain author or venue-specific embedding, for example, we can then simply multiply the base embedding by the associated transformation matrix. The main advantages of our approach are data efficiency and interpretability of the covariate transformation. Our experiments demonstrate that our joint model learns substantially better covariate-specific embeddings compared to the standard approach of learning a separate embedding for each covariate using only the relevant subset of data, as well as other related methods. Furthermore, CoVeR encourages the embeddings to be "topic-aligned" in that the dimensions have specific independent meanings. This allows our covariate-specific embeddings to be compared by topic, enabling downstream differential analysis. We empirically evaluate the benefits of our algorithm on datasets, and demonstrate how it can be used to address many natural questions about covariate effects. Accompanying code to this paper can be found at this http URL.
DeepTest: automated testing of deep-neural-network-driven autonomous cars

Recent advances in Deep Neural Networks (DNNs) have led to the development of DNN-driven autonomous cars that, using sensors like camera, LiDAR, etc., can drive without any human intervention. Most major manufacturers including Tesla, GM, Ford, BMW, and Waymo/Google are working on building and testing different types of autonomous vehicles. The lawmakers of several US states including California, Texas, and New York have passed new legislation to fast-track the process of testing and deployment of autonomous vehicles on their roads. However, despite their spectacular progress, DNNs, just like traditional software, often demonstrate incorrect or unexpected corner-case behaviors that can lead to potentially fatal collisions. Several such real-world accidents involving autonomous cars have already happened including one which resulted in a fatality. Most existing testing techniques for DNN-driven vehicles are heavily dependent on the manual collection of test data under different driving conditions which become prohibitively expensive as the number of test conditions increases. In this paper, we design, implement, and evaluate DeepTest, a systematic testing tool for automatically detecting erroneous behaviors of DNN-driven vehicles that can potentially lead to fatal crashes. First, our tool is designed to automatically generated test cases leveraging real-world changes in driving conditions like rain, fog, lighting conditions, etc. DeepTest systematically explore different parts of the DNN logic by generating test inputs that maximize the numbers of activated neurons. DeepTest found thousands of erroneous behaviors under different realistic driving conditions (e.g., blurring, rain, fog, etc.) many of which lead to potentially fatal crashes in three top performing DNNs in the Udacity self-driving car challenge.
Personalized Colorectal Cancer Survivability Prediction with Machine Learning Methods

In this work, we investigate the importance of ethnicity in colorectal cancer survivability prediction using machine learning techniques and the SEER cancer incidence database. We compare model performances for 2-year survivability prediction and feature importance rankings between Hispanic, White, and mixed patient populations. Our models consistently perform better on single-ethnicity populations and provide different feature importance rankings when trained in different populations. Additionally, we show our models achieve higher Area Under Curve (AUC) score than the best reported in the literature. We also apply imbalanced classification techniques to improve classification performance when the number of patients who have survived from colorectal cancer is much larger than who have not. These results provide evidence in favor for increased consideration of patient ethnicity in cancer survivability prediction, and for more personalized medicine in general.
Asymptotic Structure of Constrained Exponential Random Graph Models

In this paper, we study exponential random graph models subject to certain constraints. We obtain some general results about the asymptotic structure of the model. We show that there exists non-trivial regions in the phase plane where the asymptotic structure is uniform and there also exists non-trivial regions in the phase plane where the asymptotic structure is non-uniform. We will get more refined results for the star model and in particular the two-star model for which a sharp transition from uniform to non-uniform structure, a stationary point and phase transitions will be obtained.
Distribution of Descents in Matchings

The distribution of descents in certain conjugacy classes of $$S_n$$ has been previously studied, and it is shown that its moments have interesting properties. This paper provides a bijective proof of the symmetry of the descents and major indices of matchings (also known as fixed point free involutions) and uses a generating function approach to prove an asymptotic normality theorem for the number of descents in matchings.
Stochastic telegraph equation limit for the stochastic six vertex model

In this article we study the stochastic six vertex model under the scaling proposed by Borodin and Gorin (2018), where the weights of corner-shape vertices are tuned to zero, and prove Conjecture 6.1 therein: that the height fluctuation converges in finite dimensional distributions to the solution of stochastic telegraph equation.
Stochastic Zeroth-order Optimization in High Dimensions.

