Involutive Structures Research Articles

A Method for Detecting the Death State of Caged Broilers Based on Improved Yolov5

HighlightsRapid and accurate identification and detection of mortality in high-level caged broilers.Apply the state-of-the-art single-stage object detection model Yolov5 as the experimental infrastructure.Modify and improve the network structure, reduce the calculation amount of model parameters, and make the model easier to deploy.The data of dead broilers in different regions can also be quickly and accurately identified and detected, with excellent generalization.Abstract. In an unmanned broiler base, the automatic identification of the death state of broilers in a complex cage environment can effectively improve picking efficiency and reduce its negative impact. An improved Yolov5 object detection method is proposed in this study to rapidly and accurately detect the presence of dead broilers in caged structures. The Yolov5 model within the CSPDarknet53 framework is constructed, and the Yolov5 model is experimentally pruned to reduce the number of convolution kernels. The Ghost structure and the Involution structure are combined with the Yolov5 backbone network to effectively reduce the number of parameters and computations with a negligible loss of accuracy, making it easier to deploy applications. The detection accuracy of the model can reach 99.2%. The number of parameters is reduced from 7.05M to 0.31M, and the amount of calculation is reduced from 16.3 to 0.3. It can be seen that the improved Yolov5 network is practical and suitable for high-precision real-time detection and recognition of the death state of broilers in a caged structure. Keywords: Keywords.,Computer vision, Dead chicken detection, Machine vision, Yolov5.

Local solvability for real-analytic involutive structures of tube type of corank one in Besov and Triebel-Lizorkin spaces

This study shows the local solvability, in degree one, for the differential complex associated to a real-analytic, involutive structure of tube type of corank one in mixed spaces involving Besov and Triebel-Lizorkin spaces.

Elliptic involutive structures on compact Lie groups

Inspired by the work of Chevalley and Eilenberg on the de Rham cohomology on compact Lie groups, we prove that, under certain algebraic and topological conditions, the cohomology associated to left-invariant elliptic, and even hypocomplex, involutive structures on compact Lie groups can be computed by using only Lie algebras, thus reducing the analytical problem to a purely algebraic one. The main tool is the Leray spectral sequence that connects the result obtained Chevalley and Eilenberg to a result by Bott on the Dolbeault cohomology of a homogeneous manifold.

Study on Electromagnetic Heating Process of Wind Power Gear: Temperature Morphology and Evolution

Abstract As a key component of wind turbine, the surface strengthening treatment of wind turbine gear is crucial to enhance its performance and service life. In the process of tooth-by-tooth induction heating, clear temperature distribution and process evolution could realize the lean control of heating effect and quality. In this article, the tooth-by-tooth heating process under the v-shaped inductor was studied to analyze the temperature field morphology and its evolution process. The results show that in the tooth profile region, the boundary morphology of the temperature field near the central section of the heating region conforms to the Boltzmann function, while the far sections conform to the normal distribution. At the end of heating, from the surface to the depth of the heating layer and from the heating center to both sides, both the maximum temperature difference and the distribution temperature are reduced. Meanwhile, the maximum temperature point near the central section is offset during the evolution of the temperature field morphology. The change of physical properties of materials and induced eddy distribution caused by involute structure and the constant change of temperature gradient are the fundamental reasons for the appearance of nonuniform temperature field and temperature excursion. The spatiotemporal variation of the hottest point was found, and the temperature morphology and evolution were revealed, which would provide a theoretical basis for adjusting the temperature distribution of tooth profile according to the requirements of different heating layers.

Fast lightweight block cipher design with involution substitution permutation network (SPN) structure

<p>In the present paper, a new cryptographic lightweight algorithm has been developed for the Internet of Things (IoT) applications. The submitted cipher designed with the involution Substitution Permutation Network SPN structure. The involution structure means that the same encryption algorithm is used in the decryption process except the ciphering key algorithm is applied in reverse order. The introduced algorithm encrypts the data with a block size of 128-bit 192-bit or 256-bit, which iterative with 10, 12 and 14-rounds respectively similar to the AES cipher. The design aspect supports an elegant structure with a secure involution round transformation. The main round is built without S-Box stage instead that it uses the on-fly immediate computing stage and the involution of mathematical invertible affine equations. The proposed cipher is adopted to work in a restricted environment and with limited resources pertaining to embedded devices. The proposed cipher introduces an accepted security level and reasonable Gate Equivalent (GE) estimation with fast implementation.</p>

Special clean elements in rings

A clean decomposition [Formula: see text] in a ring [Formula: see text] (with idempotent [Formula: see text] and unit [Formula: see text]) is said to be special if [Formula: see text]. We show that this is a left-right symmetric condition. Special clean elements (with such decompositions) exist in abundance, and are generally quite accessible to computations. Besides being both clean and unit-regular, they have many remarkable properties with respect to element-wise operations in rings. Several characterizations of special clean elements are obtained in terms of exchange equations, Bott–Duffin invertibility, and unit-regular factorizations. Such characterizations lead to some interesting constructions of families of special clean elements. Decompositions that are both special clean and strongly clean are precisely spectral decompositions of the group invertible elements. The paper also introduces a natural involution structure on the set of special clean decompositions, and describes the fixed point set of this involution.

