Miracle-dz/UniFAR-FTUs huggingface dataset:
DIMENSION-FREE EULER ESTIMATES OF ROUGH DIFFERENTIAL EQUATIONS

Suppose that X is a continuous bounded variation path de ned on some interval I and taking its values in a Banach space V. We view this path as a stream of information and allow it to be highly oscillatory on normal scales. The theory of rough paths considers streams of information, such as X, for their e ect on other systems and provides quantitative tools to model this interaction. Consider the stream as the input to an automata or controlled di erential equation and so impacting on the evolution of the state Y in some controlled system:
Random Caching Based Cooperative Transmission in Heterogeneous Wireless Networks

Base station cooperation in heterogeneous wireless networks (HetNets) is a promising approach to improve the network performance, but it also imposes a significant challenge on backhaul. On the other hand, caching at small base stations (SBSs) is considered as an efficient way to reduce backhaul load in HetNets. In this paper, we jointly consider SBS caching and cooperation in a downlink large-scale HetNet. We propose two SBS cooperative transmission schemes under random caching at SBSs with the caching distribution as a design parameter. Using tools from stochastic geometry and adopting appropriate integral transformations, we first derive a tractable expression for the successful transmission probability under each scheme. Then, under each scheme, we consider the successful transmission probability maximization by optimizing the caching distribution, which is a challenging optimization problem with a non-convex objective function. By exploring optimality properties and using optimization techniques, under each scheme, we obtain a locally optimal solution in the general case and a globally optimal solution in some special cases. Compared with some existing caching designs in the literature, e.g., the most popular caching, the i.i. d. caching and the uniform caching, the optimal random caching under each scheme achieves a promising successful transmission probability. The analysis and optimization results provide valuable design insights for practical HetNets.
The Potential of Blockchain Technology for Health Information The Potential of Blockchain Technology for Health Information Exchange: Experimental Study From Patients’ Perspectives Exchange: Experimental Study From Patients’ Perspectives

Background: Nowadays, a number of mechanisms and tools are being used by health care organizations and physicians to electronically exchange the personal health information of patients. The main objectives of different methods of health information exchange (HIE) are to reduce health care costs, minimize medical errors, and improve the coordination of interorganizational information exchange across health care entities. The main challenges associated with the common HIE systems are privacy concerns, security risks, low visibility of system transparency, and lack of patient control. Blockchain technology is likely to disrupt the current information exchange models utilized in the health care industry. Objective: Little is known about patients’ perceptions and attitudes toward the implementation of blockchain-enabled HIE networks, and it is still not clear if patients (as one of the main HIE stakeholders) are likely to opt in to the applications of this technology in HIE initiatives. Thus, this study aimed at exploring the core value of blockchain technology in the health care industry from health care consumers’ views. Methods: To recognize the potential applications of blockchain technology in health care practices, we designed 16 information exchange scenarios for controlled Web-based experiments. Overall, 2013 respondents participated in 16 Web-based experiments. Each experiment described an information exchange condition characterized by 4 exchange mechanisms (ie, direct, lookup, patient-centered, and blockchain), 2 types of health information (ie, sensitive vs nonsensitive), and 2 types of privacy policy (weak vs strong). Results: The findings show that there are significant differences in patients’ perceptions of various exchange mechanisms with regard to patient privacy concern, trust in competency and integrity, opt-in intention, and willingness to share information. Interestingly, participants hold a favorable attitude toward the implementation of blockchain-based exchange mechanisms for privacy protection, coordination, and information exchange purposes. This study proposed the potentials and limitations of a blockchain-based attempt in the HIE context. Conclusions: The results of this research should be of interest to both academics and practitioners. The findings propose potential limitations of a blockchain-based HIE that should be addressed by health care organizations to exchange personal health information in a secure and private manner. This study can contribute to the research in the blockchain area and enrich the literature on the use of blockchain in HIE efforts. Practitioners can also identify how to leverage the benefit of blockchain to promote HIE initiatives nationwide.
Z4-linear Hadamard and extended perfect codes