We consider the problem of optimizing a high-dimensional convex function using stochastic zeroth-order queries. Under sparsity assumptions on the gradients or function values, we present two algorithms: a successive component/feature selection algorithm and a noisy mirror descent algorithm using Lasso gradient estimates, and show that both algorithms have convergence rates that de- pend only logarithmically on the ambient dimension of the problem. Empirical results confirm our theoretical findings and show that the algorithms we design outperform classical zeroth-order optimization methods in the high-dimensional setting.
A characterization of (4,2)‐choosable graphs

A graph $G$ is \emph{$(a,b)$-choosable} if given any list assignment $L$ with $|L(v)|=a$ for each $v\in V(G)$ there exists a function $\varphi$ such that $\varphi(v)\in L(v)$ and $|\varphi(v)|=b$ for all $v\in V(G)$, and whenever vertices $x$ and $y$ are adjacent $\varphi(x)\cap \varphi(y)=\emptyset$. Meng, Puleo, and Zhu conjectured a characterization of (4,2)-choosable graphs. We prove their conjecture.
Preparing for the Unknown: Learning a Universal Policy with Online System Identification

We present a new method of learning control policies that successfully operate under unknown dynamic models. We create such policies by leveraging a large number of training examples that are generated using a physical simulator. Our system is made of two components: a Universal Policy (UP) and a function for Online System Identification (OSI). We describe our control policy as universal because it is trained over a wide array of dynamic models. These variations in the dynamic model may include differences in mass and inertia of the robots' components, variable friction coefficients, or unknown mass of an object to be manipulated. By training the Universal Policy with this variation, the control policy is prepared for a wider array of possible conditions when executed in an unknown environment. The second part of our system uses the recent state and action history of the system to predict the dynamics model parameters mu. The value of mu from the Online System Identification is then provided as input to the control policy (along with the system state). Together, UP-OSI is a robust control policy that can be used across a wide range of dynamic models, and that is also responsive to sudden changes in the environment. We have evaluated the performance of this system on a variety of tasks, including the problem of cart-pole swing-up, the double inverted pendulum, locomotion of a hopper, and block-throwing of a manipulator. UP-OSI is effective at these tasks across a wide range of dynamic models. Moreover, when tested with dynamic models outside of the training range, UP-OSI outperforms the Universal Policy alone, even when UP is given the actual value of the model dynamics. In addition to the benefits of creating more robust controllers, UP-OSI also holds out promise of narrowing the Reality Gap between simulated and real physical systems.
Get Your Workload in Order: Game Theoretic Prioritization of Database Auditing

A wide variety of mechanisms, such as alert triggers and auditing routines, have been developed to notify administrators about types of suspicious activities in the daily use of large databases of personal and sensitive information. However, such mechanisms are limited in that: 1) the volume of such alerts is often substantially greater than the auditing capabilities of budget-constrained organizations and 2) strategic attackers may disguise their actions or carefully choose which records they touch, thus evading auditing routines. To address these problems, we introduce a novel approach to database auditing that explicitly accounts for adversarial behavior by 1) prioritizing the order in which types of alerts are investigated and 2) providing an upper bound on how much budget to allocate for auditing each alert type. We model the interaction between a database auditor and potential attackers as a Stackelberg game in which the auditor chooses an auditing policy and attackers choose which records in a database to target. We further introduce an efficient approach that combines linear programming, column generation, and heuristic search to derive an auditing policy, in the form of a mixed strategy. We assess the performance of the policy selection method using a publicly available credit card application dataset, the results of which indicate that our method produces high-quality database audit policies, significantly outperforming baselines that are not based in a game theoretic framing.
Discriminative sparsity for Sonar ATR

Advancements in Sonar image capture have enabled researchers to apply sophisticated object identification algorithms in order to locate targets of interest in images such as mines [1] [2]. Despite progress in this field, modern sonar automatic target recognition (ATR) approaches lack robustness to the amount of noise one would expect in real-world scenarios, the capability to handle blurring incurred from the physics of image capture, and the ability to excel with relatively few training samples. We address these challenges by adapting modern sparsity-based techniques with dictionaries comprising of training from each class. We develop new discriminative (as opposed to generative) sparse representations which can help automatically classify targets in Sonar imaging. Using a simulated SAS data set from the Naval Surface Warfare Center (NSWC), we obtained compelling classification rates for multi-class problems even in cases with considerable noise and sparsity in training samples.
On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator of orders less than one

