Miracle-dz/UniFAR-FTUs huggingface dataset:
Constrained Restless Bandits for Dynamic Scheduling in Cyber-Physical Systems

Restless multi-armed bandits are a class of discrete-time stochastic control problems which involve sequential decision making with a finite set of actions (set of arms). This paper studies a class of constrained restless multi-armed bandits (CRMAB). The constraints are in the form of time varying set of actions (set of available arms). This variation can be either stochastic or semi-deterministic. Given a set of arms, a fixed number of them can be chosen to be played in each decision interval. The play of each arm yields a state dependent reward. The current states of arms are partially observable through binary feedback signals from arms that are played. The current availability of arms is fully observable. The objective is to maximize long term cumulative reward. The uncertainty about future availability of arms along with partial state information makes this objective challenging. Applications for CRMAB abound in the domain of cyber-physical systems. This optimization problem is analyzed using Whittle's index policy. To this end, a constrained restless single-armed bandit is studied. It is shown to admit a threshold-type optimal policy, and is also indexable. An algorithm to compute Whittle's index is presented. Further, upper bounds on the value function are derived in order to estimate the degree of sub-optimality of various solutions. The simulation study compares the performance of Whittle's index, modified Whittle's index and myopic policies.
Approximate Shannon Sampling in Importance Sampling: Nearly Consistent Finite Particle Estimates

In Bayesian inference, we seek to compute information about random variables such as moments or quantiles on the basis of data and prior information. When the distribution of random variables is complicated, Monte Carlo (MC) sampling is usually required. Importance sampling is a standard MC tool for addressing this problem: one generates a collection of samples according to an importance distribution, computes their contribution to an unnormalized density, i.e., the importance weight, and then sums the result followed by normalization. This procedure is asymptotically consistent as the number of MC samples, and hence deltas (particles) that parameterize the density estimate, go to infinity. However, retaining in infnitely many particles is intractable. Thus, we propose a scheme for only keeping a nite representative subset of particles and their augmented importance weights that is nearly consistent.
Internal DLA on cylinder graphs: fluctuations and mixing

We use coupling ideas introduced in \cite{levine2018long} to show that an IDLA process on a cylinder graph $G\times \mathbb{Z}$ forgets a typical initial profile in $\mathcal{O}( N\sqrt{\tau_N} (\log \! N)^2 )$ steps for large $N$, where $N$ is the size of the base graph $G$, and $\tau_N$ is the total variation mixing time of a simple random walk on $G$. The main new ingredient is a maximal fluctuations bound for IDLA on $G\times \mathbb{Z}$ which only relies on the mixing properties of the base graph $G$ and the Abelian property.
An Adversarial Approach to Private Flocking in Mobile Robot Teams

Privacy is an important facet of defence against adversaries. In this letter, we introduce the problem of private flocking. We consider a team of mobile robots flocking in the presence of an adversary, who is able to observe all robots’ trajectories, and who is interested in identifying the leader. We present a method that generates private flocking controllers that hide the identity of the leader robot. Our approach towards privacy leverages a data-driven adversarial co-optimization scheme. We design a mechanism that optimizes flocking control parameters, such that leader inference is hindered. As the flocking performance improves, we successively train an adversarial discriminator that tries to infer the identity of the leader robot. To evaluate the performance of our co-optimization scheme, we investigate different classes of reference trajectories. Although it is reasonable to assume that there is an inherent trade-off between flocking performance and privacy, our results demonstrate that we are able to achieve high flocking performance and simultaneously reduce the risk of revealing the leader.
Blocking and sparsity for optimization of convolution calculation algorithm on GPUs

