Number Of Coordinates Research Articles

Blockchain for video watermarking: An enhanced copyright protection approach for video forensics based on perceptual hash function.

As a direct result of advancements in digital technology and the Internet, the copyright protection and information integrity of multimedia that are being published across the Internet have emerged as a major and urgent issue that needs to be addressed. The technique of digital watermarking may be used to protect intellectual property. In terms of authentication, resilience, storage, and capacity of digital watermarking information, there is still room for development. Blockchain's potential in video copyright protection and management applications has motivated researchers. Copyright owners and consumers may now communicate directly via copyright protection apps built on the blockchain, eliminating the need for distributers and the associated fees. Nonetheless, the current blockchain-based video watermarking solutions require storing a significant number of coordinates depending on the watermark size and are susceptible to video frame attacks on the video frame texture region. This study proposes an enhanced video copyright management approach that incorporates digital watermarking, the blockchain, and a perceptual hash function. Watermark information is stored on a blockchain structure, which also acts as a timestamp for verification purposes. To verify watermark data without the source video, a perceptual hash function is employed to compute a hash value based on the structural information of video frames. The contribution is in learning how to extract a hash function from a small number of video frames that still adequately represent a large amount of video content while also reducing the number of unnecessary video frames and the amount of computation required to summarize and index that content in a blockchain. This expedites the dissemination of copyrighted works and increases their security and readability, hence facilitating their circulation on the Internet. Our experimental results demonstrate that this approach is memory efficient, as it only needs to store one key for each key frame, regardless of the size of the watermark. Additionally, the overall robustness is greatly improved by using the blockchain's random hash function. Therefore, new and important advancements in video watermarking have been realized because of this effort.

Saddle-to-saddle dynamics in diagonal linear networks*

Abstract In this paper we fully describe the trajectory of gradient flow over two-layer diagonal linear networks for the regression setting in the limit of vanishing initialisation. We show that the limiting flow successively jumps from a saddle of the training loss to another until reaching the minimum ℓ 1 -norm solution. We explicitly characterise the visited saddles as well as the jump times through a recursive algorithm reminiscent of the LARS algorithm used for computing the Lasso path. Starting from the zero vector, coordinates are successively activated until the minimum ℓ 1 -norm solution is recovered, revealing an incremental learning. Our proof leverages a convenient arc-length time-reparametrisation which enables to keep track of the transitions between the jumps. Our analysis requires negligible assumptions on the data, applies to both under and overparametrised settings and covers complex cases where there is no monotonicity of the number of active coordinates. We provide numerical experiments to support our findings.

Polytopic Autoencoders with Smooth Clustering for Reduced-order Modelling of Flows

With the advancement of neural networks, there has been a notable increase, both in terms of quantity and variety, in research publications concerning the application of autoencoders to reduced-order models. We propose a polytopic autoencoder architecture that includes a lightweight nonlinear encoder, a convex combination decoder, and a smooth clustering network. Supported by several proofs, the model architecture ensures that all reconstructed states lie within a polytope, accompanied by a metric indicating the quality of the constructed polytopes, referred to as polytope error. Additionally, it offers a minimal number of convex coordinates for polytopic linear-parameter varying systems while achieving acceptable reconstruction errors compared to proper orthogonal decomposition (POD). To validate our proposed model, we conduct simulations involving two flow scenarios with the incompressible Navier-Stokes equation. Numerical results demonstrate the guaranteed properties of the model, low reconstruction errors compared to POD, and the improvement in error using a clustering network.

Modeling Conformational Transitions of Biomolecules from Atomic Force Microscopy Images using Normal Mode Analysis.