It is shown that, if all weak solutions of the evolution equation \begin{equation*} y'(t)=Ay(t),\ t\ge0, \end{equation*} with a scalar type spectral operator $A$ in a complex Banach space are Gevrey ultradifferentiable of orders less than one, then the operator $A$ is necessarily bounded.
Fully Asynchronous Push-Sum With Growing Intercommunication Intervals

We propose an algorithm for average consensus over a directed graph which is both fully asynchronous and robust to unreliable communications. We show its convergence to the average while allowing for slowly growing but potentially unbounded communication failures.
Safe and stabilizing distributed multi-path cellular flows

We study the problem of distributed traffic control in the partitioned plane, where the movement of all entities (robots, vehicles, etc.) within each geographic partition (cell) is the same. Each cell is controlled by software to move entities across the cell to route entities from sources to targets without collisions. We present a formal model of a distributed traffic control protocol that guarantees minimum separation between entities, even as the software controlling some cells fails by crashing. The distributed traffic control protocol relies on two principles: (a) temporary blocking entity transfers between adjacent cells for maintenance of safety and (b) local geographical routing for guaranteeing progress of entities to their targets. Establishing liveness in distributed traffic control systems is challenging, but liveness analysis will be necessary to apply distributed algorithms in applications like coordinating robot swarms and intelligent highway systems. Once new failures stop occurring, in the case of a single target cell, the protocol is guaranteed to self-stabilize and entities with feasible paths to the target cell make progress towards it. For multiple targets, failures may cause deadlocks in the system, so we identify a class of non-deadlocking failures where all entities are guaranteed to make progress to their respective targets. Our assertional proofs may serve as templates for the analysis of other distributed traffic control protocols. We also present simulation results to validate the formal model, and to provide estimates of entity throughput as a function of entity velocity, safety separation distance, single-target path complexity, failure-recovery rates, and multi-target path complexity.
Liquidity, risk measures, and concentration of measure

This paper studies curves of the form (ρ(λX))λ≥0, called risk profiles, where ρ is a convex risk measure and X a random variable. Financially, this captures the sensitivity of risk to the size of the investment in X, which the original axiomatic foundations of convex risk measures suggest to interpret as liquidity risk. The shape of a risk profile is intimately linked with the tail behavior of X for some notable classes of risk measures, namely shortfall risk measures and optimized certainty equivalents, and shares many useful features with cumulant generating functions. Exploiting this link leads to tractable necessary and sufficient conditions for pointwise bounds on risk profiles, which we call concentration inequalities. These inequalities admit useful dual representations related to transport inequalities, and this leads to efficient uniform bounds for risk profiles for large classes of X. Several interesting mathematical results emerge from this analysis, including a new perspective on nonexponentia...
Equivalent Bergman Spaces with Inequivalent Weights

We give a proof that every space of weighted square-integrable holomorphic functions admits an equivalent weight whose Bergman kernel has zeroes. Here the weights are equivalent in the sense that they determine the same space of holomorphic functions. Additionally, a family of radial weights in $$L^1(\mathbb {C})$$ whose associated Bergman kernels that have infinitely many zeroes is exhibited.
Square function estimates on layer potentials for higher‐order elliptic equations

In this paper we establish square-function estimates on the double and single layer potentials for divergence form elliptic operators, of arbitrary even order 2m, with variable t-independent coefficients in the upper half-space. This generalizes known results for variable-coefficient second-order operators, and also for constant-coefficient higher-order operators.
Reciprocity Laws on Algebraic Surfaces via Iterated Integrals

In this paper we introduce new local symbols, which we call 4-function local symbols. We formulate reciprocity laws for them. These reciprocity laws are proven using a new method - multidimensional iterated integrals. Besides providing reciprocity laws for the new 4-function local symbols, the same method works for proving reciprocity laws for the Parshin symbol. Both the new 4-function local symbols and the Parshin symbol can be expressed as a finite product of newly defined bi-local symbols, each of which satisfies a reciprocity law. The K-theoretic variant of the first 4-function local symbol is defined in the Appendix. It differs by a sign from the one defined via iterated integrals. Both the sign and the K-theoretic variant of the 4-function local symbol satisfy reciprocity laws, whose proof is based on Milnor K-theory (see the Appendix). The relation of the 4-function local symbols to the double free loop space of the surface is given by iterated integrals over membranes.
Prime divisors in polynomial orbits over function fields

