Miracle-dz/UniFAR-FTUs huggingface dataset:
On the tridiagonalization of systems of coupled linear differential equations

Under what conditions can one tridiagonalize a system of coupled linear differential equations with non-constant coefficients by appealing only to `well-behaved' distributions? In this work we show that if all the non-constant coefficients are smooth functions then tridiagonalisation is always possible using only piecewise smooth functions and isolated Dirac delta distributions. As a corollary, we formally establish the convergence and good behavior of the recently published Lanczos-like algorithm for solving arbitrary linear differential systems with smooth coefficients via tridiagonalization. This is a key piece in evaluating the hitherto elusively difficult ordered exponential function, both formally and numerically.
Pipeline Interventions

We introduce the pipeline intervention problem, defined by a layered directed acyclic graph and a set of stochastic matrices governing transitions between successive layers. The graph is a stylized model for how people from different populations are presented opportunities, eventually leading to some reward. In our model, individuals are born into an initial position (i.e., some node in the first layer of the graph) according to a fixed probability distribution and then stochastically progress through the graph according to the transition matrices until they reach a node in the final layer of the graph; each node in the final layer has a reward associated with it. The pipeline intervention problem asks how to best make costly changes to the transition matrices governing people’s stochastic transitions through the graph subject to a budget constraint. We consider two objectives: social welfare maximization and a fairness-motivated maximin objective that seeks to maximize the value to the population (starting node) with the least expected value. We consider two variants of the maximin objective that turn out to be distinct, depending on whether we demand a deterministic solution or allow randomization. For each objective, we give an efficient approximation algorithm (an additive fully polynomial-time approximation scheme) for constant-width networks. We also tightly characterize the “price of fairness” in our setting: the ratio between the highest achievable social welfare and the social welfare consistent with a maximin optimal solution. Finally, we show that, for polynomial-width networks, even approximating the maximin objective to any constant factor is NP hard even for networks with constant depth. This shows that the restriction on the width in our positive results is essential.
Electron pairing by Coulomb repulsion in narrow band structures

We study analytically and numerically dynamics and eigenstates of two electrons with Coulomb repulsion on a tight-binding lattice in one and two dimensions. The total energy and momentum of electrons are conserved and we show that for a certain momentum range the dynamics is exactly reduced to an evolution in an effective narrow energy band where the energy conservation forces the two electrons to propagate together through the whole system at moderate or even weak repulsion strength. We argue that such a mechanism of electron pair formation by the repulsive Coulomb interaction is rather generic and that it can be at the origin of unconventional superconductivity in twisted bilayer graphene.
Join theorem for real analytic singularities

Let f_1 and f_2 be real analytic germs of independent variables. In this paper, we assume that f_1, f_2 and f = f_1 + f_2 satisfy a_f -condition. Then we show that the tubular Milnor fiber of f is homotopy equivalent to the join of tubular Milnor fibers of f_1 and f_2.
t-viSNE: Interactive Assessment and Interpretation of t-SNE Projections

t-Distributed Stochastic Neighbor Embedding (t-SNE) for the visualization of multidimensional data has proven to be a popular approach, with successful applications in a wide range of domains. Despite their usefulness, t-SNE projections can be hard to interpret or even misleading, which hurts the trustworthiness of the results. Understanding the details of t-SNE itself and the reasons behind specific patterns in its output may be a daunting task, especially for non-experts in dimensionality reduction. In this article, we present t-viSNE, an interactive tool for the visual exploration of t-SNE projections that enables analysts to inspect different aspects of their accuracy and meaning, such as the effects of hyper-parameters, distance and neighborhood preservation, densities and costs of specific neighborhoods, and the correlations between dimensions and visual patterns. We propose a coherent, accessible, and well-integrated collection of different views for the visualization of t-SNE projections. The applicability and usability of t-viSNE are demonstrated through hypothetical usage scenarios with real data sets. Finally, we present the results of a user study where the tool's effectiveness was evaluated. By bringing to light information that would normally be lost after running t-SNE, we hope to support analysts in using t-SNE and making its results better understandable.
Convex Fairness Constrained Model Using Causal Effect Estimators