Observing a single biomolecule performing its function is fundamental in biophysics as it provides important information for elucidating the mechanism. High-speed atomic force microscopy (HS-AFM) is a unique and powerful technique that allows the observation of biomolecular motion in a near-native environment. However, the spatial resolution of HS-AFM is limited by the physical size of the cantilever tip, which restricts the ability to obtain atomic details of molecules. In this study, we propose a novel computational algorithm designed to derive atomistic models of conformational dynamics from AFM images. Our method uses normal-mode analysis to describe the expected motions of the molecule, allowing these motions to be represented with a limited number of coordinates. This approach mitigates the problem of overinterpretation inherent in the analysis of AFM images with limited resolution. We demonstrate the effectiveness of our algorithm, NMFF-AFM, using synthetic data sets for three proteins that undergo significant conformational changes. NMFF-AFM is a fast and user-friendly program that requires minimal setup and has the potential to be a valuable tool for biophysical studies using HS-AFM.

Response theory identifies reaction coordinates and explains critical phenomena in noisy interacting systems

We consider a class of nonequilibrium systems of interacting agents with pairwise interactions and quenched disorder in the dynamics featuring, in the thermodynamic limit, phase transitions. We identify mathematical conditions on the microscopic interaction structure, namely the separability of the interaction kernel, that lead to a dimension reduction of the system in terms of a finite number of reaction coordinates (RCs). Such RCs prove to be proper nonequilibrium thermodynamic variables as they carry information on correlation, memory and resilience properties of the system. Phase transitions can be identified and quantitatively characterised as singularities of the complex valued susceptibility functions associated to the RCs. We provide analytical and numerical evidence of how the singularities affect the physical properties of finite size systems.

Killer Phonon Caught: Femtosecond Stimulated Raman Spectroscopy Identifies Phonon-Induced Control of Photophysics in Rubrene Derivatives.

Molecular reaction coordinates are defined by the interplay of a number of orthogonal nuclear coordinates and are inherently multidimensional for large molecules. Identifying how specific nuclear motions along these reaction coordinates can be used to drive and control chemical processes is a promising approach for the optimization of chemical outcomes and targeted synthetic design. Here, we used femtosecond stimulated Raman spectroscopy (FSRS) to quantify the effects of individual phonon nuclear motions on singlet fission in rubrene derivatives. Rubrene readily undergoes singlet fission and is amendable to chemical derivatization, yet the factors that impact the singlet fission yield are not fully understood. Crystal packing is known to play a significant role in both fission and carrier transport, and thus, we focused on the impact of phonon nuclear motions on the photophysics. We used four halogen-substituted rubrene crystals and successfully identified one specific phonon mode that suppresses singlet fission in these crystals. We used FSRS with single-pulse excitation and double-pulse excitation to coherently amplify each phonon mode and quantify its effects on the excited-state process. We found that coherent amplification of the specific phonon vibration involving twisting of the peripheral phenyl rings and tetracene core motions resulted in less ground-state depletion and fewer triplet state absorption. Our study demonstrated that it is possible to use coherent phonon excitation to influence the photophysical outcome, while also showing that FSRS with double-pulse excitation can be a successful tool for quantifying mode-selective contributions to photophysics.

Asymptotics of Cointegration Tests for High-Dimensional Var(k)

Abstract The paper studies nonstationary high-dimensional vector autoregressions of order k, VAR(k). Additional deterministic terms such as trend or seasonality are allowed. The number of time periods, T, and the number of coordinates, N, are assumed to be large and of the same order. Under this regime the first-order asymptotics of the Johansen likelihood ratio (LR), Pillai–Bartlett, and Hotelling–Lawley tests for cointegration are derived: the test statistics converge to nonrandom integrals. For more refined analysis, the paper proposes and analyzes a modification of the Johansen test. The new test for the absence of cointegration converges to the partial sum of the Airy1 point process. Supporting Monte Carlo simulations indicate that the same behavior persists universally in many situations beyond those considered in our theorems. The paper presents empirical implementations of the approach for the analysis of S&P100 stocks and of cryptocurrencies. The latter example has a strong presence of multiple cointegrating relationships, while the results for the former are consistent with the null of no cointegration.

Choice of the Right Supporting Electrolyte in Electrochemical Reductions: A Principal Component Analysis.

