BIUP3: Boundary Topological Invariant of 3D Objects Through Front Propagation at a Constant Speed

Topological features constitute the highest abstraction in object representation. Euler characteristic is one of the most widely used topological invariants. The computation of the Euler characteristic is mainly based on three well-known mathematical formulae, which calculate either on the boundary of object or on the whole object. However, as digital objects are often non-manifolds, none of the known formulae can correctly compute the genus of digital surfaces. In this paper, we show that a new topological surface invariant of 3D digital objects, called BIUP/sup 3/, can be obtained through a special homeomorphic transform: front propagation at a constant speed. BIUP/sup 3/ overcomes the theoretic weakness of the Euler characteristic and it applies to both manifolds and non-manifolds. The computation of BIUP/sup 3/ can be done efficiently through a virtual front propagation, leaving the images unaffected

Efficient computation of the Euler-Kronecker constants of prime cyclotomic fields

We introduce a new algorithm, which is faster and requires less computing resources than the ones previously known, to compute the Euler-Kronecker constants $\mathfrak{G}_q$ for the prime cyclotomic fields $\mathbb{Q}(\zeta_q)$, where $q$ is an odd prime and $\zeta_q$ is a primitive $q$-root of unity. With such a new algorithm we evaluated $\mathfrak{G}_q$ and $\mathfrak{G}_q^+$, where $\mathfrak{G}_q^+$ is the Euler-Kronecker constant of the maximal real subfield of $\mathbb{Q}(\zeta_q)$, for some very large primes $q$ thus obtaining two new negative values of $\mathfrak{G}_q$: $\mathfrak{G}_{9109334831}= -0.248739\dotsc$ and $\mathfrak{G}_{9854964401}= -0.096465\dotsc$ We also evaluated $\mathfrak{G}_q$ and $\mathfrak{G}^+_q$ for every odd prime $q\le 10^6$, thus enlarging the size of the previously known range for $\mathfrak{G}_q$ and $\mathfrak{G}^+_q$. Our method also reveals that difference $\mathfrak{G}_q - \mathfrak{G}^+_q$ can be computed in a much simpler way than both its summands, see Section 3.4. Moreover, as a by-product, we also computed $M_q=\max_{\chi\ne \chi_0} \vert L^\prime/L(1,\chi) \vert$ for every odd prime $q\le 10^6$, where $L(s,\chi)$ are the Dirichlet $L$-functions, $\chi$ run over the non trivial Dirichlet characters mod $q$ and $\chi_0$ is the trivial Dirichlet character mod $q$. As another by-product of our computations, we will also provide more data on the generalised Euler constants in arithmetic progressions. The programs used to performed the computations here described and the numerical results obtained are available at the following web address: \url{http://www.math.unipd.it/~languasc/EK-comput.html}.Comment: 25 pages, 6 tables, 4 figures. Third known example of negative values for Ek(q) inserted. Complete set of computation of Ek(q) and Ek(q)^+ for every prime up to 10^6; computation of max|L'/L(1,chi)| for the same primes inserted. Two references added, typos correcte

A mathematical model for Tsunami generation using a conservative velocity-pressure hyperbolic system

By using the Hugoniot curve in detonics as a Riemann invariant of a velocity-pressure model, we get a conservative hyperbolic system similar to the Euler equations. The only differences are the larger value of the adiabatic constant (= 8.678 instead of 1.4 for gas dynamics) and the mass density replaced by a strain density depending on the pressure. The model is not homogeneous since it involves a gravity and a friction term. After the seismic wave reaches up the bottom of the ocean, one gets a pressure wave propagating toward the surface, which is made of a frontal shock wave followed by a regular decreasing profile. Since this regular profile propagates faster than the frontal shock waves, the amplitude of the pressure wave is strongly reduced when reaching the surface. Only in the case of a strong earth tremor the residual pressure wave is still sufficient to generate a water elevation with a sufficient wavelengths enable to propagate as a SaintVenant water wave and to become a tsunami when reaching the shore. We describe the construction of the model and the computation of the wave profile and discuss about the formation or not of a wave

Influence of interfacial force models and population balance models on the kLa value in stirred bioreactors

