Form Of Sum Research Articles

Deriving reservoir operation rule based on Bayesian deep learning method considering multiple uncertainties

Reservoir operation rules play a key role in real-time reservoir operation; the main factors affecting operation decisions are the current reservoir status and the future inflows. However, the future reservoir inflows are stochastic and always contain uncertainty. To study the influence of inflow uncertainty on reservoir operation rules, this paper proposes a Bayesian Deep learning method that considers both model parameter uncertainty and inflow uncertainty. In the model, the Monte Carlo integration is used to convert the complex integrals of inflow probability into a summation form. Variational inference is employed to obtain the posterior distribution of model parameters. The proposed method is applied to a real-world application at Three Gorges Project on the Yangtze River. The uncertainty estimation results show that the influence of inflow uncertainty on reservoir operation rule is greater than model parameter uncertainty, and the decision of reservoir operation is more sensitive to the reservoir inflow during dry season than other seasons. The experimental results demonstrate that the proposed Bayesian deep learning performs better than the comparison method in term of hydropower generation and the root mean square errors. Moreover, the proposed method is more robust than the comparison method when considering the inflow uncertainty.

Integration by Parts in Differential Summation Form

In this paper, we establish general differential summation formulas for integration by parts (IBP), more importantly a powerful tool that promotes exploration and creativity.

The processing of compound radial frequency patterns

Radial frequency (RF) patterns can be combined to construct complex shapes. Previous studies have suggested that such complex shapes may be encoded by multiple, narrowly-tuned RF shape channels. To test this hypothesis, thresholds were measured for detection and discrimination of various combinations of two RF components. Results show evidence of summation: sensitivity for the compounds was better than that for the components, with little effect of the components’ relative phase. If both RF components are processed separately at the point of detection, they would combine by probability summation (PS), resulting in only a small increase in sensitivity for the compound compared to the components. Summation exceeding the prediction of PS suggests a form of additive summation (AS) by a common mechanism. Data were compared to predictions of winner-take-all, where only the strongest component contributes to detection, a single channel AS model, and multi-channel PS and AS models. The multi-channel PS and AS models were modelled under both Fixed and Matched Attention Window scenarios, the former assuming a single internal noise source for both components and compounds or different internal noise sources for components and compounds respectively. The winner-take-all and single channel models could be rejected. Of the remaining models, the best performing one was an AS model with a Fixed Attention Window, consistent with detection being mediated by channels that are efficiently combined and limited by a single source of noise for both components and compounds.

Integral u-deformed involution modules

Let (W,S) be a Coxeter system and ⁎ an automorphism of W with order ≤2 and S⁎=S. Lusztig and Vogan ([20], [23]) have introduced a u-deformed version Mu of Kottwitz's involution module over the Iwahori–Hecke algebra Hu(W) with Hecke parameter u2, where u is an indeterminate. Lusztig has proved that Mu is isomorphic to the left Hu(W)-submodule of Hˆu generated by X∅:=∑w⁎=w∈Wu−ℓ(w)Tw, where Hˆu is the vector space consisting of all formal (possibly infinite) sums ∑x∈WcxTx (cx∈Q(u) for each x). He speculated that one can extend this by replacing u with any λ∈C∖{0,1,−1}. In this paper, we give a positive answer to his speculation for any λ∈K∖{0,1,−1} and any W, where K is an arbitrary ground field.

Stability analysis of spinning missiles induced by seeker disturbance rejection rate parasitical loop

This paper focuses on the dynamic stability of spinning missiles equipped with two-loop autopilot considering the seeker disturbance rejection rate parasitical loop (DRRPL) effect induced by attitude disturbance of projectile. The representative mathematical model of spinning missiles in the non-spinning coordinate system is established, and the cross-coupling effect between the pitch and yaw induced by the rotation motion of missile body is analyzed and decoupled. The two-loop acceleration autopilot for each channel is designed with the conventional design method, and the relationship between the autopilot gains and the expected design indexes is deduced. A proportional navigation guidance (PNG) system model with consideration for the seeker DRRPL is further proposed in the form of complex summation. After strict mathematic deduction, the sufficient and necessary condition of the dynamic stability for spinning missiles is obtained. Numerical simulations and discussions under different cases are conducted to demonstrate the validity of stability condition. The results indicate that the stability of a spinning missile is closely related to the amplitude of the seeker DRR, the rolling rate, and the autopilot design indices. The stable region of the autopilot design frequency is obtained by solving the dynamic stability condition. To meet the requirement of stable controlling at a constant spinning rate, it was found to be effective to decrease the amplitude of the seeker DRR for spinning missiles, employ the lead angle decoupling approach to the commands for the servo system, and guarantee that the autopilot design frequency is lower than the critical value. The dynamic stability condition derived in this paper is useful for evaluating the stability of a spinning missile with consideration for the seeker DRRPL, and the conclusions obtained can provide guidance for the autopilot design of spinning missiles.