Convolution neural network (CNN) plays a paramount role in machine learning, which has made significant contributions, such as medical image classification, natural language processing, and recommender system. The success convolution neural network achieved excellent performance with fast execution time. Due to the convolution operation dominate the total operation time of Convolution neural network. In this paper, we propose a novel convolution method of Graphic Processing Units (GPUs), which reduce the convolution operation time and improve the execution speed approximately 2X than the state of the art convolution algorithm. Our work based on the observation is that the sparsity of the input feature map of convolution operation is relatively large, and the zero value of the feature map is redundancy for convolution result. Therefore, we skip the zero value calculation and improve the speed by compressing the feature map. Besides, the shape of the feature map for the deep network is small, and the number of threads is limited. Therefore, for a limited number of threads, it is necessary to reduce the amount of calculation to increase the calculation speed. Our algorithm has a good effect on the convolution operation of the feature map of the deep network with large sparsity and small size. In this work, our contributions can be summarized as follows: 1) A novel store format for hight-sparsity feature map. 2) A novel convolution algorithm based on block compression and Shared memory is proposed. 3) A feature map data-set for convolution algorithm optimization. 4) We performed a single-layer convolution comparison experiment with CuDNN for different models, and it is best to achieve 3.5X speedup. We also implemented the algorithm on the VGG-19 model, which can achieve 1.3X$\sim$2.9X speedup in deep convolution operation, and the entire network can achieve 2.3X speedup.
Whitney Numbers of Combinatorial Geometries and Higher-Weight Dowling Lattices

We study the Whitney numbers of the first kind of combinatorial geometries. The first part of the paper is devoted to general results relating the Mobius functions of nested atomistic lattices, extending some classical theorems in combinatorics. We then specialize our results to restriction geometries, i.e., to sublattices $\mathcal{L}(A)$ of the lattice of subspaces of an $\mathbb{F}_q$-linear space, say $X$, generated by a set of projective points $A \subseteq X$. In this context, we introduce the notion of subspace distribution, and show that partial knowledge of the latter is equivalent to partial knowledge of the Whitney numbers of $\mathcal{L}(A)$. This refines a classical result by Dowling. The most interesting applications of our results are to be seen in the theory of higher-weight Dowling lattices (HWDLs), to which we dovote the second and most substantive part of the paper. These combinatorial geometries were introduced by Dowling in 1971 in connection with fundamental problems in coding theory, and further studied, among others, by Zaslavsky, Bonin, Kung, Brini, and Games. To date, still very little is known about these lattices. In particular, the techniques to compute their Whitney numbers have not been discovered yet. In this paper, we bring forward the theory of HWDLs, computing their Whitney numbers for new infinite families of parameters. Moreover, we show that the second Whitney numbers of HWDLs are polynomials in the underlying field size $q$, whose coefficients are expressions involving the Bernoulli numbers. This reveals a new link between combinatorics, coding theory, and number theory. We also study the asymptotics of the Whitney numbers of HWDLs as the field size grows, giving upper bounds and exact estimates in some cases. In passing, we obtain new results on the density functions of error-correcting codes.
Making a Case for MLNs for Data-Driven Analysis: Modeling, Efficiency, and Versatility

Datasets of real-world applications are characterized by entities of different types, which are defined by multiple features and connected via varied types of relationships. A critical challenge for these datasets is developing models and computations to support flexible analysis, i.e., the ability to compute varied types of analysis objectives in an efficient manner. To address this problem, in this paper, we make a case for modeling such complex data sets as multilayer networks (or MLNs), and argue that MLNs provide a more informative model than the currently popular simple and attribute graphs. Through analyzing communities and hubs on homogeneous and heterogeneous MLNs, we demonstrate the flexibility of the chosen model. We also show that compared to current analysis approaches, a network decoupling-based analysis of MLNs is more efficient and also preserves the structure and result semantics. We use three diverse data sets to showcase the effectiveness of modeling them as MLNs and analyzing them using the decoupling-based approach. We use both homogeneous and heterogeneous MLNs for modeling and community and hub computations for analysis. The data sets are from US commercial airlines and IMDb, a large international movie data set. Our experimental analysis validate modeling, efficiency of computation, and versatility of the approach. Correctness of results are verified using independently available ground truth. For the data sets used, efficiency improvement is in the range of 64% to 98%.
Locally distinguishing quantum states with limited classical communication

