Search Results (13)

Fiber orientation is an important descriptor of the microstructure for short fiber polymer composite materials where accurate and efficient prediction of the orientation state is crucial when evaluating the bulk thermo-mechanical response of the material. Macroscopic fiber orientation models employ the moment-tensor form in representing the fiber orientation state, and they all require a closure approximation for the higher-order orientation tensors. In addition, various models have more recently been developed to account for rotary diffusion due to fiber-fiber and fiber-matrix interactions which can now more accurately simulate the experimentally observed slow fiber kinematics in polymer composite processing. It is common to use explicit numerical initial value problem-ordinary differential equation (IVP-ODE) solvers such as the 4th- and 5th-order Dormand Prince Runge–Kutta (RK45) method to predict the transient and steady-state fiber orientation response. Here, we propose a computationally efficient method based on the Newton-Raphson (NR) iterative technique for determining steady state orientation tensor values by evaluating exact derivatives of the moment-tensor evolution equation with respect to the independent components of the orientation tensor. We consider various existing macroscopic-fiber orientation models and several closure approximations to ensure the robustness and reliability of the method. The performance and stability of the approach for obtaining physical solutions in various homogeneous flow fields is demonstrated through several examples. Validation of our orientation tensor exact derivatives is performed by benchmarking with results of finite difference techniques. Overall, our results show that the proposed NR method accurately predicts the steady state orientation for all tensor models, closure approximations and flow types considered in this paper and was relatively faster compared to the RK45 method. The NR convergence and stability behavior was seen to be sensitive to the initial orientation tensor guess value, the fiber orientation tensor model type and complexity, the flow type and extension to shear rate ratio. Full article

Pediatric dentistry requires different professional knowledge and skills, including technical and analytical thinking skills, essential for deep clinical reasoning. To analyze the students’ awareness of their cognitive processes when solving clinical problems, a qualitative and inductive study with second and fifth year students in the Degree Course in Dentistry and Dental Prosthetics at the University of Verona was conducted. Adopting a phenomenological approach, it focused on participants’ lived experiences, gathering their reflections on solving clinical problems through two structured questions. The data, analyzed using content analysis, revealed that sometimes students focused on operational steps rather than reflecting on them, and underscored the necessity of innovating university teaching methods to enhance reflective moments. To respond to this need, a literature review was conducted, underscoring the value of active learning in innovating dentistry education. Accordingly, a game-based learning activity was elaborated: a dental-themed adaptation of the games where you guess an image without using certain predetermined words. Its goal is to create an interactive and engaging environment that facilitates sharing and reflection, challenging students to apply their competencies to practical scenarios. Finally, our research identified students’ educational needs to develop teaching strategies that shape their reflective process in clinical reasoning so as to be more deliberate and conscious. Full article

Using majorization theory via “Robin Hood” elementary operations, optimal lower and upper bounds are derived on Rényi and guessing entropies with respect to either error probability (yielding reverse-Fano and Fano inequalities) or total variation distance to the uniform (yielding reverse-Pinsker and Pinsker inequalities). This gives a general picture of how the notion of randomness can be measured in many areas of computer science. Full article

This paper establishes a close relationship among the four information theoretic problems, namely Campbell source coding, Arikan guessing, Huleihel et al. memoryless guessing and Bunte and Lapidoth tasks’ partitioning problems in the IID-lossless case. We first show that the aforementioned problems are mathematically related via a general moment minimization problem whose optimum solution is given in terms of Renyi entropy. We then propose a general framework for the mismatched version of these problems and establish all the asymptotic results using this framework. The unified framework further enables us to study a variant of Bunte–Lapidoth’s tasks partitioning problem which is practically more appealing. In addition, this variant turns out to be a generalization of Arıkan’s guessing problem. Finally, with the help of this general framework, we establish an equivalence among all these problems, in the sense that, knowing an asymptotically optimal solution in one problem helps us find the same in all other problems. Full article