Recent years have seen much research on fairness in machine learning. Here, mean difference (MD) or demographic parity is one of the most popular measures of fairness. However, MD quantifies not only discrimination but also explanatory bias which is the difference of outcomes justified by explanatory features. In this paper, we devise novel models, called FairCEEs, which remove discrimination while keeping explanatory bias. The models are based on estimators of causal effect utilizing propensity score analysis. We prove that FairCEEs with the squared loss theoretically outperform a naive MD constraint model. We provide an efficient algorithm for solving FairCEEs in regression and binary classification tasks. In our experiment on synthetic and real-world data in these two tasks, FairCEEs outperformed an existing model that considers explanatory bias in specific cases.
Optimal Mechanism Design for Single-Minded Agents

We consider optimal (revenue maximizing) mechanism design in the interdimensional setting, where one dimension is the 'value' of the buyer, and the other is a 'type' that captures some auxiliary information. A prototypical example of this is the FedEx Problem, for which Fiat et al. [2016] characterize the optimal mechanism for a single agent. Another example of this is when the type encodes the buyer's budget [DW17]. The question we address is how far can such characterizations goIn particular, we consider the setting of single-minded agents. A seller has heterogenous items. A buyer has a valuation vfor a specific subset of items S, and obtains value vif and only if he gets all the items in S(and potentially some others too). We show the following results. Deterministic mechanisms (i.e. posted prices) are optimal for distributions that satisfy the "declining marginal revenue" (DMR) property. In this case we give an explicit construction of the optimal mechanism. Without the DMR assumption, the result depends on the structure of the minimal directed acyclic graph (DAG) representing the partial order among types. When the DAG has out-degree at most 1, we characterize the optimal mechanism àla FedEx; this can be thought of as a generalization of the FedEx characterization since FedEx corresponds to a DAG that is a line. Surprisingly, without the DMR assumption andwhen the DAG has at least one node with an out-degree of at least 2, then we show that there is no hope of such a characterization. The minimal such example happens on a DAG with 3 types. We show that in this case the menu complexity is unboundedin that for any M, there exist distributions over (v,S) pairs such that the menu complexity of the optimal mechanism is at least M. For the case of 3 types, we also show that for all distributions there exists an optimal mechanism of finitemenu complexity. This is in contrast to the case where you have 2 heterogenous items with additive utilities for which the menu complexity could be uncountably infinite [DDT15, MV07]. In addition, we prove that optimal mechanisms for Multi-Unit Pricing (without a DMR assumption) can have unbounded menu complexity as well, and we further propose an extension where the menu complexity of optimal mechanisms can be countably infinite, but not uncountably infinite. Taken together, these results establish that optimal mechanisms in interdimensional settings are both surprisingly richer than single-dimensional settings, yet also vastly more structured than multi-dimensional settings.
Studying the parton content of the proton with deep learning models

Parton Distribution Functions (PDFs) model the parton content of the proton. Among the many collaborations which focus on PDF determination, NNPDF pioneered the use of Neural Networks to model the probability of finding partons (quarks and gluons) inside the proton with a given energy and momentum. In this proceedings we make use of state of the art techniques to modernize the NNPDF methodology and study different models and optimizers in order to improve the quality of the PDF: improving both the quality and efficiency of the fits. We also present the evolutionary_keras library, a Keras implementation of the Evolutionary Algorithms used by NNPDF.
Graph Deconvolutional Generation

Graph generation is an extremely important task, as graphs are found throughout different areas of science and engineering. In this work, we focus on the modern equivalent of the Erdos-Renyi random graph model: the graph variational autoencoder (GVAE). This model assumes edges and nodes are independent in order to generate entire graphs at a time using a multi-layer perceptron decoder. As a result of these assumptions, GVAE has difficulty matching the training distribution and relies on an expensive graph matching procedure. We improve this class of models by building a message passing neural network into GVAE's encoder and decoder. We demonstrate our model on the specific task of generating small organic molecules
A Stein Goodness-of-fit Test for Directional Distributions