We consider different settings of the task to distinguish pure orthogonal quantum states under local operations and a limited amount of classical communication. In the first setting, the spatially separated parties are allowed to perform only local projective measurements without any classical communication during the measurements. Under such a restricted class of operations, if the states are indistinguishable, then within a second group of settings, the parties are allowed to use an additional resource for the distinguishing. The additional resource is either a pure entangled state or multiple identical copies of the given states. Comparisons between these two types of resources are also done in certain cases. Both probabilistic and perfect discrimination of the states are considered for the second group of settings. Within a third setting, the parties perform local projective measurements with a restriction on the availability of classical communication during the measurements. But in this setting the parties are allowed to use a maximally entangled state as a resource.
Bogolyubov invariant via relative spectral invariants on manifolds

We introduce and study new spectral invariant of two elliptic partial differential operators of Laplace and Dirac type on compact smooth manifolds without boundary that depends on both the eigenvalues and the eigensections of the operators, which is a equal to the regularized number of created particles from the vacuum when the dynamical operator depends on time. We study the asymptotic expansion of this invariant for small adiabatic parameter and compute explicitly the first two coefficients of the asymptotic expansion.
Optimal query complexity for private sequential learning

Motivated by privacy concerns in many practical applications such as Federated Learning, we study a stylized private sequential learning problem: a learner tries to estimate an unknown scalar value, by sequentially querying an external database and receiving binary responses; meanwhile, a third-party adversary observes the learner's queries but not the responses. The learner's goal is to design a querying strategy with the minimum number of queries (optimal query complexity) so that she can accurately estimate the true value, while the adversary even with the complete knowledge of her querying strategy cannot. Prior work has obtained both upper and lower bounds on the optimal query complexity, however, these upper and lower bounds have a large gap in general. In this paper, we construct new querying strategies and prove almost matching upper and lower bounds, providing a complete characterization of the optimal query complexity as a function of the estimation accuracy and the desired levels of privacy.
Training neural networks to encode symbols enables combinatorial generalization

Combinatorial generalization—the ability to understand and produce novel combinations of already familiar elements—is considered to be a core capacity of the human mind and a major challenge to neural network models. A significant body of research suggests that conventional neural networks cannot solve this problem unless they are endowed with mechanisms specifically engineered for the purpose of representing symbols. In this paper, we introduce a novel way of representing symbolic structures in connectionist terms—the vectors approach to representing symbols (VARS), which allows training standard neural architectures to encode symbolic knowledge explicitly at their output layers. In two simulations, we show that neural networks not only can learn to produce VARS representations, but in doing so they achieve combinatorial generalization in their symbolic and non-symbolic output. This adds to other recent work that has shown improved combinatorial generalization under some training conditions, and raises the question of whether specific mechanisms or training routines are needed to support symbolic processing. This article is part of the theme issue ‘Towards mechanistic models of meaning composition’.
Combinatorics of $F$-polynomials

We introduce the stabilization functors to study the combinatorial aspect of the $F$-polynomial of a representation of any finite-dimensional basic algebra. We characterize the vertices of their Newton polytopes. We give an explicit formula for the $F$-polynomial restricting to any face of its Newton polytope. For acyclic quivers, we give a complete description of all facets of the Newton polytope when the representation is general. We also prove that the support of $F$-polynomial is saturated for any rigid representation. We provide many examples and counterexamples, and pose several conjectures.
Birational and noncommutative lifts of antichain toggling and rowmotion

