Study of potential games using Ising interaction

Problems can be handled properly in game theory as long as a countable number of players are considered, whereas, in real life, we have a large number of players. Hence, games at the thermodynamic limit are analyzed in general. There is a one-to-one correspondence between classical games and the modeled Hamiltonian at a particular equilibrium condition, usually the Nash equilibrium. Such a correspondence is arrived for symmetric games, namely the Prisoner’s Dilemma using the Ising Hamiltonian. In this work, we have shown that another class of games known as potential games can be analyzed with the Ising Hamiltonian. Analysis of this work brings out very close observation with real-world scenarios. In other words, the model of a potential game studied using Ising Hamiltonian predicts behavioral aspects of a large population precisely.

OnePetri: accelerating common bacteriophage Petri dish assays with computer vision

IntroductionBacteriophage plaque enumeration is a critical step in a wide array of protocols. The current gold standard for plaque enumeration on Petri dishes is through manual counting. This approach is time-intensive, has low-throughput, is limited to Petri dishes which have a countable number of plaques, and can have variable results upon recount due to human error.MethodsWe present OnePetri, a collection of trained machine learning models and open-source mobile application for the rapid enumeration of bacteriophage plaques on circular Petri dishes.ResultsWhen compared against the current gold standard of manual counting, OnePetri was significantly faster, with minimal error. Compared against two other similar tools, Plaque Size Tool and CFU.AI, OnePetri had higher plaque recall and reduced detection times on most test images.ConclusionsThe OnePetri application can rapidly enumerate phage plaques on circular Petri dishes with high precision and recall.

Partial integral operators of Fredholm type on Kaplansky-Hilbert module over $L_0$

The article studies some characteristic properties of self-adjoint partially integral operators of Fredholm type in the Kaplansky-Hilbert module $L_{0}\left[L_{2}\left(\Omega_{1}\right)\right]$ over $L_{0}\left(\Omega_{2}\right)$. Some mathematical tools from the theory of Kaplansky-Hilbert module are used. In the Kaplansky-Hilbert module $L_{0}\left[L_{2}\left(\Omega_{1}\right)\right]$ over $ L_{0} \left (\Omega _ {2} \right)$ we consider the partially integral operator of Fredholm type $T_{1}$ ($ \Omega_{1} $ and $\Omega_{2} $ are closed bounded sets in $ {\mathbb R}^{\nu_{1}}$ and $ {\mathbb R}^{\nu_{2}},$ $\nu_{1}, \nu_{2} \in {\mathbb N} $, respectively). The existence of $ L_{0} \left (\Omega _ {2} \right) $ nonzero eigenvalues for any self-adjoint partially integral operator $T_{1}$ is proved; moreover, it is shown that $T_{1}$ has finite and countable number of real $L_{0}(\Omega_{2})$-eigenvalues. In the latter case, the sequence $ L_{0}(\Omega_{2})$-eigenvalues is order convergent to the zero function. It is also established that the operator $T_{1}$ admits an expansion into a series of $\nabla_{1}$-one-dimensional operators.

Calibrating SECCM measurements by means of a nanoelectrode ruler. The intrinsic oxygen reduction activity of PtNi catalyst nanoparticles

Scanning electrochemical cell microscopy (SECCM) is increasingly applied to determine the intrinsic catalytic activity of single electrocatalyst particle. This is especially feasible if the catalyst nanoparticles are large enough that they can be found and counted in post-SECCM scanning electron microscopy images. Evidently, this becomes impossible for very small nanoparticles and hence, a catalytic current measured in one landing zone of the SECCM droplet cannot be correlated to the exact number of catalyst particles. We show, that by introducing a ruler method employing a carbon nanoelectrode decorated with a countable number of the same catalyst particles from which the catalytic activity can be determined, the activity determined using SECCM from many spots can be converted in the intrinsic catalytic activity of a certain number of catalyst nanoparticles.

