You are probably already familiar with the concept of call to action, but if somehow you are new to web design, call to action refers to elements in a page that request an action from its visitors. If you are indeed new to web design, there are high chances that you will neglect this important […]

Sony introduced the a6400 model of digital cameras in early 2019. The a6400 rapidly became a best-seller among both professional and amateur photographers. The camera is smaller than standard digital single reflex cameras but still uses Sony’s extensive line of lenses. Sony has achieved all this using an APS-C sensor system in a mirrorless body. What is Sony a6400 crop Continue Reading

The post What is the Sony a6400 Crop Factor? appeared first on Photodoto.

Pictures and video from an action camera can be awesome. But how do you get the best shots? It’s all about the mounting of the camera and we’re going to tell you how to do it. How and where do you mount an action camera? The most popular place to mount an action camera is on a helmet using a Continue Reading

The post How (And Where) To Mount an Action Camera (On Anything!) appeared first on Photodoto.

All websites are somewhat interactive…we click on links or scroll a page, but truly interactive websites take us on a user-driven adventure or draws us in through motion and sound while giving us the power of choice. Interaction can be as simple as a series of clicks that navigate us through a story or landscape, […]

The post 30 Truly Interactive Websites Built With CSS & JavaScript appeared first on Web Designer Wall.

Have you got yourself a Sony Xperia Z1 Compact but not sure how to do something on it? Don’t worry, we’ve come up with a comprehensive guide for all the things your handset is capable of. Navigate the various sections using the links below. If you can’t find what you’re looking for just leave a … Continue reading Sony Xperia Z1 Compact Complete Guide →

By DiveIn.com This marvelous infographic, created by the scuba magazine DiveIn.com, is a deep-dive into the wonder, mystery and vital importance of our earth’s oceans. 50 fascinating facts about the ocean – Graphic by the team at DIVE.in

Photoshop is an amazing program and with our list of the 20 best free & premium Photoshop Actions, you can start creating incredible work immediately.

Zero UI is about removing everything that comes between users and their devices, about making the interaction easier, seamless, more direct. Does it sound to you like a concept from a science-fiction...

Creative interactions call for creative measures - numerous extensions reduce, minimize or dilute the frustration of the customers and resolve issues quickly without the customer support team need....

What has sometimes been described as mobile middleware has taken a new tack. Now, the idea of Backend as a Service (BaaS) has begun to take off in the mobile application development space. Proponents of BaaS say it helps developers easily build mobile apps, or any other applications connected to a cloud backend. Some of Read the rest...

Sometimes interesting things happen on Twitter. Last week Scott Jehl proposed ASPIRE as an acronym for the practices we should follow as web designers and developers. From the resulting blog post: Great websites should aspire to be: Accessible to folks with varying cognitive and physical abilities and disabilities Secure and reliable for storing, manipulating, and transferring information Performant on average devices […]

The post ASPIRE: An Acronym for Better Web Practice appeared first on MOR10.

Google’s ranking algorithm continues to get more and more complex, and the Ranking Factors 2020: Facts and Myths infographic from Link-Assistant tries to break through some of the misinformation that’s out there.

It seems a little while ago that Google hinted at having 200+ ranking factors. Though in fact, it happened in the year of 2009, and we are heading to 2020 now.

Google has drastically evolved over the past ten years. Today, neural matching — an AI-based method — processes about 30% of all searches, and Google can recognize concepts behind keywords. They have introduced RankBrain, mobile-first indexing, and HTTPS. As we need to adapt to changes and find ways to get atop of SERPs, the topic of ranking factors remains as fresh as ever.

So let's have a look at what ranking factors to consider in 2020, and what ranking myths to leave behind.

I have mixed feelings about this infographics design:

Good:

• It’s a concise summary of very complex information that’s laid out in the more detailed, full article.

• The infographic is a handy reference sheet and great for use in social media as promotion for the article.

• Clean arrangement that’s easy to read from top-to-bottom

Bad:

• Almost all text.

• Not that there’s much data that could have been visualized with charts, but some visual design elements would have made the infographic easier to read and more enticing to readers.

• Text URL to the article! When the infographic gets shared, how are readers supposed to find the article when it’s not linked??? Put it in the footer on the infographic!