The rowmotion action on order ideals or on antichains of a finite partially ordered set has been studied (under a variety of names) by many authors. Depending on the poset, one finds unexpectedly interesting orbit structures, instances of (small order) periodicity, cyclic sieving, and homomesy. Many of these nice features still hold when the action is extended to $[0,1]$-labelings of the poset or (via detropicalization) to labelings by rational functions (the birational setting). In this work, we parallel the birational lifting already done for order-ideal rowmotion to antichain rowmotion. We give explicit equivariant bijections between the birational toggle groups and between their respective liftings. We further extend all of these notions to labellings by noncommutative rational functions, setting an unpublished periodicity conjecture of Grinberg in a broader context.
Anharmonic thermodynamics of vacancies using a neural network potential

Lattice anharmonicity is thought to strongly affect vacancy concentrations in metals at high temperatures. It is however non-trivial to account for this effect directly using density functional theory (DFT). Here we develop a deep neural network potential for aluminum that overcomes the limitations inherent to DFT, and we use it to obtain accurate anharmonic vacancy formation free energies as a function of temperature. While confirming the important role of anharmonicity at high temperatures, the calculation unveils a markedly nonlinear behavior of the vacancy formation entropy and shows that the vacancy formation free energy only violates Arrhenius law at temperatures above 600 K, in contrast with previous DFT calculations.
Classification of super-modular categories

We develop categorical and number theoretical tools for the classification of super-modular categories. We apply these tools to obtain a partial classification of super-modular categories of rank $8$. In particular we find three distinct families of prime categories in rank $8$ in contrast to the lower rank cases for which there is only one such family.
LEAP: A Lightweight Encryption and Authentication Protocol for In-Vehicle Communications

The Controller Area Network (CAN) is considered as the de-facto standard for the in-vehicle communications due to its real-time performance and high reliability. Unfortunately, the lack of security protection on the CAN bus gives attackers the opportunity to remotely compromise a vehicle. In this paper, we propose a Lightweight Encryption and Authentication Protocol (LEAP) with low cost and high efficiency to address the security issue of the CAN bus. LEAP exploits the security-enhanced stream cipher primitive to provide encryption and authentication for the CAN messages. Compared with the state-of-the-art Message Authentication Code (MAC) based approaches, LEAP requires less memory, is 8X faster, and thwarts the most recently proposed attacks.
Hyperbolic metamaterials: From dispersion manipulation to applications

Manipulating the property of iso-frequency contour (IFC) will provide a powerful control for the interaction between light and matter. Importantly, hyperbolic metamaterials (HMMs), a class of artificial anisotropic materials with hyperbolic IFC have been intensively investigated. Because of the open dispersion curves, HMMs support propagating high-k modes and possess enhanced photonic density of states. As a result, HMMs can be utilized to realize hyper-lens breaking the diffraction limit, meta-cavity laser with subwavelength scale, high sensitivity sensor, long-range energy transfer and so on. In order to make it easier for people who are about to enter this burgeoning and rapidly developing research field, this tutorial article not only introduces the basic physical properties of HMMs, but also discusses the dispersion manipulation of HMMs and HMM-based structures such as hypercrystals. The theoretical methods and experimental platforms are given in this tutorial. Finally, some potential applications associated with hyperbolic dispersion are also introduced
Embedding-based Qualitative Analysis of Polarization in Turkey

On June 24, 2018, Turkey conducted a highly-consequential election in which the Turkish people elected their president and parliament in the first election under a new presidential system. During the election period, the Turkish people extensively shared their political opinions on Twitter. One access of polarization among the electorate was support for or opposition to the reelection of Recep Tayyip Erdogan. In this paper, we explore the polarization between the two groups on their political opinions and lifestyle, and examine whether polarization had increased in the lead up to the election. We conduct our analysis on two collected datasets covering the time periods before and during the election period that we split into pro- and anti-Erdogan groups. For the pro and anti splits of both datasets, we generate separate word embedding models, and then use the four generated models to contrast the neighborhood (in the embedding space) of the political leaders, political issues, and lifestyle choices (e.g., beverages, food, and vacation). Our analysis shows that the two groups agree on some topics, such as terrorism and organizations threatening the country, but disagree on others, such as refugees and lifestyle choices. Polarization towards party leaders is more pronounced, and polarization further increased during the election time.
The Kinematics of Shoulder Impingement: Glenohumeral Joint Positions and the Effects on Rotator Cuff Tendon Clearance