Global regularity and solvability of left-invariant differential systems on compact Lie groups

We are interested in global properties of systems of left-invariant differential operators on compact Lie groups: regularity properties, properties on the closedness of the range and finite dimensionality of their cohomology spaces, when acting on various function spaces e.g. smooth, analytic and Gevrey. Extending the methods of Greenfield and Wallach (1973) to systems, we obtain abstract characterizations for these properties and use them to derive some generalizations of results due to Greenfield (1972), Greenfield and Wallach (1972), as well as global versions of a result of Caetano and Cordaro (2011) for involutive structures.

Borel Kernels and their Approximation, Categorically

This paper introduces a categorical framework to study the exact and approximate semantics of probabilistic programs. We construct a dagger symmetric monoidal category of Borel kernels where the dagger-structure is given by Bayesian inversion. We show functorial bridges between this category and categories of Banach lattices which formalize the move from kernel-based semantics to predicate transformer (backward) or state transformer (forward) semantics. These bridges are related by natural transformations, and we show in particular that the Radon-Nikodym and Riesz representation theorems - two pillars of probability theory - define natural transformations.With the mathematical infrastructure in place, we present a generic and endogenous approach to approximating kernels on standard Borel spaces which exploits the involutive structure of our category of kernels. The approximation can be formulated in several equivalent ways by using the functorial bridges and natural transformations described above. Finally, we show that for sensible discretization schemes, every Borel kernel can be approximated by kernels on finite spaces, and that these approximations converge for a natural choice of topology.We illustrate the theory by showing that our approximation scheme can be used in practice as an approximate Bayesian inference algorithm and as an approximation scheme for programs in the probabilistic network specification language ProbNetKAT.

K-theory classification of graded ultramatricial algebras with involution

Abstract We consider a generalization K 0 gr ⁢ ( R ) {K_{0}^{\operatorname{gr}}(R)} of the standard Grothendieck group K 0 ⁢ ( R ) {K_{0}(R)} of a graded ring R with involution. If Γ is an abelian group, we show that K 0 gr {K_{0}^{\operatorname{gr}}} completely classifies graded ultramatricial * {*} -algebras over a Γ-graded * {*} -field A such that (1) each nontrivial graded component of A has a unitary element in which case we say that A has enough unitaries, and (2) the zero-component A 0 {A_{0}} is 2-proper ( a ⁢ a * + b ⁢ b * = 0 {aa^{*}+bb^{*}=0} implies a = b = 0 {a=b=0} for any a , b ∈ A 0 {a,b\in A_{0}} ) and * {*} -pythagorean (for any a , b ∈ A 0 {a,b\in A_{0}} one has a ⁢ a * + b ⁢ b * = c ⁢ c * {aa^{*}+bb^{*}=cc^{*}} for some c ∈ A 0 {c\in A_{0}} ). If the involutive structure is not considered, our result implies that K 0 gr {K_{0}^{\operatorname{gr}}} completely classifies graded ultramatricial algebras over any graded field A. If the grading is trivial and the involutive structure is not considered, we obtain some well-known results as corollaries. If R and S are graded matricial * {*} -algebras over a Γ-graded * {*} -field A with enough unitaries and f : K 0 gr ⁢ ( R ) → K 0 gr ⁢ ( S ) {f:K_{0}^{\operatorname{gr}}(R)\to K_{0}^{\operatorname{gr}}(S)} is a contractive ℤ ⁢ [ Γ ] {\mathbb{Z}[\Gamma]} -module homomorphism, we present a specific formula for a graded * {*} -homomorphism ϕ : R → S {\phi:R\to S} with K 0 gr ⁢ ( ϕ ) = f {K_{0}^{\operatorname{gr}}(\phi)=f} . If the grading is trivial and the involutive structure is not considered, our constructive proof implies the known results with existential proofs. If A 0 {A_{0}} is 2-proper and * {*} -pythagorean, we also show that two graded * {*} -homomorphisms ϕ , ψ : R → S {\phi,\psi:R\to S} are such that K 0 gr ⁢ ( ϕ ) = K 0 gr ⁢ ( ψ ) {K_{0}^{\operatorname{gr}}(\phi)=K_{0}^{\operatorname{gr}}(\psi)} if and only if there is a unitary element u of degree zero in S such that ϕ ⁢ ( r ) = u ⁢ ψ ⁢ ( r ) ⁢ u * {\phi(r)=u\psi(r)u^{*}} for any r ∈ R {r\in R} . As an application of our results, we show that the graded version of the Isomorphism Conjecture holds for a class of Leavitt path algebras: if E and F are countable, row-finite, no-exit graphs in which every infinite path ends in a sink or a cycle and K is a 2-proper and * {*} -pythagorean field, then the Leavitt path algebras L K ⁢ ( E ) {L_{K}(E)} and L K ⁢ ( F ) {L_{K}(F)} are isomorphic as graded rings if any only if they are isomorphic as graded * {*} -algebras. We also present examples which illustrate that K 0 gr {K_{0}^{\operatorname{gr}}} produces a finer invariant than K 0 {K_{0}} .