In many fields, data appears in the form of direction (unit vector) and usual statistical procedures are not applicable to such directional data. In this study, we propose non-parametric goodness-of-fit testing procedures for general directional distributions based on kernel Stein discrepancy. Our method is based on Stein's operator on spheres, which is derived by using Stokes' theorem. Notably, the proposed method is applicable to distributions with an intractable normalization constant, which commonly appear in directional statistics. Experimental results demonstrate that the proposed methods control type-I error well and have larger power than existing tests, including the test based on the maximum mean discrepancy.
Last iterate convergence in no-regret learning: constrained min-max optimization for convex-concave landscapes

In a recent series of papers it has been established that variants of Gradient Descent/Ascent and Mirror Descent exhibit last iterate convergence in convex-concave zero-sum games. Specifically, \cite{DISZ17, LiangS18} show last iterate convergence of the so called "Optimistic Gradient Descent/Ascent" for the case of \textit{unconstrained} min-max optimization. Moreover, in \cite{Metal} the authors show that Mirror Descent with an extra gradient step displays last iterate convergence for convex-concave problems (both constrained and unconstrained), though their algorithm does not follow the online learning framework; it uses extra information rather than \textit{only} the history to compute the next iteration. In this work, we show that "Optimistic Multiplicative-Weights Update (OMWU)" which follows the no-regret online learning framework, exhibits last iterate convergence locally for convex-concave games, generalizing the results of \cite{DP19} where last iterate convergence of OMWU was shown only for the \textit{bilinear case}. We complement our results with experiments that indicate fast convergence of the method.
LEGION: Best-First Concolic Testing

Concolic execution and fuzzing are two complementary coverage-based testing techniques. How to achieve the best of both remains an open challenge. To address this research problem, we propose and evaluate Legion. Legion re-engineers the Monte Carlo tree search (MCTS) framework from the AI literature to treat automated test generation as a problem of sequential decision-making under uncertainty. Its best-first search strategy provides a principled way to learn the most promising program states to investigate at each search iteration, based on observed rewards from previous iterations. Legion incorporates a form of directed fuzzing that we call approximate path-preserving fuzzing (APPFUZZING) to investigate program states selected by MCTS. APPFUZZING serves as the Monte Carlo simulation technique and is implemented by extending prior work on constrained sampling. We evaluate Legion against competitors on 2531 benchmarks from the coverage category of Test-Comp 2020, as well as measuring its sensitivity to hyperparameters, demonstrating its effectiveness on a wide variety of input programs.
New Constructions of Cross Z-Complementary Pairs

Spatial modulation (SM) is a new paradigm of multiple-input multiple-output (MIMO) systems, in which only one antenna at the transmitter is activated during each symbol period. Recently, it is observed that SM training sequences derived from corss Z-complementary pairs (CZCPs) lead to optimal channel estimation performance over frequency-selective channels. CZCPs are special form of sequence pairs which have zero aperiodic autocorrelation zones and cross-correlation zone at certain time-shifts. Recent paper by Liu \textit{et al.} discussed only perfect CZCPs. In this paper, we focus on non-perfect CZCPs. We introduce the term cross Z-complementary ratio and re-categorise the CZCPs, both perfect and non-perfect, based on that. We propose a systematic construction of CZCPs based on generalised Boolean functions (GBFs). We further extend the lengths of the CZCPs by using the insertion method. The proposed CZCPs are all of new lengths of the form $2^\alpha10^\beta26^\gamma+2~(\alpha\geq1)$, $10^\beta+2$, $26^\gamma+2$ and $10^\beta 26^\gamma+2$. Finally we propose a construction of optimal binary CZCPs having parameters $(12,5)$ and $(24,11)$ from binary Barker sequences. These CZCPs are also extended to $(12N,5N)$- CZCPs and $(24N,11N)$- CZCPs, where $N$ is the length of a binary Golay complementary pair (GCP). During the proof, we also found a new structural property of binary CZCPs and concluded all binary GCPs are CZCPs too. Finally, we give some numerical simulations to confirm that depending on the number of multi-paths, the proposed CZCPs can be used to design SM training matrix which attains the minimum mean square error.
Using Interlinear Glosses as Pivot in Low-Resource Multilingual Machine Translation.