American Geophysical Union (AGU) Press Release A new study finds human-caused global warming is significantly increasing the rate at which hot temperature records are being broken around the world. Global annual temperature records show there were 17 record hot years … Continue reading →

At 3.7 Designs we have an array of strategies we use to solve business problems. For example, when it comes to redesigning a website we might recommend recommend a completely custom design that starts with a design discovery engagement. Typically this process can take three to six months with ample time upfront to research the […]

The post Astra Pro with Gutenberg Review – Practical Application appeared first on Psychology of Web Design | 3.7 Blog.

In the past I’ve written about the importance of having a separate call to action for each stage of the buyers journey. In this article I’m going to expand on that concept and outline how to identify a strategy for each of these calls to action. First I’ll summarize why you need to have a […]

The post Call to Action Marketing Strategy appeared first on Psychology of Web Design | 3.7 Blog.

When you want to succeed in the organic search engine results today, you have to focus on your website and learn what you should do to optimize it. There are many factors that can help you with that, form the technical, off-page, and on-page. All these factors and parts of a website require updating and […]

Original post: 10 On-Page SEO Factors You Should Consider [2019]

The post 10 On-Page SEO Factors You Should Consider [2019] appeared first on Daily Blog Tips.

Technology has changed the way we live. A few decades back, we couldn’t even imagine making a video call to a person sitting in another corner of the world. With every technological advancement, mankind is treading towards greater development. From smart gadgets to machines, every invention has leveraged the human lifestyle.  There’s no doubt in […]

Original post: Best Alexa Skills That Will Actually Surprise You

The post Best Alexa Skills That Will Actually Surprise You appeared first on Daily Blog Tips.

Including version 4.6 it was quite difficult to add custom bulk actions to the WordPress admin pages. In version 4.7 […]

By Mason Adams Yes! Magazine A program in eastern Kentucky is retraining miners in industries that help mitigate the environmental impacts of mining on communities. Like many men raised in eastern Kentucky, Frank Morris spent a chunk of his working … Continue reading →

One of the most commonly requested software features is dark mode (or night mode, as others call it). We see dark mode in the apps that we use every day. From mobile to web apps, dark mode has become vital for companies that want to take care of their users’ eyes. Dark mode is a supplemental feature that displays mostly dark surfaces in the UI. Most major companies (such as YouTube, Twitter, and Netflix) have adopted dark mode in their mobile and web apps.

The Ionic Framework is an open-source UI toolkit for building fast, high-quality applications using web technologies with integrations for popular frameworks like Angular and React. Ionic enables cross-platform development using either Cordova or Capacitor, with the latter featuring support for desktop application development using Electron. In this article, we will explore Ionic with the React integration by building an app that displays comics using the Marvel Comics API and allows users to create a collection of their favorites.

In these strange times when everything is connected, it’s too easy to feel lonely and detached. Yes, everybody is just one message away, but there is always something in the way — deadlines to meet, Slack messages to reply, or urgent PRs to review. Connections need time and space to grow, just like learning, and conferences are a great way to find that time and that space. In fact, with SmashingConfs, we’ve always been trying to create such friendly and inclusive spaces.

We study two notions of topological entropy of correspondences introduced by Friedland and Dinh-Sibony. Upper bounds are known for both. We identify a class of holomorphic correspondences whose entropy in the sense of Dinh-Sibony equals the known upper bound. This provides an exact computation of the entropy for rational semigroups. We also explore a connection between these two notions of entropy.

We show weak-strong uniqueness and stability results for the motion of a two or three dimensional fluid governed by the Navier-Stokes equation interacting with a flexible, elastic plate of Koiter type. The plate is situated at the top of the fluid and as such determines the variable part of a time changing domain (that is hence a part of the solution) containing the fluid. The uniqueness result is a consequence of a stability estimate where the difference of two solutions is estimated by the distance of the initial values and outer forces. For that we introduce a methodology that overcomes the problem that the two (variable in time) domains of the fluid velocities and pressures are not the same. The estimate holds under the assumption that one of the two weak solutions possesses some additional higher regularity. The additional regularity is exclusively requested for the velocity of one of the solutions resembling the celebrated Ladyzhenskaya-Prodi-Serrin conditions in the framework of variable domains.

In this paper, we develop the theory for classifying all the geometric fibrations of compact, connected, flat $n$-orbifolds, over a 1-orbifold, up to affine equivalence. We apply our classification theory to classify all the geometric fibrations of compact, connected, flat $2$-orbifolds, over a 1-orbifold, up to affine equivalence. This paper is an essential part of our project to give a geometric proof of the classification of all closed flat 4-manifolds.

