Dynamic Dictionary with Subconstant Wasted Bits per Key

Dictionaries have been one of the central questions in data structures. A dictionary data structure maintains a set of key-value pairs under insertions and deletions such that given a query key, the data structure efficiently returns its value. The state-of-the-art dictionaries [Bender, Farach-Colton, Kuszmaul, Kuszmaul, Liu 2022] store $n$ key-value pairs with only $O(n \log^{(k)} n)$ bits of redundancy, and support all operations in $O(k)$ time, for $k \leq \log^* n$. It was recently shown to be optimal [Li, Liang, Yu, Zhou 2023b]. In this paper, we study the regime where the redundant bits is $R=o(n)$, and show that when $R$ is at least $n/\text{poly}\log n$, all operations can be supported in $O(\log^* n + \log (n/R))$ time, matching the lower bound in this regime [Li, Liang, Yu, Zhou 2023b]. We present two data structures based on which range $R$ is in. The data structure for $R<n/\log^{0.1} n$ utilizes a generalization of adapters studied in [Berger, Kuszmaul, Polak, Tidor, Wein 2022] and [Li, Liang, Yu, Zhou 2023a]. The data structure for $R \geq n/\log^{0.1} n$ is based on recursively hashing into buckets with logarithmic sizes.Comment: 46 pages; SODA 202

Dynamic "Succincter"

Augmented B-trees (aB-trees) are a broad class of data structures. The seminal work "succincter" by Patrascu showed that any aB-tree can be stored using only two bits of redundancy, while supporting queries to the tree in time proportional to its depth. It has been a versatile building block for constructing succinct data structures, including rank/select data structures, dictionaries, locally decodable arithmetic coding, storing balanced parenthesis, etc. In this paper, we show how to "dynamize" an aB-tree. Our main result is the design of dynamic aB-trees (daB-trees) with branching factor two using only three bits of redundancy (with the help of lookup tables that are of negligible size in applications), while supporting updates and queries in time polynomial in its depth. As an application, we present a dynamic rank/select data structure for $n$-bit arrays, also known as a dynamic fully indexable dictionary (FID). It supports updates and queries in $O(\log n/\log\log n)$ time, and when the array has $m$ ones, the data structure occupies $$\log\binom{n}{m} + O(n/2^{\log^{0.199}n})$$ bits. Note that the update and query times are optimal even without space constraints due to a lower bound by Fredman and Saks. Prior to our work, no dynamic FID with near-optimal update and query times and redundancy $o(n/\log n)$ was known. We further show that a dynamic sequence supporting insertions, deletions and rank/select queries can be maintained in (optimal) $O(\log n/\log\log n)$ time and with $O(n \cdot \text{poly}\log\log n/\log^2 n)$ bits of redundancy.Comment: 33 pages, 1 figure; in FOCS 202

Tight Cell-Probe Lower Bounds for Dynamic Succinct Dictionaries

A dictionary data structure maintains a set of at most $n$ keys from the universe $[U]$ under key insertions and deletions, such that given a query $x \in [U]$, it returns if $x$ is in the set. Some variants also store values associated to the keys such that given a query $x$, the value associated to $x$ is returned when $x$ is in the set. This fundamental data structure problem has been studied for six decades since the introduction of hash tables in 1953. A hash table occupies $O(n\log U)$ bits of space with constant time per operation in expectation. There has been a vast literature on improving its time and space usage. The state-of-the-art dictionary by Bender, Farach-Colton, Kuszmaul, Kuszmaul and Liu [BFCK+22] has space consumption close to the information-theoretic optimum, using a total of $$\log\binom{U}{n}+O(n\log^{(k)} n)$$ bits, while supporting all operations in $O(k)$ time, for any parameter $k \leq \log^* n$. The term $O(\log^{(k)} n) = O(\underbrace{\log\cdots\log}_k n)$ is referred to as the wasted bits per key. In this paper, we prove a matching cell-probe lower bound: For $U=n^{1+\Theta(1)}$, any dictionary with $O(\log^{(k)} n)$ wasted bits per key must have expected operational time $\Omega(k)$, in the cell-probe model with word-size $w=\Theta(\log U)$. Furthermore, if a dictionary stores values of $\Theta(\log U)$ bits, we show that regardless of the query time, it must have $\Omega(k)$ expected update time. It is worth noting that this is the first cell-probe lower bound on the trade-off between space and update time for general data structures.Comment: 35 page

A Review on MPPT Control Methods of Photovoltaic Systems with DC bus

Maximum point power tracking (MPPT) technology is widely used to improve photovoltaic (PV) output power, and the traditional MPPT control methods are being used more and more widely. However, the PV system controlled by MPPT cannot be directly applied to the direct-current (DC) microgrid, and the output voltage is not stable, resulting in more than the DC bus rated voltage. Based on this problem, some researchers have proposed the control method with DC bus. At present, there are few researches on this control method in the world, the research status and process of this aspect are not discussed in detail. This paper analyzes and summarizes the PV system with DC bus of MPPT control method based on referring to the existing relevant literature, hoping to provide some help for the subsequent research and experiments of relevant researchers