Coherent Interaction Graphs

We introduce the notion of coherent graphs, and show how those can be used to define dynamic semantics for Multiplicative Linear Logic (MLL) extended with non-determinism. Thanks to the use of a coherence relation rather than mere formal sums of non-deterministic possibilities, our model enjoys some finiteness and sparsity properties. We also show how studying the semantic types generated by a single "test" within our model of MLL naturally gives rise to a notion of proof net, which turns out to be exactly Retor\'e's R&B-cographs. This revisits the old idea that multplicative proof net correctness is interactive, with a twist: types are characterized not by a set of counter-proofs but by a single non-deterministic counter-proof.

On solving cycle-free context-free grammar equivalence problem using numerical analysis

Abstract In this paper we consider the problem of cycle-free context-free grammars equivalence. To every context-free grammar there corresponds a system of formal equations. Formally applying the iteration method to this system we obtain the grammar axiom in the form of a formal power series composed of the words generated by the grammar ”multiplied” by the respective ambiguities. We define a transform that attributes a matrix meaning to the system of formal equations and to formal power series: terminal symbols are substituted by matrices and formal sum and product are substituted by the matrix ones. In order to effectively compute the sum of a matrix series we numerically solve the system of matrix equations. We prove distinguishability theorems showing that if two formal power series generated by cycle-free context-free grammars are different, then there exists a matrix substitution such that the sums of the respective matrix series are different. Based on this result, we suggest a procedure that can resolve the problem of equivalence of cycle-free context-free grammars in many practical cases. The results obtained in this paper form a theoretical basis for algorithms oriented to automatic assessment of students’ answers in computer science. We present the respective algorithms. Then we compare our approach with a simple heuristic method based on CYK algorithm and discuss the limitations of our method.

The defining properties of the Kontsevich unoriented graph complex

Consider the real vector space of formal sums of non-empty, finite unoriented graphs without multiple edges and loops. Let the vertices of graphs be unlabelled but let every graph γ be endowed with an ordered set of edges E(γ). Denote by Gra the vector space of formal sums of graphs modulo the relation (γ1, E(γ1)) − sign(σ)(γ2, E(γ2)) = 0 for topologically equal graphs γ1 and γ2 whose edge orderings differ by a permutation σ. The zero class in Gra is represented by sums of graphs that cancel via the above relation. The Lie bracket of graphs with ordered edge sets is defined using the insertion of a graph into vertices of the other one. We give an explicit proof of the theorems which state that the space Gra is a well-defined differential graded Lie algebra: both the Lie bracket [⋅, ⋅] and the vertex-expanding differential d = respect the calculus modulo zero graphs.

PENGEMBANGAN BAHAN AJAR BERDASARKAN PENDEKATAN SAINTFIK UNTUK SISWA SMP NEGERI 2 SUNGAI LIMAU

Abstract Problems found in Sungai Limau 2 Public Elementary School toward teacher books and student books that researchers did still find material substance that is not in accordance with the 2013 curriculum. This research is research & development (R & D). This study aims to describe the feasibility of teaching materials in validity, effectiveness and practicality. Research and development is a research method used to develop or validate products used in education and learning. The development of teaching materials is based on the development of the ADDIE model (analysis, design, develop, implement and evaluation). First, the analysis phase is the first stage carried out by someone developing a learning module. Secondly, the design is based on what has been formulated in the analysis phase. Third, the development stage, namely the production stage, everything that has been made in the design stage is then realized. Fourth, the implementation phase is the implementation of the learning module that is ready for student use. Fifth, evaluation phase, which can be done in formative and summative forms. The results of the study show that short story text teaching materials based on the developed scientific approach are valid, practical, and effective.

