An efficient secure sum of multi-scalar products protocol base on elliptic curve

The secure scalar product protocol is widely applied to solve practical problems such as privacy-preserving data mining, secure auction, secure electronic voting, privacy-preserving recommendation system, privacy-preserving statistical data analysis, etc.. In this paper, we propose an efficient multi-party secure computation protocol using Elliptic curve cryptography, which allows to compute the sum value of multi-scalar products without revealing about the input vectors. Moreover, theoretical and experimental analysis shows that the proposed method is more efficient than others in both computation and communication.

Recurrence relations for off-shell Bethe vectors in trigonometric integrable models

The zero modes method is applied in order to get action of the monodromy matrix entries onto off-shell Bethe vectors in quantum integrable models associated with $U_q(\mathfrak{gl}_N)$-invariant $\RR$-matrices. The action formulas allowto get recurrence relations for off-shell Bethe vectors and for highest coefficients of the Bethe vectors scalar product.

Optimal recovery of operator sequences

In this paper we solve two problems of optimal recovery based on information given with an error. First is the problem of optimal recovery of the class $W^T_q = \{(t_1h_1,t_2h_2,\ldots)\,\colon \,\|h\|_{\ell_q}\le 1\}$, where $1\le q < \infty$ and $t_1\ge t_2\ge \ldots \ge 0$ are given, in the space $\ell_q$. Information available about a sequence $x\in W^T_q$ is provided either (i) by an element $y\in\mathbb{R}^n$, $n\in\mathbb{N}$, whose distance to the first $n$ coordinates $\left(x_1,\ldots,x_n\right)$ of $x$ in the space $\ell_r^n$, $0 < r \le \infty$, does not exceed given $\varepsilon\ge 0$, or (ii) by a sequence $y\in\ell_\infty$ whose distance to $x$ in the space $\ell_r$ does not exceed $\varepsilon$. We show that the optimal method of recovery in this problem is either operator $\Phi^*_m$ with some $m\in\mathbb{Z}_+$ ($m\le n$ in case $y\in\ell^n_r$), where \smallskip\centerline{$\displaystyle \Phi^*_m(y) = \Big\{y_1\left(1 - \frac{t_{m+1}^q}{t_{1}^q}\Big),\ldots,y_m\Big(1 - \frac{t_{m+1}^q}{t_{m}^q}\Big),0,\ldots\right\},\quad y\in\mathbb{R}^n\text{ or } y\in\ell_\infty,$} \smallskip\noior convex combination $(1-\lambda) \Phi^*_{m+1} + \lambda\Phi^*_{m}$. The second one is the problem of optimal recovery of the scalar product operator acting on the Cartesian product $W^{T,S}_{p,q}$ of classes $W^T_p$ and $W^S_q$, where $1 < p,q < \infty$, $\frac{1}{p} + \frac{1}{q} = 1$ and $s_1\ge s_2\ge \ldots \ge 0$ are given. Information available about elements $x\in W^T_p$ and $y\in W^S_q$ is provided by elements $z,w\in \mathbb{R}^n$ such that the distance between vectors $\left(x_1y_1, x_2y_2,\ldots,x_ny_n\right)$ and $\left(z_1w_1,\ldots,z_nw_n\right)$ in the space $\ell_r^n$ does not exceed $\varepsilon$. We show that the optimal method of recovery is delivered either by operator $\Psi^*_m$ with some $m\in\{0,1,\ldots,n\}$, where \smallskip\centerline{$\displaystyle \Psi^*_m = \sum_{k=1}^m z_kw_k\Big(1 - \frac{t_{m+1}s_{m+1}}{t_ks_k}\Big),\quad z,w\in\mathbb{R}^n,$} \smallskip\noior by convex combination $(1-\lambda)\Psi^*_{m+1} + \lambda\Psi^*_{m}$. As an application of our results we consider the problem of optimal recovery of classes in Hilbert spaces by the Fourier coefficients of its elements known with an error measured in the space $\ell_p$ with $p > 2$.

A Covariant Cauchy-Schwartz Measure’s Bounding Conditions to BSM Searches

Solving for the missing masses in the Higgs resonances, it was necessary to extend, even quantitatively via an index measurable amount, the SM using a threshold related longitudinal violation procedure. The obtained expression, by being non-contributing via its non-anomalously resulting parameter, is linked to a Cauchy-Schwartz 4-scalar product ratio type of two virtual Gauge Bosons momenta in its minimal anomalous configuration, as vs. its non-anomalous internal. Changing the bounds from energy into momenta, a convexity condition appears. Such technique clarifies the perturbative e.m. fields’ extensions into perturbative and non-perturbative QCD.In applications, there is the violation of the chiral insertion by the axion into neutrinos, and the Lepton number when passing form velocity to spin resonances, such confirming the CS procedure as plus the defiance of the SM comes through their branching ratios but not their angular distributions. Further which if remaining at the same level of minimization can restore the universality of extendibility in the Higgs self-couplings.Leading into deriving the phase of K0 → π+π-, in A(∆1=2)/A(∆1=0) so a conformal skipping dynamical shift from direct CP violation of D0 → K+K- and D0 → π+π- asymmetries, in the long-short mixing concords the phase of KL → π0ννbar, solving the KOTO anomaly.