Given a polynomial $\phi$ over a global function field $K$ and a wandering base point $b\in K$, we give a geometric condition on $\phi$ ensuring the existence of primitive prime divisors for almost all points in the orbit $\mathcal{O}_\phi(b):=\{\phi^n(b)\}_{n\geq0}$
Trace-Like Invariant for Representations of Nilpotent Liftings of Quantum Planes

We derive a formula for the trace of the antipode on endomorphism algebras of simple self-dual modules of nilpotent liftings of quantum planes. We show that the trace is equal to the quantum dimension of the module up to a nonzero scalar depending on the simple module.
On global solutions of a Zakharov type system

We consider a class of wave-Schrodinger systems in three dimensions with a Zakharov-type coupling. This class of systems is indexed by a parameter γ which measures the strength of the null form in the nonlinearity of the wave equation. The case corresponds to the well-known Zakharov system, while the case corresponds to the Yukawa system. Here we show that sufficiently smooth and localized Cauchy data lead to pointwise decaying global solutions which scatter, for any .
Categorified Young symmetrizers and stable homology of torus links II

We construct complexes $$P_{1^{n}}$$ of Soergel bimodules which categorify the Young idempotents corresponding to one-column partitions. A beautiful recent conjecture (Flag Hilbert schemes, colored projectors and Khovanov–Rozansky homology. arXiv:1608.07308 , 2016) of Gorsky–Neguț–Rasmussen relates the Hochschild homology of categorified Young idempotents with the flag Hilbert scheme. We prove this conjecture for $$P_{1^{n}}$$ and its twisted variants. We also show that this homology is also a certain limit of Khovanov–Rozansky homologies of torus links. Along the way we obtain several combinatorial results which could be of independent interest.
Testing normality for unconditionally heteroscedastic macroeconomic variables

Abstract In this paper the testing of normality for unconditionally heteroscedastic macroeconomic time series is studied. It is underlined that the classical Jarque-Bera test (JB hereafter) for normality is inadequate in our framework. On the other hand it is found that the approach which consists in correcting the heteroscedasticity by kernel smoothing for testing normality is justified asymptotically. Nevertheless it appears from Monte Carlo experiments that such a methodology can noticeably suffer from size distortion for samples that are typical for macroeconomic variables. As a consequence a parametric bootstrap methodology for correcting the problem is proposed. The innovations distribution of a set of inflation measures for the U.S., Korea and Australia are analyzed.
Persistence of sums of correlated increments and clustering in cellular automata

Abstract Let T be the first return time to ( − ∞ , 0 ] of sums of increments given by a functional of a stationary Markov chain. We determine the asymptotic behavior of the survival probability, P ( T ≥ t ) ∼ C t − 1 ∕ 2 for an explicit constant C . Our analysis is based on a connection between the survival probability and the running maximum of the time-reversed process, and relies on a functional central limit theorem for Markov chains. As applications, we recover known clustering results for the 3-color cyclic cellular automaton and the Greenberg–Hastings model, and we prove a new clustering result for the 3-color firefly cellular automaton.
Distributed consensus with mixed time/communication bandwidth performance metrics

In this paper we study the inherent trade-off between time and communication complexity for the distributed consensus problem. In our model, communication complexity is measured as the maximum data throughput (in bits per second) sent through the network at a given instant. Such a notion of communication complexity, referred to as bandwidth complexity, is related to the frequency bandwidth a designer should collectively allocate to the agents if they were to communicate via a wireless channel, which represents an important constraint for robotic networks. We prove a lower bound on the bandwidth complexity of the consensus problem and provide a matching consensus algorithm that is bandwidth-optimal for a wide class of consensus functions. We then propose a distributed algorithm that can trade communication complexity versus time complexity and robustness as a function of a tunable parameter, which can be adjusted by a system designer as a function of the properties of the wireless communication channel. We rigorously characterize the tunable algorithm's worst-case bandwidth complexity and show that it compares favorably with the bandwidth complexity of well-known consensus algorithms.
A decentralized mechanism for computing competitive equilibria in deregulated electricity markets