We demonstrate a new approach to Neural Machine Translation (NMT) for low-resource languages using a ubiquitous linguistic resource, Interlinear Glossed Text (IGT). IGT represents a non-English sentence as a sequence of English lemmas and morpheme labels. As such, it can serve as a pivot or interlingua for NMT. Our contribution is four-fold. Firstly, we pool IGT for 1,497 languages in ODIN (54,545 glosses) and 70,918 glosses in Arapaho and train a gloss-to-target NMT system from IGT to English, with a BLEU score of 25.94. We introduce a multilingual NMT model that tags all glossed text with gloss-source language tags and train a universal system with shared attention across 1,497 languages. Secondly, we use the IGT gloss-to-target translation as a key step in an English-Turkish MT system trained on only 865 lines from ODIN. Thirdly, we we present five metrics for evaluating extremely low-resource translation when BLEU is no longer sufficient and evaluate the Turkish low-resource system using BLEU and also using accuracy of matching nouns, verbs, agreement, tense, and spurious repetition, showing large improvements.
Scalable Quantitative Verification for Deep Neural Networks

Despite the functional success of deep Neural Networks, their trustworthiness remains a crucial open challenge. To address this challenge, both testing and verification techniques have been proposed. But these existing techniques provide either scalability to large networks or formal guarantees, not both. In this paper, we propose a scalable quantitative verification framework for deep Neural Networks, i.e., a test-driven approach that comes with formal guarantees that a desired probabilistic property is satisfied. Our technique performs enough tests until soundness of a formal probabilistic property can be proven. It can be used to certify properties of both deterministic and randomized DNNs. We implement our approach in a tool called PROVERO and apply it in the context of certifying adversarial robustness of DNNs. In this context, we first show a new attack-agnostic measure of robustness which offers an alternative to purely attack-based methodology of evaluating robustness being reported today. Second, PROVERO provides certificates of robustness for large DNNs, where existing state-of-the-art verification tools fail to produce conclusive results. Our work paves the way forward for verifying properties of distributions captured by real-world deep Neural Networks, with provable guarantees, even where testers only have black-box access to the neural network.
Kruskal-based approximation algorithm for the multi-level Steiner tree problem

We study the multi-level Steiner tree problem: a generalization of the Steiner tree problem in graphs where terminals $T$ require varying priority, level, or quality of service. In this problem, we seek to find a minimum cost tree containing edges of varying rates such that any two terminals $u$, $v$ with priorities $P(u)$, $P(v)$ are connected using edges of rate $\min\{P(u),P(v)\}$ or better. The case where edge costs are proportional to their rate is approximable to within a constant factor of the optimal solution. For the more general case of non-proportional costs, this problem is hard to approximate with ratio $c \log \log n$, where $n$ is the number of vertices in the graph. A simple greedy algorithm by Charikar et al., however, provides a $\min\{2(\ln |T|+1), \ell \rho\}$-approximation in this setting, where $\rho$ is an approximation ratio for a heuristic solver for the Steiner tree problem and $\ell$ is the number of priorities or levels (Byrka et al. give a Steiner tree algorithm with $\rho\approx 1.39$, for example). In this paper, we describe a natural generalization to the multi-level case of the classical (single-level) Steiner tree approximation algorithm based on Kruskal's minimum spanning tree algorithm. We prove that this algorithm achieves an approximation ratio at least as good as Charikar et al., and experimentally performs better with respect to the optimum solution. We develop an integer linear programming formulation to compute an exact solution for the multi-level Steiner tree problem with non-proportional edge costs and use it to evaluate the performance of our algorithm on both random graphs and multi-level instances derived from SteinLib.
On Model Comparison: Application of Savage-Dickey Density Ratio to Bayes Factor