We examine Chern-Simons theory as a deformation of a 3-dimensional BF theory that is partially holomorphic and partially topological. In particular, we introduce a novel gauge that leads naturally to a one-loop exact quantization of this BF theory and Chern-Simons theory. This approach illuminates several important features of Chern-Simons theory, notably the bulk-boundary correspondence of Chern-Simons theory with chiral WZW theory. In addition to rigorously constructing the theory, we also explain how it applies to a large class of closely related 3-dimensional theories and some of the consequences for factorization algebras of observables.

We prove the following result: Let $(M,g_0)$ be a compact manifold of dimension $ngeq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or a compact quotient manifold of $mathbb{S}^{n-1} imes mathbb{R}$ by diffeomorphisms, or a connected sum of a finite number of such manifolds. This extends a recent work of Brendle, and implies a conjecture of Schoen in dimensions $ngeq 12$. The proof uses Ricci flow with surgery on compact orbifolds with isolated singularities.

The central aim of this paper is to study (regional) fractional Poincar'e type inequalities on unbounded domains satisfying the finite ball condition. Both existence and non existence type results are established depending on various conditions on domains and on the range of $s in (0,1)$. The best constant in both regional fractional and fractional Poincar'e inequality is characterized for strip like domains $(omega imes mathbb{R}^{n-1})$, and the results obtained in this direction are analogous to those of the local case. This settles one of the natural questions raised by K. Yeressian in [ extit{Asymptotic behavior of elliptic nonlocal equations set in cylinders, Asymptot. Anal. 89, (2014), no 1-2}].

In this paper, we are concerned with the numerical solution of one type integro-differential equation by a probability method based on the fundamental martingale of mixed Gaussian processes. As an application, we will try to simulate the estimation of ruin probability with an unknown parameter driven not by the classical L'evy process but by the mixed fractional Brownian motion.

In this paper we consider Wronskian polynomials labeled by partitions that can be factorized via the combinatorial concepts of $p$-cores and $p$-quotients. We obtain the asymptotic behavior for these polynomials when the $p$-quotient is fixed while the size of the $p$-core grows to infinity. For this purpose, we associate the $p$-core with its characteristic vector and let all entries of this vector simultaneously tend to infinity. This result generalizes the Wronskian Hermite setting which is recovered when $p=2$.

A reaction-diffusion model was developed describing the spread of the COVID-19 virus considering the mean daily movement of susceptible, exposed and asymptomatic individuals. The model was calibrated using data on the confirmed infection and death from France as well as their initial spatial distribution. First, the system of partial differential equations is studied, then the basic reproduction number, R0 is derived. Second, numerical simulations, based on a combination of level-set and finite differences, shown the spatial spread of COVID-19 from March 16 to June 16. Finally, scenarios of unlockdown are compared according to variation of distancing, or partially spatial lockdown.

We define local indices for projective umbilics and godrons (also called cusps of Gauss) on generic smooth surfaces in projective 3-space. By means of these indices, we provide formulas that relate the algebraic numbers of those characteristic points on a surface (and on domains of the surface) with the Euler characteristic of that surface (resp. of those domains). These relations determine the possible coexistences of projective umbilics and godrons on the surface. Our study is based on a "fundamental cubic form" for which we provide a closed simple expression.

This paper develops a method for obtaining guaranteed outer approximations for global attractors of continuous and discrete time nonlinear dynamical systems. The method is based on a hierarchy of semidefinite programming problems of increasing size with guaranteed convergence to the global attractor. The approach taken follows an established line of reasoning, where we first characterize the global attractor via an infinite dimensional linear programming problem (LP) in the space of Borel measures. The dual to this LP is in the space of continuous functions and its feasible solutions provide guaranteed outer approximations to the global attractor. For systems with polynomial dynamics, a hierarchy of finite-dimensional sum-of-squares tightenings of the dual LP provides a sequence of outer approximations to the global attractor with guaranteed convergence in the sense of volume discrepancy tending to zero. The method is very simple to use and based purely on convex optimization. Numerical examples with the code available online demonstrate the method.