If N = 2k ≥ 16 then there exist exactly ⌊(k − 1)/2⌋ pairwise nonequivalent Z4linear Hadamard (N, 2N,N/2)-codes and ⌊(k + 1)/2⌋ pairwise nonequivalent Z4linear extended perfect (N, 2N/2N, 4)-codes. A recurrent construction of Z4-linear Hadamard codes is given.
J ul 2 01 5 SAT-based Analysis of Large Real-world Feature Models is Easy

Modern conflict-driven clause-learning (CDCL) Boolean SAT solvers provide efficient automatic analysis of real-world feature models (FM) of systems ranging from cars to operating systems. It is well-known that solver-based analysis of real-world FMs scale very well even though SAT instances obtained from such FMs are large, and the corresponding analysis problems are known to be NP-complete. To better understand why SAT solvers are so effective, we systematically studied many syntactic and semantic characteristics of a representative set of large real-world FMs. We discovered that a key reason why large real-world FMs are easy-toanalyze is that the vast majority of the variables in these models are unrestricted, i.e., the models are satisfiable for both true and false assignments to such variables under the current partial assignment. Given this discovery and our understanding of CDCL SAT solvers, we show that solvers can easily find satisfying assignments for such models without too many backtracks relative to the model size, explaining why solvers scale so well. Further analysis showed that the presence of unrestricted variables in these real-world models can be attributed to their high-degree of variability. Additionally, we experimented with a series of well-known nonbacktracking simplifications that are particularly effective in solving FMs. The remaining variables/clauses after simplifications, called the core, are so few that they are easily solved even with backtracking, further strengthening our conclusions. In contrast to our findings, previous research characterizes the difficulty of analyzing randomly-generated FMs in terms of treewidth. Our experiments suggest that the difficulty of analyzing real-world FMs cannot be explained in terms of treewidth.
Memorizing Gaussians with no over-parameterizaion via gradient decent on neural networks

Many results in recent years established polynomial time learnability of various 1 models via neural networks algorithms (e.g. [3, 9, 7, 6, 17, 28, 18, 10, 4, 23, 19, 2 13, 5]). However, unless the model is linearly separable [5], or the activation is 3 quadratic [13], these results require very large networks – much more than what is 4 needed for the mere existence of a good predictor. 5 In this paper we make a step towards learnability results with near optimal network 6 size. We give a tight analysis on the rate in which the Neural Tangent Kernel[16], a 7 fundamental tool in the analysis of SGD on networks, converges to its expectations. 8 This results enable us to prove that SGD on depth two neural networks, starting 9 from a (non standard) variant of Xavier initialization [15] can memorize samples, 10 learn polynomials with bounded weights, and learn certain kernel spaces, with 11 near optimal network size, sample complexity, and runtime. In particular, we show 12 that SGD on depth two network with ˜ O (cid:0) md (cid:1) hidden neurons (and hence ˜ O ( m ) 13 parameters) can memorize m random labeled points in S d − 1 . 14
Modeling correlated noise is necessary to 1 decode uncertainty 2

Brain decoding algorithms form an important part of the arsenal of analysis 7 tools available to neuroscientists, allowing for a more detailed study of the kind of 8 information represented in patterns of cortical activity. While most current decoding 9 algorithms focus on estimating a single, most likely stimulus from the pattern of noisy 10 fMRI responses, the presence of noise causes this estimate to be uncertain. This 11 uncertainty in stimulus estimates is a potentially highly relevant aspect of cortical 12 stimulus processing, and features prominently in Bayesian or probabilistic models of 13 neural coding. Here, we focus on sensory uncertainty and how best to extract this 14 information with fMRI. We first demonstrate in simulations that decoding algorithms 15 that take into account correlated noise between fMRI voxels better recover the amount 16 of uncertainty (quantified as the width of a probability distribution over possible stimuli) 17 associated with the decoded estimate. Furthermore, we show that not all correlated 18 variability should be treated equally, as modeling tuning-dependent correlations has the 19 greatest impact on decoding performance. Next, we examine actual noise correlations 20 in human visual cortex, and find that shared variability in areas V1-V3 depends on the 21 tuning properties of fMRI voxels. In line with our simulations, accounting for this shared 22 noise between similarly tuned voxels produces important benefits in decoding. Our 23 findings underscore the importance of accurate noise models in fMRI decoding 24 approaches, and suggest a statistically feasible method to incorporate the most relevant 25 forms of shared noise. 26
Second-order Slepian-Wolf coding theorems for non-mixed and mixed sources