EVALUATION IN THE EDUCATIONAL PROCESS

The necessity for evaluation occurs in relativly recent time, in order to determine the effectiveness of educational process in pupils. The evaluation in teaching process is carried out through assessment of written assigments, objective tasks and oral answers. The most common type of evaluation is summative form and in this type pupils learn only for grade, adjusting their learning to the criteria of individual teachers. The only motive for learning represents number (grade). Formative evaluation is not common or is present in a very small number of teachers. Summative grade does not provide students with feedback on how they are progressing, and in what way they could make progress. A grade does not have a prognostic, motivational and a diagnostic role,and various types of evaluation are not used. Reproductive knowledge which is not in function of education for life is not valued. The existing concept of education does not adjust teaching content to the need and abilities of pupils, therefore a functional knowledge which is a criteria for a qualitative education of pupils is not developed.

Constructing solutions to two-way diffusion problems

A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward–backward, type. In such problems boundary data are specified only on part of the boundary, which introduces several technical challenges. Existence and uniqueness theorems have been established in the literature under various assumptions; however, calculating solutions in practice has proven difficult. Here we present one possible means of practical calculation. By formulating the problem in terms of projection operators, we derive a formal sum for the solution whose terms are readily calculated. We demonstrate the validity of this approach for a variety of physical problems, with focus on a periodic problem from the field of active matter.

Distributed Decomposed Data Analytics in Fog Enabled IoT Deployments

The edge of the network plays a vital role in an Internet of Things (IoT) system, serving as an optimal site to perform an operation on data before transmitting it over the network. We present the fog-specific decomposition of multivariate linear regression as the predictive analytic model in our work using the statistical query model and summation form. The decomposition method used is not the contribution, but applying the decomposition method to the analytics model to run in a distributed manner in the fog-enabled IoT deployments is the contribution. What is novel is the decomposition made on a fog-based distributed setting. To test the performance, our proposed approach has been applied to a real-world dataset and evaluated using a fog computing testbed. The proposed method avoids sending raw data to the cloud and offers balanced computation in the infrastructure. The results show an 80% reduction in the amount of data transferred to the cloud using the proposed fog-based distributed data analytics approach compared with the conventional cloud-based approach. Furthermore, by adopting the proposed distributed approach, we observed a 98% drop in the time taken to arrive at the final result compared with the cloud-centric approach. We also present the results on the quality of analytics solution obtained in both approaches, and they suggest that the fog-based distributed analytics approach can serve as equally as the traditional cloud-centric approach.

THE FORMULA nCr REVISITED

A formula expressing nCr in summation form is formulated by the use of algorithmic counting techniques. Initially, a general counting problem is mathematically modeled and its solution is given by a formula derived using algorithmic counting. Thus, by generalization a formula for nCr as a series is obtained.

Developing Computer-Based Test (CBT) to Improve Students’ Achievement

This research aims to develop Computer-Based Test (CBT) by using hot potatoes software, which is believed to be able to improve students’ achievement. Formative and summative questions were previously given using paper only, making the questions presented less interactive, resulting in low achievement of the students. This new procedure was adapted from ADDIE Model (Analysis, Design, Development, Implementation, and Evaluation). The development of the model results in the creation of a package called Computer based Test-English Computer (CBT-EC) that contains 9 sub-packages, divided into two divisions. The first division is composed of 8 packages that contain formative tests, where as the second division consists of 1 package of summative tests. Data of this research were collected using tests and questionnaires. The test instrument used multiple choices with formative form consists of 15 questions from each chapter, while summative form consists of 120 questions. Students’ responses were measured by distributing the questionnaires about the usage of CBT-EC product to 10 students. The questionnaires were given to the media expert and material expert to assess their feasibility. The results showed that the expert of material gave 79 out of 84 maximum point, or almost excellent, meaning that the questionnaires developed as the product of CBT-EC are worth implemented. Meanwhile, the assessment of the media expert gave a score of 63 out of 68 maximum points classified as good, meaning that the CBT-EC product is feasible to be implemented. Based on learning result from the formative and summative test, there was an increase of the students' achievement. In formative test, the students got the average score of 69%, whereas in summative test they recorded average score of 79%. In conclusion, CBT-EC product could increase students’ achievement.

Multi-block Analysis of Genomic Data Using Generalized Canonical Correlation Analysis.