Lie bialgebra structure on cyclic cohomology of Fukaya categories

Let M be an exact symplectic manifold with contact type boundary such that c1(M) = 0. Motivated by noncommutative symplectic geometry and string topology, we show that the cyclic cohomology of the Fukaya category of M has an involutive Lie bialgebra structure.

Role of coaptation imaging of mitral valve on ischemic mitral regurgitation by real-time three-dimensional transesophageal echocardiography

Objective To explore the impact of morphological changes of mitral valve coaptation on ischemic mitral regurgitation (IMR), and observe coaptation image of mitral valve in systole in patients with IMR by using real-time three-dimensional transesophageal echocardiography (RT3D-TEE). Methods RT3D-TEE was performed on 112 patients with IMR and 38 patients without MR as the control. Patients with IMR were divided into group of mild IMR (n=46), group of moderate IMR (n=45) and group of severe IMR (n=21), according to the severity of mitral regurgitation. Mitral valve quantification (MVQ) software of Qlab 8.1 was used for image post-processing of RT3D-TEE. The coaptation parameters was measured, included length of anterior combination(LCA3dlf), length of posterior combination(LCP3dlf), area of anterior combination(A3DTANT) and area of posterior combination(A3DTPOST) at end-systole. Then, these coaptation parameters of mitral valve were compared statistically. Logistic regression assessing was applied for analyzing the results. Results Coaptation line of anterior and posterior leaflets was almost same in normal subjects. With increasing of mitral regurgitation, a tendency to prolong in LCA3dlf and LCP3dlf were observed in IMR (P<0.05). Compared to that in mild and moderate IMR groups, besides A3DTANT and A3DTPOST, LCA3dlf and LCP3dlf were also increased significantly in severe IMR group (P<0.05). LCP3dlf was an independent correlation factor of IMR by Logistic regression analysis. The sensitivity was 73.3% and the specificity was 94.7% when LCP3dlf ≥32 mm was regarded as cut-off point, and the area under the ROC curve was 0.949 (0.900~0.999). Conclusions Abnormal coaptation of anterior and posterior leaflets of mitral valve might be one of main cause of IMR. Involution structure of mitral valve before surgery is helpful for surgeon to select an optical surgical procedure and evaluate effects of treatment in patients with IMR. Key words: Echocardiography, real-time three-dimensional; Echocardiography, transesophageal; Mitral valve insufficiency; Myocardial ischemia

On the Generality of Assuming that a Family of Continuous Functions Separates Points

For an algebra $${\mathcal{A}}$$ of complex-valued, continuous functions on a compact Hausdorff space (X, τ), it is standard practice to assume that $${\mathcal{A}}$$ separates points in the sense that for each distinct pair $${x, y \in X}$$ , there exists an $${f \in \mathcal{A}}$$ such that $${f(x) \neq f(y)}$$ . If $${\mathcal{A}}$$ does not separate points, it is known that there exists an algebra $${\widehat{\mathcal{A}}}$$ on a compact Hausdorff space $${(\widehat{X}, \widehat{\tau})}$$ that does separate points such that the map $${\mathcal{A} \mapsto \widehat{\mathcal{A}}}$$ is a uniform norm isometric algebra isomorphism. So it is, to a degree, without loss of generality that we assume $${\mathcal{A}}$$ separates points. The construction of $${{\widehat{\mathcal{A}}}}$$ and $${(\widehat{X}, \widehat{\tau})}$$ does not require that $${\mathcal{A}}$$ has any algebraic structure nor that $${(X, \tau)}$$ has any properties, other than being a topological space. In this work we develop a framework for determining the degree to which separation of points may be assumed without loss of generality for any family $${\mathcal{A}}$$ of bounded, complex-valued, continuous functions on any topological space $${(X, \tau)}$$ . We also demonstrate that further structures may be preserved by the mapping $${\mathcal{A} \mapsto \widehat{\mathcal{A}}}$$ , such as boundaries of weak peak points, the Lipschitz constant when the functions are Lipschitz on a compact metric space, and the involutive structure of real function algebras on compact Hausdorff spaces.