The second-order achievable rate region in Slepian-Wolf source coding systems is investigated. The concept of second-order achievable rates, which enables us to make a finer evaluation of achievable rates, has already been introduced and analyzed for general sources in the single-user source coding problem. Accordingly, in this paper, we first define the second-order achievable rate region for the Slepian-Wolf coding system and establish the source coding theorem for general sources in the second-order sense. Moreover, we compute the explicit second-order achievable rate region for i.i. d. correlated sources with countably infinite alphabets and mixed correlated sources, respectively, using the relevant asymptotic normality.
nnMobileNet: RETHINKING CNN FOR RETINOPATHY RESEARCH

Over the past few decades, convolutional neural networks (CNNs) have been at the forefront of the detection and tracking of various retinal diseases (RD). Despite their success, the emergence of vision transformers (ViT) in the 2020s has shifted the trajectory of RD model development. The leading-edge performance of ViT-based models in RD can be largely credited to their scalability—their ability to improve as more parameters are added. As a result, ViT-based models tend to outshine traditional CNNs in RD applications, albeit at the cost of increased data and computational demands. ViTs also differ from CNNs in their approach to processing images, working with patches rather than local regions, which can complicate the precise identification of small, variably presented lesions in RD. In our study, we revisited and updated the architecture of a CNN model, specifically MobileNet, to enhance its utility in RD diagnostics. We found that an optimized MobileNet, through selective modifications, can surpass ViT-based models in various RD benchmarks, including diabetic retinopathy grading, detection of multiple fundus diseases, and classification of diabetic macular edema. The code is available at https://github.com/ Retinal-Research/NN-MOBILENET
An innovative tour recommendation system for tourists in Japan

The paper demonstrates prototype of system that is capable of suggesting optimal touring plans which are composed of various points of interest (POI) and take travelers' preferences and context into account. It systematically collects and analyzes information on thousands of tourists attraction areas and geographical nodes of Japan Railway (JR) train stations together with concurrent weather information, estimated travel time, associated expenses, and lists of multiple cultural events in order to demonstrate practicality as well as reliability of the system. A programmatic approach based on the heuristic greedy search is employed for transforming the obtained data into informative routes. It demonstrates the feasibility of the approach through its mobile prototype on web platform and tests it under various scenarios in eight different places in Japan which includes Tokyo, Osaka, Kyoto, Kobe, Yokohama, Nagoya, Fukuoka and Sapporo. Its result and the performance can be considered as a stepping stone towards a more localized and practical recommendation system in the field of tourism in the near future.
MaskReID: A Mask Based Deep Ranking Neural Network for Person Re-identification

Person retrieval faces many challenges including cluttered background, appearance variations (e.g., illumination, pose, occlusion) among different camera views and the similarity among different person's images. To address these issues, we put forward a novel mask based deep ranking neural network with a skipped fusing layer. Firstly, to alleviate the problem of cluttered background, masked images with only the foreground regions are incorporated as input in the proposed neural network. Secondly, to reduce the impact of the appearance variations, the multi-layer fusion scheme is developed to obtain more discriminative fine-grained information. Lastly, considering person retrieval is a special image retrieval task, we propose a novel ranking loss to optimize the whole network. The proposed ranking loss can further mitigate the interference problem of similar negative samples when producing ranking results. The extensive experiments validate the superiority of the proposed method compared with the state-of-the-art methods on many benchmark datasets.
HIERARCHICAL UNAMBIGUITY