Some Resultats on Optimal Allocation of Policy Limits and Deductibles: Mixture Model

The main purpose of this paper is to introduce and investigate stochastic orders of scalar products of random vectors. We study the problem of finding maximal expected utility for some functional on insurance portfolios involving some additional (independent) randomization. Furthermore, applications in policy limits and deductible are obtained, we consider the scalar product of two random vectors which separates the severity effect and the frequency effect in the study of the optimal allocation of policy limits and deductibles. In that respect, we obtain the ordering of the optimal allocation of policy limits and deductibles when the dependence structure of the losses is unknown. Our application is a further study of [1 − 6].

The basic architecture of mobile robotic platform with intelligent motion control system and data transmission protection

The requirements for a mobile robotic platform (MRP) with an intelligent traffic control system and data transmission protection are determined. Main requirements are the reduction of dimensions, energy consumption, and cost; remote and intelligent autonomous traffic control; real-time cryptographic data protection; preservation of working capacity in the conditions of action of external factors; adaptation to customer requirements; ability to perform tasks independently in conditions of uncertainty of the external environment. It is proposed to develop a mobile robotic platform based on an integrated approach including: navigation methods, methods of pre-processing and image recognition; modern methods and algorithms of intelligent control, artificial neural networks, and fuzzy logic; neuro-like methods of cryptographic data transmission protection; modern components and modern element base; methods of intellectual processing and evaluation of data from sensors in the conditions of interference and incomplete information; methods and means of automated design of MRP hardware and software. The following principles were chosen for the development of a mobile robotic platform with an intelligent control system and cryptographic protection of data transmission: hierarchical construction of an intelligent control system; systematicity; variable composition of equipment; modularity; software openness; compatibility; specialization and adaptation of hardware and software to the structure of algorithms for data processing and protection; use of a set of basic design solutions. The basic architecture of a mobile robotic platform with an intelligent traffic control system and data transmission protection has been developed, which is the basis for the construction of mobile robotic platforms with specified technical and operational parameters. To implement neuro-like tools, the method of tabular-algorithmic calculation of the scalar product was improved, which due to the simultaneous formation of k macroparticle products provides k times reduction of the time of the scalar product calculation. Keywords: mobile robotic platform; intelligent processing; architecture; neural network; autonomous control; sensors; data protection.

Co-Homology of Differential Forms and Feynman Diagrams

In the present review we provide an extensive analysis of the intertwinement between Feynman integrals and cohomology theories in light of recent developments. Feynman integrals enter in several perturbative methods for solving non-linear PDE, starting from Quantum Field Theories and including General Relativity and Condensed Matter Physics. Precision calculations involve several loop integrals and an onec strategy to address, which is to bring them back in terms of linear combinations of a complete set of integrals (the master integrals). In this sense Feynman integrals can be thought as defining a sort of vector space to be decomposed in term of a basis. Such a task may be simpler if the vector space is endowed with a scalar product. Recently, it has been discovered that, if these spaces are interpreted in terms of twisted cohomology, the role of a scalar product is played by intersection products. The present review is meant to provide the mathematical tools, usually familiar to mathematicians but often not in the standard baggage of physicists, such as singular, simplicial and intersection (co)homologies, and hodge structures, that are apt to restate this strategy on precise mathematical grounds. It is intended to be both an introduction for beginners interested in the topic, as well as a general reference providing helpful tools for tackling the several still-open problems.

On electromagnetic radiation of individual charges

The aim of the study is to establish the conditions for synchrotron radiation based on significant differences between tangential and centripetal accelerations of electric charges. From the fact that electromagnetic radiation carries away energy, it follows that the energy of the radiating system changes during radiation. Related to this is the following well-known rule: a change in energy is equal to work done. Three relevant theorems are proved. Theorem 1 states that a tangentially accelerated electric charge emits electromagnetic waves. Theorem 2 states that a normally accelerated electric charge does not emit electromagnetic waves. It is a well-known circumstance that the centripetal force does not perform work (since the scalar product of orthogonal vectors must be equal to zero). The proofs of Theorems 1 and 2 are performed in terms of forces. For electric charges, the transition to the terms of accelerations is carried out in accordance with Theorem 3which states that an electric charge satisfies Newton's second law. The tangential acceleration of an electric charge leads to the emission of electromagnetic waves. Generalization of the phenomenon of radiation to acceleration in general, including. normal charge acceleration, is false. The cause of synchrotron radiation should be sought in the tangential acceleration due to Coulomb interactions between the beam charges.

Invariant Scalar Product and Associated Structures for Tachyonic Klein–Gordon Equation and Helmholtz Equation

Although describing very different physical systems, both the Klein–Gordon equation for tachyons (m2<0) and the Helmholtz equation share a remarkable property: a unitary and irreducible representation of the corresponding invariance group on a suitable subspace of solutions is only achieved if a non-local scalar product is defined. Then, a subset of oscillatory solutions of the Helmholtz equation supports a unirrep of the Euclidean group, and a subset of oscillatory solutions of the Klein–Gordon equation with m2<0 supports the scalar tachyonic representation of the Poincaré group. As a consequence, these systems also share similar structures, such as certain singularized solutions and projectors on the representation spaces, but they must be treated carefully in each case. We analyze differences and analogies, compare both equations with the conventional m2>0 Klein–Gordon equation, and provide a unified framework for the scalar products of the three equations.