With the increased level of distributed generation and demand response comes the need for associated mechanisms that can perform well in the face of increasingly complex deregulated energy market structures. Using Lagrangian duality theory, we develop a decentralized market mechanism that ensures that, under the guidance of a market operator, self-interested market participants:generation companies (GenCos), distribution companies (DistCos), and transmission companies (TransCos), reach a competitive equilibrium. We show that even in the presence of informational asymmetries and nonlinearities (such as power losses and transmission constraints), the resulting competitive equilibrium is Pareto efficient.
Privacy Against Statistical Matching: Inter-User Correlation

Modern applications significantly enhance user experience by adapting to each user's individual condition and/or preferences. While this adaptation can greatly improve utility or be essential for the application to work (e.g., for ride-sharing applications), the exposure of user data to the application presents a significant privacy threat to the users, even when the traces are anonymized, since the statistical matching of an anonymized trace to prior user behavior can identify a user and their habits. Because of the current and growing algorithmic and computational capabilities of adversaries, provable privacy guarantees as a function of the degree of anonymization and obfuscation of the traces are necessary. Our previous work has established the requirements on anonymization and obfuscation in the case that data traces are independent between users. However, the data traces of different users will be dependent in many applications, and an adversary can potentially exploit such. In this paper, we consider the impact of correlation between user traces on their privacy. First, we demonstrate that the adversary can readily identify the association graph, revealing which user data traces are correlated. Next, we demonstrate that the adversary can use this association graph to break user privacy with significantly shorter traces than in the case when traces are independent between users, and that independent obfuscation of the data traces is often insufficient to remedy such. Finally, we discuss how the users can employ dependency in their obfuscation to improve their privacy.
A computation in Khovanov-Rozansky homology

We investigate the Khovanov-Rozansky invariant of a certain tangle and its compositions. Surprisingly the complexes we encounter reduce to ones that are very simple. Furthermore, we discuss a "local" algorithm for computing Khovanov-Rozansky homology and compare our results with those for the "foam" version of sl_3-homology.
Derivative-Free Optimization of Rate Parameters of Capsid Assembly Models from Bulk in Vitro Data

The assembly of virus capsids proceeds by a complicated cascade of association and dissociation steps, the great majority of which cannot be directly experimentally observed. This has made capsid assembly a rich field for computational models, but there are substantial obstacles to model inference for such systems. Here, we describe progress on fitting kinetic rate constants defining capsid assembly models to experimental data, a difficult data-fitting problem because of the high computational cost of simulating assembly trajectories, the stochastic noise inherent to the models, and the limited and noisy data available for fitting. We evaluate the merits of data-fitting methods based on derivative-free optimization (DFO) relative to gradient-based methods used in prior work. We further explore the advantages of alternative data sources through simulation of a model of time-resolved mass spectrometry data, a technology for monitoring bulk capsid assembly that can be expected to provide much richer data than previously used static light scattering approaches. The results show that advances in both the data and the algorithms can improve model inference. More informative data sources lead to high-quality fits for all methods, but DFO methods show substantial advantages on less informative data sources that better represent current experimental practice.
Matrix Completion has No Spurious Local Minimum

Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent progress in proving various non-convex algorithms converge from a good initial point, it remains unclear why random or arbitrary initialization suffices in practice. We prove that the commonly used non-convex objective function for matrix completion has no spurious local minima \--- all local minima must also be global. Therefore, many popular optimization algorithms such as (stochastic) gradient descent can provably solve matrix completion with \textit{arbitrary} initialization in polynomial time.
The Heisenberg group acts on a strictly convex domain

Author(s): Cooper, D | Abstract: This paper gives the first example of a unipotent group that is not virtually abelian and preserves a strictly convex domain.
Elasticity in Polynomial-Type Extensions

The elasticity of an atomic integral domain is, in some sense, a measure of how far the domain is from being a half-factorial domain. We consider the relationship between the elasticity of a domain R and the elasticity of its polynomial ring R [ x ]. For example, if R has at least one atom, a sufficient condition for the polynomial ring R [ x ] to have elasticity 1 is that every non-constant irreducible polynomial f ∈ R [ x ] be irreducible in K [ x ]. We will determine the integral domains R whose polynomial rings satisfy this condition.
Geometric properties of noncommutative symmetric spaces of measurable operators and unitary matrix ideals