Categories with fuzzy sets and relations

We define a 2-category whose objects are fuzzy sets and whose maps are relations subject to certain natural conditions. We enrich this category with additional monoidal and involutive structure coming from t-norms and negations on the unit interval. We develop the basic properties of this category and consider its relation to other familiar categories. A discussion is made of extending these results to the setting of type-2 fuzzy sets.

Existence of Gevrey approximate solutions for certain systems of linear vector fields applied to involutive systems of first-order nonlinear pdes

Given a G s -involutive structure, ( M , V ) , a Gevrey submanifold X ⊂ M which is maximally real and a Gevrey function u 0 on X we construct a Gevrey function u which extends u 0 and is a Gevrey approximate solution for V . We then use our construction to study Gevrey micro-local regularity of solutions, u ∈ C 2 ( R N ) , of a system of nonlinear pdes of the form F j ( x , u , u x ) = 0 , j = 1 , … , n , where F j ( x , ζ 0 , ζ ) are Gevrey functions of order s > 1 and holomorphic in ( ζ 0 , ζ ) ∈ C × C N . The functions F j satisfy an involutive condition and d ζ F 1 ∧ ⋯ ∧ d ζ F n ≠ 0 .

Global Analytic Regularity for Structures of Co-Rank One

We consider real analytic involutive structures 𝒱, of co-rank one, defined on a real analytic paracompact orientable manifold M. To each such structure we associate certain connected subsets of M which we call the level sets of 𝒱. We prove that analytic regularity propagates along them. With a further assumption on the level sets of 𝒱 we characterize the global analytic hypoellipticity of a differential operator naturally associated to 𝒱. As an application we study a case of tube structures.

A generalization of Borel's theorem and microlocal Gevrey regularity in involutive structures

In this paper, we use Borel's procedure to construct Gevrey approximate solutions of an initial value problem for involutive systems of Gevrey complex vector fields. As an application, we describe the Gevrey wave-front set of the boundary values of approximate solutions in wedges W of Gevrey involutive structures ( M , V ) . We prove that the Gevrey wave-front set of the boundary value is contained in the polar of a certain cone Γ T ( W ) contained in R V ∩ T X where X is a maximally real edge of W . We also prove a partial converse.

Local solvability for real-analytic involutive structures of tube type of corank one

This work is a continuation of [P.D. Cordaro, E.R. da Silva, Local solvability in corank one involutive real-analytic structures, Indiana Univ. Math. J. 53 (2004) 1605–1628]. We study the problem of local solvability, in degree one, for the differential complex associated to a real-analytic, involutive structure of tube type of corank one. In the present case we obtain more accurate results.

Simple proofs of open problems about the structure of involutions in the Riordan group

We prove that if D = ( g ( x ) , f ( x ) ) is an element of order 2 in the Riordan group then g ( x ) = ± exp [ Φ ( x , xf ( x ) ] for some antisymmetric function Φ ( x , z ) . Also we prove that every element of order 2 in the Riordan group can be written as BMB - 1 for some element B and M = ( 1 , - 1 ) in the Riordan group. These proofs provide solutions to two open problems presented by L. Shapiro [L.W. Shapiro, Some open questions about random walks, involutions, limiting distributions and generating functions, Adv. Appl. Math. 27 (2001) 585–596].

Edge of the wedge theory in involutive structures

Edge of the wedge theory in involutive structures

The word problem for involutive residuated lattices and related structures

It will be shown that the word problem is undecidable for involutive residuated lattices, for finite involutive residuated lattices and certain related structures like residuated lattices. The proof relies on the fact that the monoid reduct of a group can be embedded as a monoid into a distributive involutive residuated lattice. Thus, results about groups by P. S. Novikov and W. W. Boone and about finite groups by A. M. Slobodskoi can be used. Furthermore, for any non-trivial lattice variety \( \user1{\mathcal{V}} \), the word problem is undecidable for those involutive residuated lattices and finite involutive residuated lattices whose lattice reducts belong to \( \user1{\mathcal{V}} \). In particular, the word problem is undecidable for modular and distributive involutive residuated lattices.