Proper Definitions and Demonstration of Dirichlet Conditions

<div>Fourier theory is the backbone of the area of Signal Processing (SP) and Communication Engineering. However, Fourier series (FS) or Fourier transform (FT) do not exist for some signals that fail to fulfill a predefined set of Dirichlet conditions (DCs). We note a subtle gap in the explanation of these conditions as available in the popular signal processing literature. They lack a certain degree of explanation essential for the proper understanding of the same. For example, </div><div>the original second Dirichlet condition is the requirement of bounded variations over one time period for the convergence of Fourier Series, where there can be at most infinite but countable number of maxima and minima, and at most infinite but countable number of discontinuities of finite magnitude. However, a large body of the literature replaces this statement with the requirements of finite number of maxima and minima over one time period, and finite number of discontinuities. The latter incorrectly disqualifies some signals from having valid FS representation. Similar problem holds in the description of DCs for the Fourier transform. Likewise, while it is easy to relate the first DC with the finite value of FS or FT coefficients, it is hard to relate the second and third DCs as specified in the signal processing literature with the Fourier representation as to how the failure to satisfy these conditions disqualifies those signals from having valid FS or FT representation. <br></div><div><br></div>

Proper Definitions and Demonstration of Dirichlet Conditions

<div>Fourier theory is the backbone of the area of Signal Processing (SP) and Communication Engineering. However, Fourier series (FS) or Fourier transform (FT) do not exist for some signals that fail to fulfill a predefined set of Dirichlet conditions (DCs). We note a subtle gap in the explanation of these conditions as available in the popular signal processing literature. They lack a certain degree of explanation essential for the proper understanding of the same. For example, </div><div>the original second Dirichlet condition is the requirement of bounded variations over one time period for the convergence of Fourier Series, where there can be at most infinite but countable number of maxima and minima, and at most infinite but countable number of discontinuities of finite magnitude. However, a large body of the literature replaces this statement with the requirements of finite number of maxima and minima over one time period, and finite number of discontinuities. The latter incorrectly disqualifies some signals from having valid FS representation. Similar problem holds in the description of DCs for the Fourier transform. Likewise, while it is easy to relate the first DC with the finite value of FS or FT coefficients, it is hard to relate the second and third DCs as specified in the signal processing literature with the Fourier representation as to how the failure to satisfy these conditions disqualifies those signals from having valid FS or FT representation. <br></div><div><br></div>

High-throughput systematic topological generation of low-energy carbon allotropes

The search for new materials requires effective methods for scanning the space of atomic configurations, in which the number is infinite. Here we present an extensive application of a topological network model of solid-state transformations, which enables one to reduce this infinite number to a countable number of the regions corresponding to topologically different crystalline phases. We have used this model to successfully generate carbon allotropes starting from a very restricted set of initial structures; the generation procedure has required only three steps to scan the configuration space around the parents. As a result, we have obtained all known carbon structures within the specified set of restrictions and discovered 224 allotropes with lattice energy ranging in 0.16–1.76 eV atom−1 above diamond including a phase, which is denser and probably harder than diamond. We have shown that this phase has a quite different topological structure compared to the hard allotropes from the diamond polytypic series. We have applied the tiling approach to explore the topology of the generated phases in more detail and found that many phases possessing high hardness are built from the tiles confined by six-membered rings. We have computed the mechanical properties for the generated allotropes and found simple dependences between their density, bulk, and shear moduli.

Timed Bounded Verification of Inclusion Based on Timed Bounded Discretized Language

The inclusion problem is one of the common problems in real-time systems. The general form of this problem is undecidable; however, the time-bounded verification of inclusion problem is decidable for timed automata. In this study, we propose a new discretization technique to verify the inclusion problem. The proposed technique is applied to a non-Zeno timed automaton with an upper bound that does not contain a non-reachable space for each transition. The new approach is based on the generation of timed bounded discretized language that represents an abstraction of timed words in the form of a set of a countable number of discrete timed words. A discrete timed word aggregates all timed words that share the same actions and their execution times that create the time continuous intervals. The lower and the upper bounds of an interval in a discrete timed word is defined by the minimum and maximum execution times associated to a given transition-run. In addition, we propose the verification schema of the inclusion between two timed bounded discretized languages generated by two non-Zeno timed automata.

Решения гамильтоновой системы с двумерным управлением в окрестности особой экстремали второго порядка

We consider a Hamiltonian system that is affine in two-dimensional bounded control that takes values in an ellipse. In the neighborhood of a singular extremal of the second order, we find two families of optimal solutions: chattering trajectories that attain the singular point in a finite time with a countable number of control switchings, and logarithmic-like spirals that reach the singular point in a finite time and undergo an infinite number of rotations.

A Note on Generalized Solution of a Cauchy Problem Given by a Nonhomogeneous Linear Differential System

Generalized solution of a Cauchy problem given by a nonhomogeneous linear differential system is recovered to this approach. It considers the case of the free term having at most countable number of discontinuity points. The method, called successive approach, uses the solution on the previous interval (except the first one) for the condition on the given interval. The sequence of commands for a computer algebra system to this method is given.