This is a survey article of geometric properties of noncommutative symmetric spaces of measurable operators $E(\mathcal{M},\tau)$, where $\mathcal{M}$ is a semifinite von Neumann algebra with a faithful, normal, semifinite trace $\tau$, and $E$ is a symmetric function space. If $E\subset c_0$ is a symmetric sequence space then the analogous properties in the unitary matrix ideals $C_E$ are also presented. In the preliminaries we provide basic definitions and concepts illustrated by some examples and occasional proofs. In particular we list and discuss the properties of general singular value function, submajorization in the sense of Hardy, Littlewood and Polya, Kothe duality, the spaces $L_p(\mathcal{M},\tau)$, $1\le p<\infty$, the identification between $C_E$ and $G(B(H), \rm{tr})$ for some symmetric function space $G$, the commutative case when $E$ is identified with $E(\mathcal{N}, \tau)$ for $\mathcal{N}$ isometric to $L_\infty$ with the standard integral trace, trace preserving $*$-isomorphisms between $E$ and a $*$-subalgebra of $E(\mathcal{M},\tau)$, and a general method of removing the assumption of non-atomicity of $\mathcal{M}$. The main results on geometric properties are given in separate sections. We present the results on (complex) extreme points, (complex) strict convexity, strong extreme points and midpoint local uniform convexity, $k$-extreme points and $k$-convexity, (complex or local) uniform convexity, smoothness and strong smoothness, (strongly) exposed points, (uniform) Kadec-Klee properties, Banach-Saks properties, Radon-Nikodým property and stability in the sense of Krivine-Maurey. We also state some open problems.
Highly decentralized solar geoengineering

ABSTRACTNonstate actors appear to have increasing power, in part due to new technologies that alter actors’ capacities and incentives. Although solar geoengineering is typically conceived of as cen...
Time-Series Insights into the Process of Passing or Failing Online University Courses Using Neural-Induced Interpretable Student States.

This paper addresses a key challenge in Educational Data Mining, namely to model student behavioral trajectories in order to provide a means for identifying students most at-risk, with the goal of providing supportive interventions. While many forms of data including clickstream data or data from sensors have been used extensively in time series models for such purposes, in this paper we explore the use of textual data, which is sometimes available in the records of students at large, online universities. We propose a time series model that constructs an evolving student state representation using both clickstream data and a signal extracted from the textual notes recorded by human mentors assigned to each student. We explore how the addition of this textual data improves both the predictive power of student states for the purpose of identifying students at risk for course failure as well as for providing interpretable insights about student course engagement processes.
Assessment and Treatment Recommendations for Pediatric Pain: The Influence of Patient Race, Patient Gender, and Provider Pain-Related Attitudes.

Abstract Previous studies have documented that racial minorities and women receive poorer pain care than their demographic counterparts. Providers contribute to these disparities when their pain-related decision-making systematically varies across patient groups. Less is known about racial and gender disparities in children with pain or the extent to which providers contribute to these disparities. In a sample of 129 medical students (henceforth referred to as "providers"), Virtual Human methodology and a pain-related version of the Implicit Association Test (IAT) were used to examine the effects of patient race/gender on providers’ pain assessment/treatment decisions for pediatric chronic abdominal pain, as well as the moderating role of provider implicit pain-related race/gender attitudes. Findings indicated that providers rated Black patients as more distressed (mean difference [MD] = 2.33, P Perspective Providers’ pain assessment (ie, pain distress/pain interference) and treatment (ie, opioids) of pediatric pain differs across patient race and to a lesser extent, patient gender. This study represents a critical step in research on pain-related disparities in pediatric pain.
A conceptual study on real-time adaptive radiation therapy optimization through ultra-fast beamlet control.

