112,488 research outputs found
Sensory analysis of juices from apples of different varieties
No full textDotsenko Y. I. Sensory analysis of juices from apples of different varieties / Y.I. Dotsenko, N. V. Dotsenko, T. A. Manoli // Збірник наукових праць молодих учених, аспірантів та студентів / Одес. нац. технол. ун-т; гол. ред. Л. В. Іванченкова. – Одеса, 2023. – С. 55-57: рис. – Бібліогр.: 3 назв
REPLICA-SYMMETRY BREAKING IN NEURAL NETWORKS
No full textReplica-symmetry breaking is studied in fully connected neural networks with modified pseudo-inverse interactions. The interaction matrix has an intermediate form between the Hebb learning rule and the pseudo-inverse one. At low temperature there is a region of parameters where the replica-symmetric solution is stable while its entropy is negative. It indicates the existence of the alternative solution in which the replica symmetry is broken. A one-step replica-symmetry breaking solution is found and its properties are analyzed
The associative filtration of the dendriform operad
No full textThe associative filtration of the dendriform operad Norah Mohammed Alghamdi A dendriform algebra is a vector space V with two binary operations denoted that satisfy the following three algebraic properties for all elements a1, a2, a3 of V : (a1 > a2) (a2 a3), (a1 a2) > a3 = a1 > (a2 > a3). It is well known that the sum of the two operations in any dendriform algebra, the operation a1 ?a2 = a1 a2, is always associative. We consider the filtration of the nonsymmetric operad Dend by powers of the ideal generated by this associative operation, and the associated graded operad. For pre-Lie algebras, a similar question was considered in a recent paper of Dotsenko, where the associated graded operad was related to the so called F-manifolds. Similarly to the pre-Lie case, the associated graded operad of the dendriform operad turns out to be presented by quadratic and cubic relations. However, the cubic relations have more complicated structure than the ones found by Dotsenko in the pre-Lie case, so his approach is not applicable. However, we were able to make more use of operadic Gröbner bases than it is possible in the pre-Lie case, leading to a complete description of the associated graded operad
MODIFIED PSEUDO-INVERSE NEURAL NETWORKS STORING CORRELATED PATTERNS
No full textNeural networks with symmetric couplings which have an intermediate form between the Hebb learning rule and the pseudo-inverse one, storing strongly correlated patterns, are studied. Signal-to-noise analysis is made and replica-symmetric thermodynamic Calculations are performed. Both approaches show that both in the Hopfield model limit and in the Pseudo-inverse model limit the maximal capacity of the order of (2p/In(1/p)-1 (where p << 1 is the average neural activity) can be achieved by appropriate adjustment of the threshold term of the Hamiltonian
Combinatorics, homotopy, and embedding of operads
No full textLes opérades algébriques sont un outil algébrique permettant d’encoder certaines variétés d’algèbres non-nécessairement associatives, comme les algèbres de Lie ou les algèbres pre-Lie. De plus, les opérades algébriques peuvent elles-mêmes être vues comme des algèbres dans une catégorie bien choisie. Cette remarque permet l’étude des opérades via les puissants outils de l’algèbre homologique. En parallèle, la catégorie monoïdale telle que les objets en monoïde de cette catégorie sont les opérades est la catégorie des espèces combinatoires munie du pléthysme. Cela permet d’adopter un point de vue très combinatoire sur les opérades donnant ainsi des descriptions très explicites des objets considérés. Ces deux approches synergisent très bien ensemble et cette thèse se concentrera sur l'interaction entre ces deux points de vue. En effet, nous utiliserons des outils homotopiques tels que la dualité de Koszul opéradique pour obtenir des informations combinatoires sur les opérades que nous étudions. Nous utilisons ensuite celles-ci pour obtenir des descriptions combinatoires permettant d'effectuer des calculs explicites. Cette thèse est divisée en trois parties. La première partie est une introduction à la théorie des espèces. Ensuite, nous donnons une introduction à la théorie des opérades algébriques et à la dualité de Koszul opéradique. Enfin, nous calculons certaines descriptions combinatoires d’opérades, et les appliquons pour prouver une conjecture de Dotsenko sur un plongement de l'opérade encodant la structure algébrique sur le champ de vecteurs des variétés de Frobenius.Algebraic operads are an algebraic tool for encoding some varieties of algebras, not necessarily associative, such as Lie algebras or pre-Lie algebras. Moreover, algebraic operads can themselves be viewed as algebras in a well-chosen category. This observation allows the study of operads using the powerful tools of homological algebra. Simultaneously, the monoidal category where the monoid objects are operads is the category of combinatorial species equipped with plethysm. This enables a very combinatorial perspective on operads, providing explicit descriptions of the considered objects. These two approaches synergize well together, and this thesis will focus on the interaction between these two viewpoints. Indeed, we will use homotopical tools such as operadic Koszul duality to obtain combinatorial information on the operads we study. We then use this information to derive combinatorial descriptions that allow for explicit computations. This thesis is divided into three parts. The first part is an introduction to the theory of species. Next, we provide an introduction to the theory of algebraic operads and operadic Koszul duality. Finally, we compute descriptions of operads and apply them to prove a conjecture by Dotsenko on embedding the operad encoding the algebraic structure on the vector field of Frobenius manifolds
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