We develop techniques to investigate relativized hierarchical unambiguous computation. We apply our techniques to generalize known constructs involving relativized unambiguity based complexity classes (UP and Promise-UP) to new constructs involving arbitrary higher levels of the relativized unambiguous polynomial hierarchy (UPH). Our techniques are developed on constraints imposed by hierarchical arrangement of unambiguous nondeterministic polynomial-time Turing machines, and so they differ substantially, in applicability and in nature, from standard methods (such as the switching lemma [J. H̊astad, Computational Limitations of Small-Depth Circuits, MIT Press, Cambridge, 1987]), which play roles in carrying out similar generalizations. Aside from achieving these generalizations, we resolve a question posed by Cai, Hemachandra, and Vyskoč in [Complexity Theory, Cambridge University Press, Cambridge, UK, 1993, pp. 101–146], on an issue related to nonadaptive Turing access to UP and adaptive smart Turing access to Promise-UP.
A Unified View of Td Algorithms Introducing Full-gradient Td and Equi-gradient Descent Td

This paper addresses the issue of policy evaluation in Markov Decision Processes, using linear function approximation. It provides a unified view of algorithms such as TD(λ), LSTD(λ), iLSTD, residual-gradient TD. It is asserted that they all consist in minimizing a gradient function and differ by the form of this function and their means of minimizing it. Two new schemes are introduced in that framework: Full-gradient TD which uses a generalization of the principle introduced in iLSTD, and EGD TD, which reduces the gradient by successive equi-gradient descents. These three algorithms form a new intermediate family with the interesting property of making much better use of the samples than TD while keeping a gradient descent scheme, which is useful for complexity issues and optimistic policy iteration. 1 The policy evaluation problem A Markov Decision Process (MDP) describes a dynamical system and an agent. The system is described by its state s ∈ S. When considering discrete time, the agent can apply at each time step an action u ∈ U which drives the system to a state s = u(s) at the next time step. u is generally non-deterministic. To each transition is associated a reward r ∈ R ⊂ R. A policy π is a function that associates to any state of the system an action taken by the agent. Given a discount factor γ, the value function v of a policy π associates to any state the expected discounted sum of rewards received when applying π from that state for an infinite time:
SAM: The Sensitivity of Attribution Methods to Hyperparameters

Attribution methods can provide powerful insights into the reasons for a classifier’s decision. We argue that a key desideratum of an explanation method is its robustness to input hyperparameters which are often randomly set or empirically tuned. High sensitivity to arbitrary hyperparameter choices does not only impede reproducibility but also questions the correctness of an explanation and impairs the trust of end-users. In this paper, we provide a thorough empirical study on the sensitivity of existing attribution methods. We found an alarming trend that many methods are highly sensitive to changes in their common hyperparameters e.g. even changing a random seed can yield a different explanation! Interestingly, such sensitivity is not reflected in the average explanation accuracy scores over the dataset as commonly reported in the literature. In addition, explanations generated for robust classifiers (i.e. which are trained to be invariant to pixel-wise perturbations) are surprisingly more robust than those generated for regular classifiers.
On Distributed Computing for Functions With Certain Structures

The problem of distributed function computation is studied, where functions to be computed is not necessarily symbol-wise. A new method to derive a converse bound for distributed computing is proposed; from the structure of functions to be computed, information that is inevitably conveyed to the decoder is identified, and the bound is derived in terms of the optimal rate needed to send that information. The class of informative functions is introduced, and, for the class of smooth sources, the optimal rate for computing those functions is characterized. Furthermore, for i.i. d. sources with joint distribution that may not be full support, functions that are composition of symbol-wise function and the type of a sequence are considered, and the optimal rate for computing those functions is characterized in terms of the hypergraph entropy. As a byproduct, our method also provides a conceptually simple proof of the known fact that computing a Boolean function may require as large rate as reproducing the entire source.
Estimating the size of the solution space of metabolic networks