We present an analysis of a set of molecular, electrical, and electronic properties for a large number of the cations of quaternary ammonium salts usually employed as supporting electrolytes in cathodic reduction reactions. The goal of the present study is to define a measure for the quality of a supporting electrolyte in terms of the yield of the reaction considered. We performed a principal component analysis using the normalized values of the properties in order to lower the number of relevant reaction coordinates and find that the integral variance of 13 properties can well be represented by three principal components. The yield of the electrochemical hydrodimerization of acrylonitrile employing different quaternary ammonium salts as supporting electrolytes was determined in a series of experiments. We found only a very weak correlation between the yield and the values of the properties but a strong correlation between the yield and the values of the most important principal component. Very similar results are obtained for two further existing systematic experimental studies of the impact of the supporting electrolyte on the yield of cathodic reductions. For all three example reactions, a supervised regression using the two most important principal components as variables yields excellent values for the coefficients of determination. For comparison, we also applied our methodology to sets of purely structure-based features that are usually employed in cheminformatics and obtained results of almost similar quality. We therefore conjecture that our methodology in combination with a small number of experiments can be used to predict the yield of a given cathodic reduction on the basis of the properties of the supporting electrolyte.

Statistical Mechanics Approaches for Studying Temperature and Rate Effects in Multistable Systems

Systems with a multistable energy landscape are widespread in physics, biophysics, technology, and materials science. They are strongly influenced by thermal fluctuations and external mechanical actions that can be applied at different rates, moving the system from equilibrium to non-equilibrium regimes. In this paper, we focus on a simple system involving a single breaking phenomenon to describe the various theoretical approaches used to study these problems. To begin with, we propose the exact solution at thermodynamic equilibrium based on the calculation of the partition function without approximations. We then introduce the technique of spin variables, which is able to simplify the treatment even for systems with a large number of coordinates. We then analyze the energy balance of the system to better understand its underlying physics. Finally, we introduce a technique based on transition state theory useful for studying the non-equilibrium dynamical regimes of these systems. This method is appropriate for the evaluation of rate effects and hysteresis loops. These approaches are developed for both the Helmholtz ensemble (prescribed extension) and the Gibbs ensemble (applied force) of statistical mechanics. The symmetry and duality of these two ensembles is discussed in depth. While these techniques are used here for a simple system with theoretical purposes, they can be applied to complex systems of interest for several physical, biophysical, and technological applications.

Energy efficient simplified MIMO with spatial four-dimensional modulated signals

The article represents a method of simplifying MIMO by increasing energy efficiency, where each transmitting antenna transmits not a chosen signal, but its base signals weighted by the corresponding coordinates of the chosen signal. It is shown that in this case, high efficiency of the system can be achieved if a multidimensional biorthogonal signal is used. Since such signals have a minimum number of non-zero coordinates, the number of active transmitting antennas will also be minimal. Examples of the implementation of used four-dimensional signals and corresponding simulation results for Rayleigh and generalized fading (Nakagami-m) conditions are given. In provided examples, cases are considered for a specific number of transmitting antennas, while the number of receiving antennas is different. The obtained results indicate the advantage of simplified MIMO, both in terms of simplicity and energy efficiency, compared to the traditional one.

Digital model of automated unmanned aerial vehicle with edge computing application for railway reconnaissance

In the last decade, unmanned aerial vehicles have been widely used in various civil and military field operations. Most modern drones are manually controlled by an operator and require decision making, which requires experience gained through training, which is time consuming and expensive, and even with experienced operators, the human factor can never be excluded. In this paper, an algorithm for an automatic flight mode of unmanned aerial vehicles without an operator’s participation has been developed. The proposed algorithm has been considered in the military reconnaissance of railways using edge computing and computer vision approaches to recognise railroads and moving trains for simulated and real cases as well as send report data to the web platform. As a result, the head of the operation received information about the number of carriages and Global Positioning System coordinates of the recognised train to make the necessary decisions.