Optimal oxygen supply is vitally important for the cultivation of aerobically growing cells, as it has a direct influence on cell growth and product formation. A process engineering parameter directly related to oxygen supply is the volumetric oxygen mass transfer coefficient kLa. It is the influences on kLa and computing time of different interfacial force and population balance models in stirred bioreactors that have been evaluated in this study. For this investigation, the OpenFOAM 7 open-source toolbox was utilized. Firstly, the Euler–Euler model with a constant bubble diameter was applied to a 2L scale bioreactor to statistically examine the influence of different interfacial models on the kLa value. It was shown that the kL model and the constant bubble diameter have the greatest influence on the calculated kLa value. To eliminate the problem of a constant bubble diameter and to take effects such as bubble breakup and coalescence into account, the Euler–Euler model was coupled with population balance models (PBM). For this purpose, four coalescence and five bubble breakup models were examined. Ultimately, it was established that, for all of the models tested, coupling computational fluid dynamics (CFD) with PBM resulted in better agreement with the experimental data than using the Euler–Euler model. However, it should be noted that the higher accuracy of the PBM coupled models requires twice the computation time

Modelling and Experimental Evaluation of a Static Balancing Technique for a new Horizontally Mounted 3-UPU Parallel Mechanism

This paper presents the modelling and experimental evaluation of the gravity compensation of a horizontal 3-UPU parallel mechanism. The conventional Newton-Euler method for static analysis and balancing of mechanisms works for serial robots; however, it can become computationally expensive when applied to the analysis of parallel manipulators. To overcome this difficulty, in this paper we propose an approach, based on a Lagrangian method, that is more efficient in terms of computation time. The derivation of the gravity compensation model is based on the analytical computation of the total potential energy of the system at each position of the end-effector. In order to satisfy the gravity compensation condition, the total potential energy of the system should remain constant for all of the manipulator's configurations. Analytical and mechanical gravity compensation is taken into account, and the set of conditions and the system of springs are defined. Finally, employing a virtual reality environment, some experiments are carried out and the reliability and feasibility of the proposed model are evaluated in the presence and absence of the elastic components

Data-Oblivious Graph Algorithms in Outsourced External Memory

Motivated by privacy preservation for outsourced data, data-oblivious external memory is a computational framework where a client performs computations on data stored at a semi-trusted server in a way that does not reveal her data to the server. This approach facilitates collaboration and reliability over traditional frameworks, and it provides privacy protection, even though the server has full access to the data and he can monitor how it is accessed by the client. The challenge is that even if data is encrypted, the server can learn information based on the client data access pattern; hence, access patterns must also be obfuscated. We investigate privacy-preserving algorithms for outsourced external memory that are based on the use of data-oblivious algorithms, that is, algorithms where each possible sequence of data accesses is independent of the data values. We give new efficient data-oblivious algorithms in the outsourced external memory model for a number of fundamental graph problems. Our results include new data-oblivious external-memory methods for constructing minimum spanning trees, performing various traversals on rooted trees, answering least common ancestor queries on trees, computing biconnected components, and forming open ear decompositions. None of our algorithms make use of constant-time random oracles.Comment: 20 page

A Note on the Rotationally Symmetric SO(4) Euler Rigid Body

We consider an SO(4) Euler rigid body with two 'inertia momenta' coinciding. We study it from the point of view of bihamiltonian geometry. We show how to algebraically integrate it by means of the method of separation of variables.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Symbolic Computation of Conservation Laws of Nonlinear Partial Differential Equations in Multi-dimensions

A direct method for the computation of polynomial conservation laws of polynomial systems of nonlinear partial differential equations (PDEs) in multi-dimensions is presented. The method avoids advanced differential-geometric tools. Instead, it is solely based on calculus, variational calculus, and linear algebra. Densities are constructed as linear combinations of scaling homogeneous terms with undetermined coefficients. The variational derivative (Euler operator) is used to compute the undetermined coefficients. The homotopy operator is used to compute the fluxes. The method is illustrated with nonlinear PDEs describing wave phenomena in fluid dynamics, plasma physics, and quantum physics. For PDEs with parameters, the method determines the conditions on the parameters so that a sequence of conserved densities might exist. The existence of a large number of conservation laws is a predictor for complete integrability. The method is algorithmic, applicable to a variety of PDEs, and can be implemented in computer algebra systems such as Mathematica, Maple, and REDUCE.Comment: To appear in: Thematic Issue on ``Mathematical Methods and Symbolic Calculation in Chemistry and Chemical Biology'' of the International Journal of Quantum Chemistry. Eds.: Michael Barnett and Frank Harris (2006