The main aim of this paper is to detect dynamical properties of the Gy"orgyi-Field model of the Belousov-Zhabotinsky chemical reaction. The corresponding three-variable model given as a set of nonlinear ordinary differential equations depends on one parameter, the flow rate. As certain values of this parameter can give rise to chaos, the analysis was performed in order to identify different dynamics regimes. Dynamical properties were qualified and quantified using classical and also new techniques. Namely, phase portraits, bifurcation diagrams, the Fourier spectra analysis, the 0-1 test for chaos, and approximate entropy. The correlation between approximate entropy and the 0-1 test for chaos was observed and described in detail. Moreover, the three-stage system of nested subintervals of flow rates, for which in every level the 0-1 test for chaos and approximate entropy was computed, is showing the same pattern. The study leads to an open problem whether the set of flow rate parameters has Cantor like structure.

Predicting the spatial configuration of gas molecules in nanopores of shale formations is crucial for fluid flow forecasting and hydrocarbon reserves estimation. The key challenge in these tight formations is that the majority of the pore sizes are less than 50 nm. At this scale, the fluid properties are affected by nanoconfinement effects due to the increased fluid-solid interactions. For instance, gas adsorption to the pore walls could account for up to 85% of the total hydrocarbon volume in a tight reservoir. Although there are analytical solutions that describe this phenomenon for simple geometries, they are not suitable for describing realistic pores, where surface roughness and geometric anisotropy play important roles. To describe these, molecular dynamics (MD) simulations are used since they consider fluid-solid and fluid-fluid interactions at the molecular level. However, MD simulations are computationally expensive, and are not able to simulate scales larger than a few connected nanopores. We present a method for building and training physics-based deep learning surrogate models to carry out fast and accurate predictions of molecular configurations of gas inside nanopores. Since training deep learning models requires extensive databases that are computationally expensive to create, we employ active learning (AL). AL reduces the overhead of creating comprehensive sets of high-fidelity data by determining where the model uncertainty is greatest, and running simulations on the fly to minimize it. The proposed workflow enables nanoconfinement effects to be rigorously considered at the mesoscale where complex connected sets of nanopores control key applications such as hydrocarbon recovery and CO2 sequestration.

The connection between visual input and tactile sensing is critical for object manipulation tasks such as grasping and pushing. In this work, we introduce the challenging task of estimating a set of tactile physical properties from visual information. We aim to build a model that learns the complex mapping between visual information and tactile physical properties. We construct a first of its kind image-tactile dataset with over 400 multiview image sequences and the corresponding tactile properties. A total of fifteen tactile physical properties across categories including friction, compliance, adhesion, texture, and thermal conductance are measured and then estimated by our models. We develop a cross-modal framework comprised of an adversarial objective and a novel visuo-tactile joint classification loss. Additionally, we develop a neural architecture search framework capable of selecting optimal combinations of viewing angles for estimating a given physical property.

Event-related desynchronization and synchronization (ERD/S) and movement-related cortical potential (MRCP) play an important role in brain-computer interfaces (BCI) for lower limb rehabilitation, particularly in standing and sitting. However, little is known about the differences in the cortical activation between standing and sitting, especially how the brain's intention modulates the pre-movement sensorimotor rhythm as they do for switching movements. In this study, we aim to investigate the decoding of continuous EEG rhythms during action observation (AO), motor imagery (MI), and motor execution (ME) for standing and sitting. We developed a behavioral task in which participants were instructed to perform both AO and MI/ME in regard to the actions of sit-to-stand and stand-to-sit. Our results demonstrated that the ERD was prominent during AO, whereas ERS was typical during MI at the alpha band across the sensorimotor area. A combination of the filter bank common spatial pattern (FBCSP) and support vector machine (SVM) for classification was used for both offline and pseudo-online analyses. The offline analysis indicated the classification of AO and MI providing the highest mean accuracy at 82.73$pm$2.38\% in stand-to-sit transition. By applying the pseudo-online analysis, we demonstrated the higher performance of decoding neural intentions from the MI paradigm in comparison to the ME paradigm. These observations led us to the promising aspect of using our developed tasks based on the integration of both AO and MI to build future exoskeleton-based rehabilitation systems.

The global health threat from COVID-19 has been controlled in a number of instances by large-scale testing and contact tracing efforts. We created this document to suggest three functionalities on how we might best harness computing technologies to supporting the goals of public health organizations in minimizing morbidity and mortality associated with the spread of COVID-19, while protecting the civil liberties of individuals. In particular, this work advocates for a third-party free approach to assisted mobile contact tracing, because such an approach mitigates the security and privacy risks of requiring a trusted third party. We also explicitly consider the inferential risks involved in any contract tracing system, where any alert to a user could itself give rise to de-anonymizing information.

More generally, we hope to participate in bringing together colleagues in industry, academia, and civil society to discuss and converge on ideas around a critical issue rising with attempts to mitigate the COVID-19 pandemic.