Conditional nonlinear optimal perturbation (CNOP) represents the initial perturbation that satisfies a certain physical constraint condition, and leads to a maximum prediction error at the moment of prediction. The CNOP method is a useful tool in studying atmosphere and ocean predictability problems. Generally, the optimization algorithm based on the gradient of the cost function to compute CNOP requires an initial guess. The traditional scheme randomly chooses the initial guess of CNOP within the constraint range and therefore this scheme is called RIG-CNOP. However, the RIG-CNOP scheme reduces the probability of capturing the global CNOP in many cases, such as the prediction model is strongly nonlinear or long-term prediction is performed, or multiple extreme values existed in the cost function. Considering the limitations of the RIG-CNOP scheme, we propose a new initial guess selection scheme. In this scheme, we first pre-analyze a series of random initial guesses, and then, an optimal initial guess is selected. The above process replaces the initial guess selection scheme in the traditional scheme, which is called PAIG-CNOP. Numerical experiments are conducted utilizing the Lorenz-63 model. Also, to compare the performance of the PAIG-CNOP method with the RIG-CNOP method in capturing global CNOP, the CNOP and the maximum cost function value (MCFV) obtained by the filtering method (FM) are used as benchmarks (this value is called FMMCFV in brief). The experimental results show that even the prediction model is strongly nonlinear or the prediction time is long, or the cost function has multiple extreme values, the PAIG-CNOP method can capture the global CNOP with a high probability. The results show that the PAIG-CNOP method has a higher probability of capturing the global CNOP than the RIG-CNOP method. In addition, we use an ensemble-based technique in the computation of gradients, thus avoiding the use of adjoint techniques in the maximization process. Due to the attractive features of the new method, the PAIG-CNOP method is an efficient and useful method for solving CNOP, it can be more easily applied to obtain the global CNOP of operational prediction models. Full article

Applications of a novel time-integration technique to the non-linear and linear dynamics of mechanical structures are presented, using an extended Picard-type iteration. Explicit discrete-mechanics approximations are taken as starting guess for the iteration. Iteration and necessary symbolic operations need to be performed only before time-stepping procedure starts. In a previous investigation, we demonstrated computational advantages for free vibrations of a hanging pendulum. In the present paper, we first study forced non-linear vibrations of a tower-like mechanical structure, modeled by a standing pendulum with a non-linear restoring moment, due to harmonic excitation in primary parametric vertical resonance, and due to excitation recordings from a real earthquake. Our technique is realized in the symbolic computer languages Mathematica and Maple, and outcomes are successfully compared against the numerical time-integration tool NDSolve of Mathematica. For out method, substantially smaller computation times, smaller also than the real observation time, are found on a standard computer. We finally present the application to free vibrations of a hanging double pendulum. Excellent accuracy with respect to the exact solution is found for comparatively large observation periods. Full article

Stationary memoryless sources produce two correlated random sequences $X^n$ and $Y^n$. A guesser seeks to recover $X^n$ in two stages, by first guessing $Y^n$ and then $X^n$. The contributions of this work are twofold: (1) We characterize the least achievable exponential growth rate (in n) of any positive $\rho$-th moment of the total number of guesses when $Y^n$ is obtained by applying a deterministic function f component-wise to $X^n$. We prove that, depending on f, the least exponential growth rate in the two-stage setup is lower than when guessing $X^n$ directly. We further propose a simple Huffman code-based construction of a function f that is a viable candidate for the minimization of the least exponential growth rate in the two-stage guessing setup. (2) We characterize the least achievable exponential growth rate of the $\rho$-th moment of the total number of guesses required to recover $X^n$ when Stage 1 need not end with a correct guess of $Y^n$ and without assumptions on the stationary memoryless sources producing $X^n$ and $Y^n$. Full article