DOI: 10.9734/AJPAS/2020/v6i330162 Editor(s): (1) Dr. Jiteng Jia, School of Mathematics and Statistics, Xidian University, China. (2) Dr. S. M. Aqil Burney, Department of Computer Science, University of Karachi, Pakistan. (3) Dr. Manuel Alberto M. Ferreira, Retired Professor, Department of Mathematics, ISTA-School of Technology and Architecture, Lisbon University, Portugal. Reviewers: (1) Francisco Bulnes, Tecnológico de Estudios Superiores de Chalco, Mexico. (2) Sie Long Kek, Universiti Tun Hussein Onn Malaysia, Malaysia. (3) Josua Mwanyekange, University of Namibia, Namibia. Complete Peer review History: http://www.sdiarticle4. com/review-history/54061
On Optimized Manufacture of Bipolar Hetero transistors in a High-Voltage Element or for Increasing of their Integration Rate. Accounting Mismatch-Induced Stress

In the present time several actual problems of the solid state electronics (such as increasing of performance, reliability and density of elements of integrated circuits: diodes, field-effect and bipolar transistors) are intensively solving [1-6]. To increase the performance of these devices it is attracted an interest determination of materials with higher values of charge carriers mobility [7-10]. One way to decrease dimensions of elements of integrated circuits is manufacturing them in thin film heterostructures [3-5,11]. In this case it is possible to use inhomogeneity of heterostructure and necessary optimization of doping of electronic materials [12,13] and development of epitaxial technology to improve these materials (including analysis of mismatch induced stress) [14-16]. An alternative approaches to increase dimensions of integrated circuits are using of laser and microwave types of annealing [17-19].
Validation of Novel Prognostic Biomarkers for Early-Stage Clear-Cell, Endometrioid and Mucinous Ovarian Carcinomas Using Immunohistochemistry

Early-stage (I and II) ovarian carcinoma patients generally have good prognosis. Yet, some patients die earlier than expected. Thus, it is important to stratify early-stage patients into risk groups to identify those in need of more aggressive treatment regimens. The prognostic value of 29 histotype-specific biomarkers identified using RNA sequencing was evaluated for early-stage clear-cell (CCC), endometrioid (EC) and mucinous (MC) ovarian carcinomas (n = 112) using immunohistochemistry on tissue microarrays. Biomarkers with prognostic significance were further evaluated in an external ovarian carcinoma data set using the web-based Kaplan-Meier plotter tool. Here, we provide evidence of aberrant protein expression patterns and prognostic significance of 17 novel histotype-specific prognostic biomarkers [10 for CCC (ARPC2, CCT5, GNB1, KCTD10, NUP155, RPL13A, RPL37, SETD3, SMYD2, TRIO), three for EC (CECR1, KIF26B, PIK3CA), and four for MC (CHEK1, FOXM1, KIF23, PARPBP)], suggesting biological heterogeneity within the histotypes. Combined predictive models comprising the protein expression status of the validated CCC, EC and MC biomarkers together with established clinical markers (age, stage, CA125, ploidy) improved the predictive power in comparison with models containing established clinical markers alone, further strengthening the importance of the biomarkers in ovarian carcinoma. Further, even improved predictive powers were demonstrated when combining these models with our previously identified prognostic biomarkers PITHD1 (CCC) and GPR158 (MC). Moreover, the proteins demonstrated improved risk prediction of CCC-, EC-, and MC-associated ovarian carcinoma survival. The novel histotype-specific prognostic biomarkers may not only improve prognostication and patient stratification of early-stage ovarian carcinomas, but may also guide future clinical therapy decisions.