Narrow Results

In the field of cytopathology, the accurate identification and counting of white blood cells (WBCs) in blood smears is crucial for diagnosing various types of cancer. The process of manually detecting and segmenting these structures, however, can be challenging due to their variable morphologies and the presence of overlapping objects in the images. This makes manual detection time-consuming, labor-intensive, and prone to error, particularly for individuals without extensive experience in cytopathology. In this paper, a deep learning algorithm is developed based on a Mask R-CNN model and driven by a sub-algorithm called KOWN (Keep Only White Blood Cells with Nuclei) for WBC segmentation and counting. The proposed algorithm improves the accuracy of measurements compared to other rapidly growing deep learning works, providing maximum precision in detecting and counting WBCs in both low- and high-blood-cell-density images.

Valiant defined #P-completeness using Turing reductions. We propose a more restrictive definition, a variant of many-one reductions, and prove that the (0, 1)-permanent remains #P-complete under this definition.

Mantispids are small brown bugs about 1.5 cm in length. Mantispid eggs are produced in large quantities, with about 1000 eggs per spawning, and are tiny and densely packed. Traditionally, mantispid eggs are counted manually. However, counting such a large quantity of eggs is difficult. To provide accurate data for researchers, we detail methods to accurately detect and count the number of mantispid eggs using image processing. The following methods were used to count the mantispid eggs: background estimation, morphological image processing, background subtraction, stretching, image thresholding, gray-level transformation, labeling and counting. The results of automated counting were compared with the results of manual counting. The segmentation results were verified, and the accuracy of the mantispid egg counts was determined to be 100%. This provides a useful resource for mantispid egg counting. The automatic counting system cannot only count mantispid eggs, it can also be used to count other similar insect eggs.

Pass transistor logic (PTL) is a circuit design technique wherein transistors are used as switches. The reconfigurable mesh (RM) is a model that exploits the power of PTLs signal switching, by enabling flexible bus connections in a grid of processing elements containing switches. RM algorithms have theoretical results proving that $\mathrm{\text{switching}}+\mathrm{\text{signal}}-\mathrm{\text{broadcasting}}$ can speed up computations significantly. However, the RM assumes that the latency of broadcasting a signal through $n$ switches (bus length) is 1. This is an unrealistic assumption preventing physical realizations of the RM.

We propose the restricted-RM (RRM) wherein the bus lengths are restricted to $k=n^{\frac{1}{d}}$, $d=2,3,\dots$. We show that counting the number of 1-bits in an input of $n$ bits can be done in $2\cdot d$ steps for $d=2,3,\dots$ by an $n\times n$ RRM. An almost matching lower bound is presented, using a technique which adds to the few existing lower-bound techniques in this area. Finally, the algorithm was directly coded over an FPGA, outperforming an optimal tree of adders.

This work presents an alternative way of counting, which is fundamental for summing, beating regular Boolean circuits for large numbers, where summing a vast amount of numbers is the basis of any accelerator in embedded systems such as neural-nets and streaming.^a

We show that finding the simplices containing a fixed given point among those defined on a set of n points can be done in O(n + k) time for the two-dimensional case, and in O(n² + k) time for the three-dimensional case, where k is the number of these simplices.

As a byproduct, we give an alternative (to the algorithm in Ref. 4) O(n log r) algorithm that finds the red-blue boundary for n bichromatic points on the line, where r is the size of this boundary. Another byproduct is an O(n² + t) algorithm that finds the intersections of line segments having two red endpoints with those having two blue endpoints defined on a set of n bichromatic points in the plane, where t is the number of these intersections.

Finding the extreme value of a database or a function plays an important role in computing and communication applications. Unfortunately, classical solutions suffer from computational complexity if the database is unsorted or, equivalently, the function has many local minimum/maximum points. Proposed quantum computing based solutions can guarantee success only in terms of the expected value of the database queries. In this paper we introduce a new technique exploiting the parallel processing capabilities of quantum computing in a different way. We derive quantum existence testing which allows adapting the classical logarithmic search algorithm suitable for structured databases to unstructured ones while maintaining its efficiency.

In this paper, for odd primes p we find a recursive formula for the number of regular orbits of an extra-special p-group of exponent p² acting on a faithful irreducible module over a finite field. This complements an earlier result of Foulser for extra-special groups of order p.