In this paper, the predictive power of diffracxtive magneto-optics concerning domain structure and reversal mechanisms in ordered arrays of magnetic elements is demonstrated. A simple theoretical model based on Fraunhoffer diffraction theory is used to predict the magnetisation reversal mechanisms in an array of magnetic elements. Different domain structures and simplified models (or educated guesses) of the associated reversal mechanisms produce marked differences in the spatial distributions of the magnetisation. These differences and the associated magnetisation distribution moments are experimentally accessible through conventional and diffractive magneto-optical Kerr effect measurements. The domain and magnetisation reversal predictions are corroborated with Magnetic Force Microscopy (MFM) measurements. Full article

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for quantities that involve expectations of the logarithm of a positive random variable. Here, in the same spirit, we derive an exact integral representation (in one or two dimensions) of the moment of a nonnegative random variable, or the sum of such independent random variables, where the moment order is a general positive non-integer real (also known as fractional moments). The proposed formula is applied to a variety of examples with an information-theoretic motivation, and it is shown how it facilitates their numerical evaluations. In particular, when applied to the calculation of a moment of the sum of a large number, n, of nonnegative random variables, it is clear that integration over one or two dimensions, as suggested by our proposed integral representation, is significantly easier than the alternative of integrating over n dimensions, as needed in the direct calculation of the desired moment. Full article

What is the value of just a few bits to a guesser? We study this problem in a setup where Alice wishes to guess an independent and identically distributed (i.i.d.) random vector and can procure a fixed number of k information bits from Bob, who has observed this vector through a memoryless channel. We are interested in the guessing ratio, which we define as the ratio of Alice’s guessing-moments with and without observing Bob’s bits. For the case of a uniform binary vector observed through a binary symmetric channel, we provide two upper bounds on the guessing ratio by analyzing the performance of the dictator (for general $k\ge 1$ ) and majority functions (for $k=1$ ). We further provide a lower bound via maximum entropy (for general $k\ge 1$ ) and a lower bound based on Fourier-analytic/hypercontractivity arguments (for $k=1$ ). We then extend our maximum entropy argument to give a lower bound on the guessing ratio for a general channel with a binary uniform input that is expressed using the strong data-processing inequality constant of the reverse channel. We compute this bound for the binary erasure channel and conjecture that greedy dictator functions achieve the optimal guessing ratio. Full article

Two correlated sources emit a pair of sequences, each of which is observed by a different encoder. Each encoder produces a rate-limited description of the sequence it observes, and the two descriptions are presented to a guessing device that repeatedly produces sequence pairs until correct. The number of guesses until correct is random, and it is required that it have a moment (of some prespecified order) that tends to one as the length of the sequences tends to infinity. The description rate pairs that allow this are characterized in terms of the Rényi entropy and the Arimoto–Rényi conditional entropy of the joint law of the sources. This solves the guessing analog of the Slepian–Wolf distributed source-coding problem. The achievability is based on random binning, which is analyzed using a technique by Rosenthal. Full article

This paper provides tight bounds on the Rényi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one to one. To that end, a tight lower bound on the Rényi entropy of a discrete random variable with a finite support is derived as a function of the size of the support, and the ratio of the maximal to minimal probability masses. This work was inspired by the recently published paper by Cicalese et al., which is focused on the Shannon entropy, and it strengthens and generalizes the results of that paper to Rényi entropies of arbitrary positive orders. In view of these generalized bounds and the works by Arikan and Campbell, non-asymptotic bounds are derived for guessing moments and lossless data compression of discrete memoryless sources. Full article

A new approach to the many-electron correlation problem, termed the method of moments of coupled-cluster equations (MMCC), is further developed and tested. The main idea of the MMCC theory is that of the noniterative energy corrections which, when added to the energies obtained in the standard coupled-cluster calculations, recover the exact (full configuration interaction) energy. The MMCC approximations require that a guess is provided for the electronic wave function of interest. The idea of using simple estimates of the wave function, provided by the inexpensive configuration interaction (CI) methods employing small sets of active orbitals to define higher–than–double excitations, is tested in this work. The CI-corrected MMCC methods are used to study the single bond breaking in HF and the simultaneous breaking of both O–H bonds in H₂O. Full article