Recently, there have been many studies in medicine related to genetic analysis. Many genetic studies have been performed to find genes associated with complex diseases. To find out how genes are related to disease, we need to understand not only the simple relationship of genotypes but also the way they are related to phenotype. Multi-block data, which is a summation form of variable sets, is used for enhancing the analysis of the relationships of different blocks. By identifying relationships through a multi-block data form, we can understand the association between the blocks in comprehending the correlation between them. Several statistical analysis methods have been developed to understand the relationship between multi-block data. In this paper, we will use generalized canonical correlation methodology to analyze multi-block data from the Korean Association Resource project, which has a combination of single nucleotide polymorphism blocks, phenotype blocks, and disease blocks.

Groups whose proper Schur rings are commutative

A Schur ring [Formula: see text] is called Dedekind if the formal sum of every [Formula: see text]-subgroup is in the center of [Formula: see text]. In this paper, we find all finite groups [Formula: see text] such that every proper Schur ring over [Formula: see text] is Dedekind. As a corollary of our main theorem, we find all finite groups [Formula: see text] such that every proper Schur ring over [Formula: see text] is commutative.

Calibration and ranking of Valiantzas reference evapotranspiration equations under the humid climate of northeast India

Abstract This study aims to compare and calibrate seven different types of Valiantzas (Valiz) ET0 equations against FAO Penman–Monteith (P-M) equation at three sites under the humid climatic condition of northeast India. In the first stage, the different Valiantzas equations were ranked based on their original coefficient (OC) at each site. In the second stage, Valiz equations were assessed based on local calibrated coefficient (LCC). In the third stage, the selected Valiz equations were assessed based on global calibrated coefficient (GCC) considering pooled data for all the selected stations. The ranking of equations was done using a summative form of global positioning index (GPI). Different Valiantzas equations showed different performances relative to the sites having similar climate class (warm and temperate). With the OC, the Valiz 7 is ranked one at Dibrugarh and Shillong, and Valiz 2 for Aizawl. After local calibration, again, Valiz 7 is best at Dibrugarh and Shillong while Valiz 6 is best at Aizawl. With global calibration coefficient, Valiz 7 ranked best at all three selected stations. The suitable equations identified for the region are Valiz 7, Valiz 6 if full data are available, and Valiz 2 under limiting data conditions.

A canonical basis of two-cycles on a surface

We construct a basis of two-cycles on a surface; in this basis, the intersection form takes the canonical form . Elements of the basis are realized by formal sums of smooth submanifolds. Bibliography: 8 titles.

Distributed Network Center and Size Estimation

A fully distributed algorithm for estimating the center and the radius of the smallest sphere that contains a wireless sensor network is proposed. The center finding problem is formulated as a convex optimization problem in summation form by using a soft-max approximation to the maximum function. Diffusion adaptation method is used where states of nodes converge to the estimated center distributively. Then, distributed max consensus is used to compute the radius. The proposed algorithm is fully distributed in the sense that each node in the network only needs to know its own location and nodes do not need to be pre-labeled. The algorithm works for any connected graph structure. The performance of the proposed algorithm is analyzed and it is shown that there is a tradeoff: a larger design parameter results in a more accurate center estimation but also makes the convergence speed of the distributed algorithm slower. It is also shown that the proposed algorithm can also be used to estimate the center and radius of the (not necessarily location-based) data at sensor nodes in a distributed way, thereby providing information and insights about the global data at each sensor. Simulation results corroborating the theory are also provided.

Developing student-centered assessment for a postgraduate course designed for Basic Education Teachers

The Constructive Alignment theory, by Biggs, relies on students’ self-construction of meaning by relevant learning activities. To accomplish this goal, teachers have to align four essential elements: curriculum, Intended Learning Outcomes (ILOs), methodologies and assessment. In this paper, we describe an implementation of a constructively aligned postgraduate course on active learning methodologies for basic education teachers. The syllabus was comprised of four well-established active learning methods: Predict-Observe-Explain (POE), Peer Instruction (PI), Jigsaw and Six Thinking Hats (STH). Students had to plan, discuss in pairs, perform a real active lesson with their own pupils and observe and provide peer feedback to their colleague. Assessment was carried out as the following forms: self-reflection, active lesson plan, peer assessment and self-assessment and one summative form: active lesson report. Each assessment evaluated distinct skills related to both specifics ILOs and learning activities. The results reveal that aligned assessment fostered learning, encouraged self and peer reflection, improved teacher feedback and promoted an effective collaboration among students.