We live and cooperate in networks. However, links in networks only allow for pairwise interactions, thus making the framework suitable for dyadic games, but not for games that are played in groups of more than two players. To remedy this, we introduce higher-order interactions, where a link can connect more than two individuals, and study their evolutionary dynamics. We first consider a public goods game on a uniform hypergraph, showing that it corresponds to the replicator dynamics in the well-mixed limit, and providing an exact theoretical foundation to study cooperation in networked groups. We also extend the analysis to heterogeneous hypergraphs that describe interactions of groups of different sizes and characterize the evolution of cooperation in such cases. Finally, we apply our new formulation to study the nature of group dynamics in real systems, showing how to extract the actual dependence of the synergy factor on the size of a group from real-world collaboration data in science and technology. Our work is a first step towards the implementation of new actions to boost cooperation in social groups.

Introduction of spectrum-sharing in 5G and subsequent generation networks demand base-station(s) with the capability to characterize the wideband spectrum spanned over licensed, shared and unlicensed non-contiguous frequency bands. Spectrum characterization involves the identification of vacant bands along with center frequency and parameters (energy, modulation, etc.) of occupied bands. Such characterization at Nyquist sampling is area and power-hungry due to the need for high-speed digitization. Though sub-Nyquist sampling (SNS) offers an excellent alternative when the spectrum is sparse, it suffers from poor performance at low signal to noise ratio (SNR) and demands careful design and integration of digital reconstruction, tunable channelizer and characterization algorithms. In this paper, we propose a novel deep-learning framework via a single unified pipeline to accomplish two tasks: 1)~Reconstruct the signal directly from sub-Nyquist samples, and 2)~Wideband spectrum characterization. The proposed approach eliminates the need for complex signal conditioning between reconstruction and characterization and does not need complex tunable channelizers. We extensively compare the performance of our framework for a wide range of modulation schemes, SNR and channel conditions. We show that the proposed framework outperforms existing SNS based approaches and characterization performance approaches to Nyquist sampling-based framework with an increase in SNR. Easy to design and integrate along with a single unified deep learning framework make the proposed architecture a good candidate for reconfigurable platforms.

Interaction languages such as MSC are often associated with formal semantics by means of translations into distinct behavioral formalisms such as automatas or Petri nets. In contrast to translational approaches we propose an operational approach. Its principle is to identify which elementary communication actions can be immediately executed, and then to compute, for every such action, a new interaction representing the possible continuations to its execution. We also define an algorithm for checking the validity of execution traces (i.e. whether or not they belong to an interaction's semantics). Algorithms for semantic computation and trace validity are analyzed by means of experiments.

Due to the exponential growth of biomedical literature, event and relation extraction are important tasks in biomedical text mining. Most work only focus on relation extraction, and detect a single entity pair mention on a short span of text, which is not ideal due to long sentences that appear in biomedical contexts. We propose an approach to both relation and event extraction, for simultaneously predicting relationships between all mention pairs in a text. We also perform an empirical study to discuss different network setups for this purpose. The best performing model includes a set of multi-head attentions and convolutions, an adaptation of the transformer architecture, which offers self-attention the ability to strengthen dependencies among related elements, and models the interaction between features extracted by multiple attention heads. Experiment results demonstrate that our approach outperforms the state of the art on a set of benchmark biomedical corpora including BioNLP 2009, 2011, 2013 and BioCreative 2017 shared tasks.

We investigate sparse matrix bipartitioning -- a problem where we minimize the communication volume in parallel sparse matrix-vector multiplication. We prove, by reduction from graph bisection, that this problem is $mathcal{NP}$-complete in the case where each side of the bipartitioning must contain a linear fraction of the nonzeros.

We present an improved exact branch-and-bound algorithm which finds the minimum communication volume for a given matrix and maximum allowed imbalance. The algorithm is based on a maximum-flow bound and a packing bound, which extend previous matching and packing bounds.

We implemented the algorithm in a new program called MP (Matrix Partitioner), which solved 839 matrices from the SuiteSparse collection to optimality, each within 24 hours of CPU-time. Furthermore, MP solved the difficult problem of the matrix cage6 in about 3 days. The new program is on average more than ten times faster than the previous program MondriaanOpt.

Benchmark results using the set of 839 optimally solved matrices show that combining the medium-grain/iterative refinement methods of the Mondriaan package with the hypergraph bipartitioner of the PaToH package produces sparse matrix bipartitionings on average within 10% of the optimal solution.