What is the probability for a number field of composite degree d to have a nontrivial subfield? As the reader might expect the answer heavily depends on the interpretation of probability. We show that if the fields are enumerated by the smallest height of their generators the probability is zero, at least if d > 6. This is in contrast to what one expects when the fields are enumerated by the discriminant. The main result of this paper is an estimate for the number of algebraic numbers of degree d = en and bounded height which generate a field that contains an unspecified subfield of degree e. If n > max{e² + e, 10}, we get the correct asymptotics as the height tends to infinity.

We give an efficient encoding and decoding scheme for computing a compact representation of a graph in one of unordered reduced trees, cographs and series-parallel graphs. The unordered reduced trees are rooted trees in which (i) the ordering of children of each vertex does not matter, and (ii) no vertex has exactly one child. This is one of basic models frequently used in many areas. Our algorithm computes a bit string of length 2ℓ – 1 for a given unordered reduced tree with ℓ ≥ 1 leaves in O(ℓ) time, whereas a known folklore algorithm computes a bit string of length 2n – 2 for an ordered tree with n vertices. Note that in an unordered reduced tree, ℓ ≤ n < 2ℓ holds. To the best of our knowledge this is the first of such a compact representation for unordered reduced trees. From the theoretical point of view, the length of the representation gives us an upper bound of the number of unordered reduced trees with ℓ leaves. Precisely, the number of unordered reduced trees with ℓ leaves is at most 2^2ℓ–2 for ℓ ≥ 1. Moreover, the encoding and decoding can be done in linear time. Therefore, from the practical point of view, our representation is also useful to store a lot of unordered reduced trees efficiently. We also apply the scheme for computing a compact representation to cographs and series-parallel graphs. We show that each of cographs with n vertices has a compact representation in 2n – 1 bits, and the number of cographs with n vertices is at most 2^2n–1. The resulting number is close to the number of cographs with n vertices obtained by the enumeration for small n that approximates Cdⁿ/n^3/2, where C = 0.4126⋯ and d = 3.5608⋯. Series-parallel graphs are well-investigated in the context of the graphs of bounded treewidth. We give a method to represent a series-parallel graph with m edges in ⌈2.5285m – 2⌉ bits. Hence the number of series-parallel graphs with m edges is at most 2^{⌈2.5285m–2⌉}. As far as the authors know, this is the first non-trivial result about the number of series-parallel graphs. The encoding and decoding of the cographs and series-parallel graphs also can be done in linear time.

We present in this paper a code for the class of unlabeled split–indifference graphs. This codification allows us to establish the exact number of elements of the class up to isomorphism. In order to obtain this result, structural properties of the class are explored, including a new approach for the characterization theorem.

Apoptosis is an erratic physiological process whereby cells undergo a self-destruction process. A quantitative analysis of apoptosis, namely counting the number of cells undergoing apoptosis, is required not only to understand the mechanism of this process but also to quantitatively evaluate the effect of anticancer drugs as many anticancer drugs attempt to achieve their effects by inducing the cancer cell to apoptosis. Currently, counting cells undergoing apoptosis is generally carried out manually by the naked eyes. Although these methods are accurate and appropriate in some cases, they can be extremely time consuming and labor intensive. Also, manual counting is subjective and difficult to achieve high throughput. There is compelling necessity for developing an automatic apoptosis-counting method. In this paper, we described an image-based method, which is applied in HCT116 human colon adenocarcinoma cell culture to count the number of apoptosis induced by anticancer drug oxaliplatin. Our methods are mostly based on well-known and mature algorithms in image processing and pattern recognition such as the contrast-limited adaptive histogram equalization, pixel classification, size distribution detection by granulometries, watershed algorithm, and artificial neural networks. We evaluated our segmentation results using the area overlap measurement, and the best achieved performance that can reach over 98%. We also evaluated our apoptosis detection results against the results of four biomedical experts and compared the results with other existing efforts. The final performance shows that our method is more reliable and accurate for detecting apoptosis than the previous methods.

Mantispids are small brown bugs about 1.5 cm in length. Mantispid eggs are produced in large quantities, with about 1000 eggs per spawning, and are tiny and densely packed. Traditionally, mantispid eggs are counted manually. However, counting such a large quantity of eggs is difficult. To provide accurate data for researchers, we detail methods to accurately detect and count the number of mantispid eggs using image processing. The following methods were used to count the mantispid eggs: background estimation, morphological image processing, background subtraction, stretching, image thresholding, gray-level transformation, labeling and counting. The results of automated counting were compared with the results of manual counting. The segmentation results were verified, and the accuracy of the mantispid egg counts was determined to be 100%. This provides a useful resource for mantispid egg counting. The automatic counting system cannot only count mantispid eggs, it can also be used to count other similar insect eggs.