Search Results (6)

The article deals with the problem of calculating the volume calendar plan of a paper mill. The presented mathematical model and methods make it possible to schedule paper production orders between several paper machines (PM) to even their loading, devise cutting plans for each winder and arrange the order of their implementation. When forming cutting plans, orders are grouped in accordance with such parameters as grammage, roll diameter, core diameter, product type and number of layers. Deadlines and volumes in customer orders are taken into account. The cutting plans for each winder account for the allowable roll width limits and the maximum number of knives. To find the optimal schedule, a combination of the following criteria is used: minimal trim loss, minimal changes to the knives’ setup and smooth transitions by product grades. Solution algorithms are presented that use a combination of the simplex method, the column generation, the branch and bound methods, the greedy algorithm and the local search procedure. We tested the solution approach on real production data from a paper mill in European Russia and obtained the production sequence that better matches deadlines in customer orders compared to the plan devised manually by production planners. Full article

The study shows that the volumes and surfaces of n-balls, n-simplices, and n-orthoplices are holomorphic functions of n, which makes those objects omnidimensional, that is well defined in any complex dimension. Applications of these formulas to the omnidimensional polytopes inscribed in and circumscribed about n-balls reveal previously unknown properties of these geometric objects. In particular, for $0<n<1$, the volumes of the omnidimensional polytopes are larger than those of circumscribing n-balls, and both their volumes and surfaces are smaller than those of inscribed n-balls. The surface of an n-simplex circumscribing a unit diameter n-ball is spirally convergent to zero with real n approaching negative infinity but first has a local maximum at $n=-3.5$. The surface of an n-orthoplex circumscribing a unit diameter n-ball is spirally divergent with real n approaching negative infinity but first has a local minimum at $n=-1.5$, where its real and imaginary parts are equal to each other; similarly, is its volume, where the similar local minimum occurs at $n=-3.5$. Reflection functions for volumes and surfaces of these polytopes inscribed in and circumscribed about n-balls are proposed. Symmetries of products and quotients of the volumes in complex dimensions n and $-n$ and of the surfaces in complex dimensions n and $2-n$ are shown to be independent of the metric factor and the gamma function. Specific symmetries also hold between the volumes and surfaces in dimensions $n=-1/2$ and $n=1/2$. Full article

The existence of intra-class spectral variability caused by differential scene components and illumination conditions limits the improvement of endmember extraction accuracy, as most endmember extraction algorithms directly find pixels in the hyperspectral image as endmembers. This paper develops a quadratic clustering-based simplex volume maximization (CSVM) approach to effectively alleviate spectral variability and extract endmembers. CSVM first adopts spatial clustering based on simple linear iterative clustering to obtain a set of homogeneous partitions and uses spectral purity analysis to choose pure pixels. The average of the chosen pixels in each partition is taken as a representative endmember, which reduces the effect of local-scope spectral variability. Then an improved spectral clustering based on k-means is implemented to merge homologous representative endmembers to further reduce the effect of large-scope spectral variability, and final endmember collection is determined by the simplex with maximum volume. Experimental results show that CSVM reduces the average spectral angle distance on Samson, Jasper Ridge and Cuprite datasets to below 0.02, 0.06 and 0.09, respectively, provides the root mean square errors of abundance maps on Samson and Jasper Ridge datasets below 0.25 and 0.10, and exhibits good noise robustness. By contrast, CSVM provides better results than other state-of-the-art algorithms. Full article

The study aimed to define the ideal proportions of pseudocereal flours (PF) in sensory-accepted gluten-free bread (GFB) formulations. The characteristics of GFB developed with PF (amaranth, buckwheat, and quinoa) were verified through a mixture design and response surface methodology. Three simplex-centroid designs were studied to analyze the effects of each PF and their interactions with potato starch (PS), and rice flour (RF) on GFB’s physical and sensory characteristics, each design producing three single, three binary and six ternary GFB formulations. Results showed that using PF alone resulted in unacceptable GFB. However, the interactions between PF and RF improved the loaf specific volume and the crumb softness and also enhanced appearance, color, odor, texture, flavor, and overall liking. Moreover, the composite formulations prepared with 50% PF and 50% RF (flour basis) presented physical properties and acceptability scores like those of white GFB, prepared with 100% RF or a 50% RF + 50% PS blend (flour basis). Maximum proportions of PF to obtain well-accepted GFB (scores ≥7 for all evaluated attributes on a 10-cm hybrid hedonic scale) were defined at 60% for amaranth flour (AF), 85% for buckwheat flour (BF), and 82% for quinoa flour (QF) in blends with RF. Full article

Most traditional endmember extraction algorithms focus on spectral information, which limits the effectiveness of endmembers. This paper develops a spatial potential energy weighted maximum simplex algorithm (SPEW) for hyperspectral endmember extraction, combining the relevance of hyperspectral spatial context with spectral information to effectively extract endmembers. Specifically, for pixels in a uniform spatial area, SPEW assigns a high weight to pixels with higher spatial potential energy. For pixels scattered in a spatial area, the high weights are assigned to the representative pixels with a smaller spectral angle distance. Then, the optimal endmember collection is determined by the simplex with maximum volume in the space of representative pixels. SPEW not only reduces the complexity of searching for the maximum simplex volume but also improves the performance of endmember extraction. In particular, compared with other newly proposed spatial-spectral hyperspectral endmember extraction methods, SPEW can effectively extract the hidden endmembers in a spatial area without adjusting any parameters. Experiments on synthetic and real data show that the SPEW algorithm has also provides better results than the traditional algorithms. Full article

Endmember estimation plays a key role in hyperspectral image unmixing, often requiring an estimation of the number of endmembers and extracting endmembers. However, most of the existing extraction algorithms require prior knowledge regarding the number of endmembers, being a critical process during unmixing. To bridge this, a new maximum distance analysis (MDA) method is proposed that simultaneously estimates the number and spectral signatures of endmembers without any prior information on the experimental data containing pure pixel spectral signatures and no noise, being based on the assumption that endmembers form a simplex with the greatest volume over all pixel combinations. The simplex includes the farthest pixel point from the coordinate origin in the spectral space, which implies that: (1) the farthest pixel point from any other pixel point must be an endmember, (2) the farthest pixel point from any line must be an endmember, and (3) the farthest pixel point from any plane (or affine hull) must be an endmember. Under this scenario, the farthest pixel point from the coordinate origin is the first endmember, being used to create the aforementioned point, line, plane, and affine hull. The remaining endmembers are extracted by repetitively searching for the pixel points that satisfy the above three assumptions. In addition to behaving as an endmember estimation algorithm by itself, the MDA method can co-operate with existing endmember extraction techniques without the pure pixel assumption via generalizing them into more effective schemes. The conducted experiments validate the effectiveness and efficiency of our method on synthetic and real data. Full article