This work deals with the efficient numerical solution of the time-fractional heat equation discretized on non-uniform temporal meshes. Non-uniform grids are essential to capture the singularities of "typical" solutions of time-fractional problems. We propose an efficient space-time multigrid method based on the waveform relaxation technique, which accounts for the nonlocal character of the fractional differential operator. To maintain an optimal complexity, which can be obtained for the case of uniform grids, we approximate the coefficient matrix corresponding to the temporal discretization by its hierarchical matrix (${cal H}$-matrix) representation. In particular, the proposed method has a computational cost of ${cal O}(k N M log(M))$, where $M$ is the number of time steps, $N$ is the number of spatial grid points, and $k$ is a parameter which controls the accuracy of the ${cal H}$-matrix approximation. The efficiency and the good convergence of the algorithm, which can be theoretically justified by a semi-algebraic mode analysis, are demonstrated through numerical experiments in both one- and two-dimensional spaces.

Assistive shared-control robots have the potential to transform the lives of millions of people afflicted with severe motor impairments. The usefulness of shared-control robots typically relies on the underlying autonomy's ability to infer the user's needs and intentions, and the ability to do so unambiguously is often a limiting factor for providing appropriate assistance confidently and accurately. The contributions of this paper are four-fold. First, we introduce the idea of intent disambiguation via control mode selection, and present a mathematical formalism for the same. Second, we develop a control mode selection algorithm which selects the control mode in which the user-initiated motion helps the autonomy to maximally disambiguate user intent. Third, we present a pilot study with eight subjects to evaluate the efficacy of the disambiguation algorithm. Our results suggest that the disambiguation system (a) helps to significantly reduce task effort, as measured by number of button presses, and (b) is of greater utility for more limited control interfaces and more complex tasks. We also observe that (c) subjects demonstrated a wide range of disambiguation request behaviors, with the common thread of concentrating requests early in the execution. As our last contribution, we introduce a novel field-theoretic approach to intent inference inspired by dynamic field theory that works in tandem with the disambiguation scheme.

In response to the coronavirus disease (COVID-19) outbreak, there is an ever-increasing number of national governments that are rolling out contact-tracing Apps to aid the containment of the virus. The first hugely contentious issue facing the Apps is the deployment framework, i.e. centralised or decentralised. Based on this, the debate branches out to the corresponding technologies that underpin these architectures, i.e. GPS, QR codes, and Bluetooth. This work conducts a pioneering review of the above scenarios and contributes a geolocation mapping of the current deployment. The vulnerabilities and the directions of research are identified, with a special focus on the Bluetooth-based decentralised scheme.

We present a new system, EEV, for verifying binarized neural networks (BNNs). We formulate BNN verification as a Boolean satisfiability problem (SAT) with reified cardinality constraints of the form $y = (x_1 + cdots + x_n le b)$, where $x_i$ and $y$ are Boolean variables possibly with negation and $b$ is an integer constant. We also identify two properties, specifically balanced weight sparsity and lower cardinality bounds, that reduce the verification complexity of BNNs. EEV contains both a SAT solver enhanced to handle reified cardinality constraints natively and novel training strategies designed to reduce verification complexity by delivering networks with improved sparsity properties and cardinality bounds. We demonstrate the effectiveness of EEV by presenting the first exact verification results for $ell_{infty}$-bounded adversarial robustness of nontrivial convolutional BNNs on the MNIST and CIFAR10 datasets. Our results also show that, depending on the dataset and network architecture, our techniques verify BNNs between a factor of ten to ten thousand times faster than the best previous exact verification techniques for either binarized or real-valued networks.

Domain of mathematical logic in computers is dominated by automated theorem provers (ATP) and interactive theorem provers (ITP). Both of these are hard to access by AI from the human-imitation approach: ATPs often use human-unfriendly logical foundations while ITPs are meant for formalizing existing proofs rather than problem solving. We aim to create a simple human-friendly logical system for mathematical problem solving. We picked the case study of Euclidean geometry as it can be easily visualized, has simple logic, and yet potentially offers many high-school problems of various difficulty levels. To make the environment user friendly, we abandoned strict logic required by ITPs, allowing to infer topological facts from pictures. We present our system for Euclidean geometry, together with a graphical application GeoLogic, similar to GeoGebra, which allows users to interactively study and prove properties about the geometrical setup.