Computer vision-based 3D coordinate acquisition of surface feature points of building structures

In the present structure health monitoring work, regular monitoring of the deformation and displacement of the target building structure is an important means to evaluate the safety of the structure. Aiming at the difficulties of traditional measurement methods such as complex operation, high cost and too few monitoring points, this paper proposes a method based on computer vision to obtain 3D coordinates of surface feature points of building structures. Based on the principle of restoring the target structure from the camera motion, the sparse point cloud model of the target building is initially reconstructed and the attitude information of each camera is obtained simultaneously. The depth information of each pixel in the original image is obtained by trial matching based on the principle of pole line search, and corrected and optimized based on the consistency of optics and geometry. Based on the original sparse point cloud, the depth information of each image was fused and reprojected based on the depth map registration principle to reconstruct the dense point cloud model of the target building. Finally, the 3D coordinates of the target building surface points are obtained and measured based on the scale factor method. In order to verify the feasibility of the method, seven buildings of different sizes were selected for field measurement and compared with manual measurement results. The results show that the measurement results of the proposed method are almost the same as those of manual measurement, and the error level fully meets the requirement of the error limit of the general structural health monitoring work. The method described in this paper obtains a large number of 3D coordinates of detection points on the surface of building structures in a non-contact form at one time, improves the flexibility and intensity of measurement point layout in the actual measurement work, and its operation is simple and low cost.

Sparks of symmetric matrices and their graphs

The spark of a matrix is the smallest number of nonzero coordinates of any nonzero null vector. For real symmetric matrices, the sparsity of null vectors is shown to be associated with the structure of the graph obtained from the off-diagonal pattern of zero and nonzero entries. The smallest possible spark of a matrix corresponding to a graph is defined as the spark of the graph. Connections are established between graph spark and well-known concepts including minimum rank, forts, orthogonal representations, Parter and Fiedler vertices, and vertex connectivity.

Grouping one-degree trapezoids into biostatistical areas on example of the Okhotsk Sea

A method for grouping one-degree trapezoids into biostatistical areas of any size is proposed. For this purpose, all stations of survey are marked by the number of trapezoid, its area and central coordinates. Then the stations are sorted by the trapezoid numbers; their biological parameters (biomass, abundance, etc.). The mean values are integral parameters with the weights proportional to size of trapezoids — they can be easily grouped into small or large areas of any shape, depending on research tasks.

Vibrations control of railway vehicles using decentralized proportional integral derivative controller with flow direction optimization algorithm

The reduction of vibration-induced discomfort in vehicles is an important goal in the field of transportation engineering. Several mathematical models with various controlling techniques, from classical to modern, have been employed to achieve better ride comfort. Still, no comprehensive solution has yet been found. Therefore, this paper proposes a 17-degree-of-freedom (minimum number of coordinates) dynamic model of a full-scale railway vehicle integrated with wheel-rail contact forces and an active suspension system. Two controllers, termed system and force tracking controllers, suppress the vehicle body's vibrations. Based on a multi-loop control structure, three optimally tuned Proportional Integral Derivative controllers evaluate the desired control forces and performs the system controller’s action. While the force-tracking controller generates the command voltage to track that forces. The parameters of controllers are tuned with a novel metaheuristic optimization algorithm known as the flow direction algorithm (FDA), and the results are compared with two other optimization techniques, i.e., particle swarm optimization and ant colony optimization. The simulated results show that the ride comfort of the vehicle is improved with FDA, as the root mean square values of the lateral, roll, and yaw accelerations are reduced by 42.01%, 33.12%, and 48.24%, respectively. Moreover, the simulated results of the proposed model are validated with the experimental results of accelerations. The simulated results show that the proposed system tuned with the metaheuristic algorithm outperforms with a significant reduction in vehicle vibrations.

Gμ-covers, strongly compact cardinals and factorization of maps from products in Unif and Top

It is shown that numbers of coordinates of factorized (uniformly) continuous maps on limits of inverse systems in special subclasses of Unif or Top are bounded from above by μ-strongly compact cardinals and those bounds cannot be decreased. For instance, if there is no ω1-strongly compact (or uncountable measurable) cardinal, then for every cardinal κ there exists a (uniformly) continuous map from a limit of an inverse system into a countable space that cannot be factorized via a limit of a subsystem of cardinality less than κ.

Characterizing the Folding Transition-State Ensembles in the Energy Landscape of an RNA Tetraloop.