The infraspinatus, supraspinatus, and subscapularis were considered when looking at impingement in ten subject anatomical models. The infraspinatus and supraspinatus were found to be the sources of impingement for symptomatic subjects in two representative positions: reaching up behind the back and reaching into the back pocket. The minimum distances were found to be smaller and area of contact between the tissues and the acromion and coracoacromial ligament were found to be larger in symptomatic subjects. These results support that the impingement of these structures may cause symptoms in the subjects.
Omnidirectional Tractable Three Module Robot

This paper introduces the Omnidirectional Tractable Three Module Robot for traversing inside complex pipe networks. The robot consists of three omnidirectional modules fixed 120° apart circumferentially which can rotate about their own axis allowing holonomic motion of the robot. The holonomic motion enables the robot to overcome motion singularity when negotiating T-junctions and further allows the robot to arrive in a preferred orientation while taking turns inside a pipe. We have developed a closed-form kinematic model for the robot in the paper and propose the ‘Motion Singularity Region' that the robot needs to avoid while negotiating T-junction. The design and motion capabilities of the robot are demonstrated both by conducting simulations in MSC ADAMS on a simplified lumped-model of the robot and with experiments on its physical embodiment.
BinarySDG: binary sensor data generation with R

The scarcity of Smart Home data is still a pretty big problem, and in a world where the size of a dataset can often make the difference between a poor performance and a good performance for problems related to machine learning projects, this needs to be resolved. But whereas the problem of retrieving real data can't really be resolved, as most of the time the process of installing sensors and retrieving data can be found to be really expensive and time-consuming, we need to find a faster and easier solution, which is where synthetic data comes in. Here we propose BinarySDG (Binary Synthetic Data Generator) as a flexible and easy way to generate synthetic data for binary sensors.
Edge Isoperimetric Inequalities for Powers of the Hypercube

For positive integers $n$ and $r$, we let $Q_n^r$ denote the $r$th power of the $n$-dimensional discrete hypercube graph, i.e., the graph with vertex-set $\{0,1\}^n,$ where two 0-1 vectors are joined if they are Hamming distance at most $r$ apart. We study edge isoperimetric inequalities for this graph. Harper, Bernstein, Lindsey and Hart proved a best-possible edge isoperimetric inequality for this graph in the case $r=1$. For each $r \geq 2$, we obtain an edge isoperimetric inequality for $Q_n^r$; our inequality is tight up to a constant factor depending only upon $r$. Our techniques also yield an edge isoperimetric inequality for the `Kleitman-West graph' (the graph whose vertices are all the $k$-element subsets of $\{1,2,\ldots,n\}$, where two $k$-element sets have an edge between them if they have symmetric difference of size two); this inequality is sharp up to a factor of $2+o(1)$ for sets of size $\binom{n -s}{k-s}$, where $k=o(n)$ and $s \in \mathbb{N}$.
The Graph Isomorphism Problem: Local Certificates for Giant Action

This thesis provides an explanation of Laszlo Babai's quasi-polynomial algorithm for the Graph Isomorphism Problem published in 2015 with a particular focus on the case of local certificates, i.e. the case that cannot be dealt with by Luks' method. The thesis extends the explanations provided by Harald Andres Helfgott in 2017. It is concluded that the complexity of Babai's algorithm is $\exp\left(C \left(\log n\right)^3\right)$ for $n$ the number of vertices, $C$ a constant. Group theoretical and combinatorial arguments are used to give more details on Babai's method of local certificates. They treat Luks' barrier case in which the imprimitve permutation group $G$ can be mapped onto an alternating group with large domain.