In this work we propose a novel algorithmic strategy that allows for an efficient characterization of the whole set of stable fluxes compatible with the metabolic constraints. The algorithm, based on the well-known Bethe approximation, allows the computation in polynomial time of the volume of a non full-dimensional convex polytope in high dimensions. The result of our algorithm match closely the prediction of Monte Carlo based estimations of the flux distributions of the Red Blood Cell metabolic network but in incomparably shorter time. We also analyze the statistical properties of the average fluxes of the reactions in the E-Coli metabolic network and finally to test the effect of gene knock-outs on the size of the solution space of the E-Coli central metabolism.
A New Entropy Power Inequality for Integer-Valued Random Variables

The entropy power inequality (EPI) yields lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have been obtained for special families of distributions with the differential entropy replaced by the discrete entropy, but no universal inequality is known (beyond trivial ones). More recently, the sumset theory for the entropy function yields a sharp inequality H(X + X') - H(X) ≥ 1/2 - o(1) when X, X' are independent identically distributed (i.i.d.) with high entropy. This paper provides the inequality H(X + X') - H(X)≥ g(H(X)), where X, X' are arbitrary i.i. d. integer-valued random variables and where g is a universal strictly positive function on R+ satisfying g(0) = 0. Extensions to nonidentically distributed random variables and to conditional entropies are also obtained.
The statistics of critical points of Gaussian fields on large-dimensional spaces

The statistics of random fields have been studied in detail in the mathematics and physics literature [1]. Gaussian random fields are of particular importance, as they can be argued to occur spontaneously in systems with a large number of degrees of freedom by appealing to the central limit theorem. Recently string theorists have postulated that the effective theory arising from string theory is highly complex leading to a string landscape with a huge number of possible minima, each of which could describe a potential universe [2], thus a statistical study of this complex landscape may well be necessary. Gaussian fields arise generically in the study of classical complex systems such as spin glasses, optimization problems and protein folding [3]. In many of these systems, jamming or the onset of a glass transition occurs due to the presence of a large number of metastable states or local minima in the energy landscape. High-dimensional complex potentials also occur as the potential energy of interacting particle systems which exhibit a structural glass transition (no quenched disorder is present). Many numerical results exist on these potential energy landscapes, notably for Lennard-Jones and soft-sphere glass forming mixtures [4]. Scaling arguments relating the number of critical points (points where the gradient of the potential energy vanishes) of various types also exist [5] and the onset of the glass transition is often identified with the point where the critical points in the free energy landscape become dominated by minima [6]. In this Letter we compute the average number of critical points of a Gaussian potential, on a high dimensional space, at fixed value of the potential and at fixed number of negative eigenvalues at the critical point. We shall consider a Gaussian field φ defined over volume V of an N -dimensional Euclidean space. The field has zero mean and correlation function:
Gaussian orthogonal ensemble for quasiperiodic tilings without unfolding: 
r
-value statistics

We study the level-spacing statistics for non-interacting Hamiltonians defined on the two-dimensional quasiperiodic Ammann--Beenker (AB) tiling. When applying the numerical procedure of"unfolding", these spectral properties in each irreducible sector are known to be well-described by the universal Gaussian orthogonal random matrix ensemble. However, the validity and numerical stability of the unfolding procedure has occasionally been questioned due to the fractal self-similarity in the density of states for such quasiperiodic systems. Here, using the so-called $r$-value statistics for random matrices, $P(r)$, for which no unfolding is needed, we show that the Gaussian orthogonal ensemble again emerges as the most convincing level statistics for each irreducible sector. The results are extended to random-AB tilings where random flips of vertex connections lead to the irreducibility.