Molecular dynamics (MD) simulations have become increasingly powerful and can now describe the folding/unfolding of small biomolecules in atomic detail. However, a major challenge in MD simulations is to represent the complex energy landscape of biomolecules using a small number of reaction coordinates. In this study, we investigate the folding pathways of an RNA tetraloop, gcGCAAgc, using five classical MD simulations with a combined simulation time of approximately 120 μs. Our approach involves analyzing the tetraloop dynamics, including the folding transition state ensembles, using the energy landscape visualization method (ELViM). The ELViM is an approach that uses internal distances to compare any two conformations, allowing for a detailed description of the folding process without requiring root mean square alignment of structures. This method has previously been applied to describe the energy landscape of disordered β-amyloid peptides and other proteins. The ELViM results in a non-linear projection of the multidimensional space, providing a comprehensive representation of the tetraloop's energy landscape. Our results reveal four distinct transition-state regions and establish the paths that lead to the folded tetraloop structure. This detailed analysis of the tetraloop's folding process has important implications for understanding RNA folding, and the ELViM approach can be used to study other biomolecules.

Forbidden intersections for codes

AbstractDetermining the maximum size of a ‐intersecting code in was a longstanding open problem of Frankl and Füredi, solved independently by Ahlswede and Khachatrian and by Frankl and Tokushige. We extend their result to the setting of forbidden intersections, by showing that for any and large compared with (but not necessarily ) that the same bound holds for codes with the weaker property of being ‐avoiding, that is, having no two vectors that agree on exactly coordinates. Our proof proceeds via a junta approximation result of independent interest, which we prove via a development of our recent theory of global hypercontractivity: we show that any ‐avoiding code is approximately contained in a ‐intersecting junta (a code where membership is determined by a constant number of coordinates). In particular, when , this gives an alternative proof of a recent result of Eberhard, Kahn, Narayanan and Spirkl that symmetric intersecting codes in have size .

Advances in Peptide/Protein Structure Prediction Tools and their Relevance for Structural Biology in the Last Decade

Abstract: Peptides and proteins are involved in several biological processes at a molecular level. In this context, three-dimensional structure characterization and determination of peptides and proteins have helped researchers unravel the chemical and biological role of these macromolecules. Over 50 years, peptide and protein structures have been determined by experimental methods, including nuclear magnetic resonance (NMR), X-ray crystallography, and cryo-electron microscopy (cryo-EM). Therefore, an increasing number of atomic coordinates for peptides and proteins have been deposited in public databases, thus assisting the development of computational tools for predicting unknown 3D structures. In the last decade, a race for innovative methods has arisen in computational sciences, including more complex biological activity and structure prediction algorithms. As a result, peptide/protein theoretical models have achieved a new level of structure prediction accuracy compared with experimentally determined structures. Machine learning and deep learning approaches, for instance, incorporate fundamental aspects of peptide/protein geometry and include physical/biological knowledge about these macromolecules' experimental structures to build more precise computational models. Additionally, computational strategies have helped structural biology, including comparative, threading, and ab initio modeling and, more recently, prediction tools based on machine learning and deep learning. Bearing this in mind, here we provide a retrospective of protein and peptide structure prediction tools, highlighting their advances and obstacles and how they have assisted researchers in answering crucial biological questions.

Fast and Interpretable Dynamics for Fisher Markets via Block-Coordinate Updates

We consider the problem of large-scale Fisher market equilibrium computation through scalable first-order optimization methods. It is well-known that market equilibria can be captured using structured convex programs such as the Eisenberg-Gale and Shmyrev convex programs. Highly performant deterministic full-gradient first-order methods have been developed for these programs. In this paper, we develop new block-coordinate first-order methods for computing Fisher market equilibria, and show that these methods have interpretations as tâtonnement-style or proportional response-style dynamics where either buyers or items show up one at a time. We reformulate these convex programs and solve them using proximal block coordinate descent methods, a class of methods that update only a small number of coordinates of the decision variable in each iteration. Leveraging recent advances in the convergence analysis of these methods and structures of the equilibrium-capturing convex programs, we establish fast convergence rates of these methods.