A central problem in the field of radiation therapy (RT) is how to optimally deliver dose to a patient in a way that fully accounts for anatomical position changes over time. As current RT is a static process, where beam intensities are calculated before the start of treatment, anatomical deviations can result in poor dose conformity. To overcome these limitations, we present a simulation study on a fully dynamic real-time adaptive radiation therapy (RT-ART) optimization approach that uses ultra-fast beamlet control to dynamically adapt to patient motion in real-time.a#13; a#13; A virtual RT-ART machine was simulated with a rapidly rotating linear accelerator (LINAC) source (60 RPM) and a binary 1D multi-leaf collimator (MLC) operating at 100 Hz. If the real-time tracked target motion exceeded a predefined threshold, a time dependent objective function was solved using fast optimization methods to calculate new beamlet intensities that were then delivered to the patient.a#13; a#13; To evaluate the approach, system response was analyzed for patient derived continuous drift, step-like, and periodic intra-fractional motion. For each motion type investigated, the RT-ART method was compared against the ideal case with no patient motion (static case) as well as to the case without the use RT-ART. In all cases, isodose lines and dose-volume-histograms (DVH) showed that RT-ART plan quality was approximately the same as the static case, and considerably better than the no RT-ART case.a#13; a#13; Based on tests using several different motion types, RT-ART was able to recover dose conformity to the level that it was similar to an ideal RT delivery with no anatomical changes. With continued advances in real-time patient motion tracking and fast computational processes, there is significant potential for the RT-ART optimization process to be realized on next generation RT machines.
Evolution of Regional Innovation with Spatial Knowledge Spillovers: Convergence or Divergence?

This paper extends endogenous economic growth models to incorporate knowledge externality. We explore whether spatial knowledge spillovers among regions exist, whether spatial knowledge spillovers promote regional innovative activities, and whether external knowledge spillovers affect the evolution of regional innovations in the long run. We empirically verify the theoretical results through applying spatial statistics and econometric models in the analysis of panel data of 31 regions in China. An accurate estimate of the range of knowledge spillovers is achieved and the convergence of regional knowledge growth rate is found, with clear evidences that developing regions benefit more from external knowledge spillovers than developed regions.
Control Barrier Functions: Theory and Applications

This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems.
UAV Swarms as Amplify-and-Forward MIMO Relays

Unmanned aerial vehicles provide new opportunities for performance improvements in future wireless communications systems. For example, they can act as relays that extend the range of a communication link and improve the capacity. Unlike conventional relays that are deployed at fixed locations, UAVs can change their positions to optimize the capacity or range on demand. In this paper, we consider using a swarm of UAVs as amplify-and-forward MIMO relays to provide connectivity between an obstructed multi-antenna equipped source and destination. We start by optimizing UAV placement for the single antenna case, and analyze its dependence on the noise introduced by the relay, its gain, and transmit power constraint. We extend our analysis for an arbitrary UAV swarm and show how the MIMO link capacity can be optimized by changing the distance of the swarm to the source and the destination. Then, we consider the effect of optimizing the positions of the UAVs within the swarm and derive an upper bound for the capacity at any given placement of the swarm. We also propose a simple near optimal approach to find the positions that optimize the capacity for the end-to-end link given that the source and the destination have uniform rectangular arrays.
Neural Gaussian Copula for Variational Autoencoder

Variational language models seek to estimate the posterior of latent variables with an approximated variational posterior. The model often assumes the variational posterior to be factorized even when the true posterior is not. The learned variational posterior under this assumption does not capture the dependency relationships over latent variables. We argue that this would cause a typical training problem called posterior collapse observed in all other variational language models. We propose Gaussian Copula Variational Autoencoder (VAE) to avert this problem. Copula is widely used to model correlation and dependencies of high-dimensional random variables, and therefore it is helpful to maintain the dependency relationships that are lost in VAE. The empirical results show that by modeling the correlation of latent variables explicitly using a neural parametric copula, we can avert this training difficulty while getting competitive results among all other VAE approaches.
Effective Floquet Hamiltonian in the low-frequency regime

We develop a theory to derive effective Floquet Hamiltonians in the weak-drive and low-frequency regime. We construct the theory in analogy with band theory for electrons in a spatially periodic and weak potential, such as occurs in some crystalline materials. As a prototypical example, we apply this theory to graphene driven by circularly polarized light of low intensity. We find an analytic expression for the effective Floquet Hamiltonian in the low-frequency regime which accurately predicts the quasienergy spectrum and the Floquet states. Furthermore, we identify self-consistency as the crucial feature effective Hamiltonians in this regime need to satisfy to achieve high accuracy. The method is useful in providing a realistic description of off-resonant drives for multiband solid-state systems where light-induced topological band structure changes are sought.