Interface Characteristics and Mechanical Properties of Ultrasonic-Assisted Friction Stir Lap Welded 7075-T6 Aluminium Alloy

In this work, friction stir lap welding (FSLW) and ultrasonic-assisted friction stir lap welding (UAFSLW) was applied to 6-mm-thick 7075-T6 alloy sheets using three welding tools with the same process parameters. The joint formation, microstructural characteristics, and mechanical properties of the resulting lap joints were then investigated. The results showed that ultrasonic vibration significantly promoted the flow of metal at the interface, enlarged the size of the stirred zone (SZ), and reduced the angle between the hook defect and the interface. During lap shear testing, the FSLW and UAFSLW joints fractured in a similar manner. The fracture modes included tensile fracture, shear fracture, and a mixture of both. Cold lap and hook defects may have served as crack-initiation zones within the joint. Under configuration A (i.e., upper sheet on the retreating side (RS)), all joints failed in the shear-fracture mode. The effective lap width (ELW) of the joint welded using tool T2 was the greatest. This resulted in a higher shear fracture strength. The maximum shear fracture strength of the UAFSLW joint was 663.1 N/mm. Under configuration B (i.e., upper sheet on the advancing side (AS)), the shear fracture strength was greatly affected by the fracture mode. The highest shear fracture strength of the UAFSLW joint, 543.7 N/mm, was welded by tool T3. Thus, under otherwise identical conditions, UAFSLW joints can withstand a greater fracture shear strength than FSLW joints, as ultrasonic vibration helps to mix the material at the interface, thus, enlarging the SZ and diminishing the cold lap defects

Restirring and Reheating Effects on Microstructural Evolution of Al&ndash;Zn&ndash;Mg&ndash;Cu Alloy during Underwater Friction Stir Additive Manufacturing

Friction stir additive manufacturing (FSAM) can be potentially used for fabricating high-performance components owing to its advantages of solid-state processing. However, the inhomogeneous microstructures and mechanical properties of the build attributed to the complex process involving restirring and reheating deserve attention. This study is based on the previous research of the underwater FSAMed 7A04 aluminum alloy and adopts a quasi in situ experimental method, i.e., after each pass of the underwater FSAM, samples were taken from the build for microstructural observation to investigate the restirring and reheating effects on microstructural evolution during the underwater FSAM. Fine-grain microstructures were formed in the stir zone during the single-pass underwater FSAM. After restirring, the grain size at the bottom of the overlapping region decreased from 1.97 to 0.87 &mu;m, the recrystallization degree reduced from 74.0% to 29.8%, and the initial random texture transformed into a strong shear texture composed of the C {110}&lt;11&macr;0&gt;. After reheating, static recrystallization occurred in the regions close to the new additive zones, increasing the grain size and recrystallization degree. This study not only revealed the microstructural evolution during the underwater FSAM but also provided a guideline for further optimization of the mechanical properties of the Al&ndash;Zn&ndash;Mg&ndash;Cu alloy build

Effect of Post-Fabricated Aging on Microstructure and Mechanical Properties in Underwater Friction Stir Additive Manufacturing of Al–Zn–Mg–Cu Alloy

The fabricated Al–Zn–Mg–Cu alloy build has low mechanical properties due to the dissolution of strengthening precipitates back into the matrix during friction stir additive manufacturing (FSAM). Post-fabricated aging was considered an effective approach to improve the mechanical performance of the build. In this study, various post-fabricated aging treatments were applied in the underwater FSAM of Al–7.5 Zn–1.85 Mg–1.3 Cu–0.135 Zr alloy. The effect of the post-fabricated aging on the microstructure, microhardness, and local tensile properties of the build was investigated. The results indicated that over-aging occurred in the low hardness zone (LHZ) of the build after artificial aging at 120 °C for 24 h as the high density of grain boundaries, subgrain boundaries, dislocations, and Al3Zr particles facilitated the precipitation. Low-temperature aging treatment can effectively avoid the over-aging problem. After aging at 100 °C for 48 h, the average microhardness value of the build reached 178 HV; the yield strength of the LHZ and high hardness zone (HHZ) was 453 MPa and 463 MPa, respectively; and the ultimate tensile strength of the LHZ and HHZ increased to 504 MPa and 523 MPa, respectively

Fluid‐Driven High‐Performance Bionic Artificial Muscle with Adjustable Muscle Architecture

High‐performance artificial muscle is always the pursuit of researchers for robotics. Herein, a bionic artificial muscle is reported called “ExoMuscle” mimicking the sarcomere in skeletal muscle with a bio‐inspired structure to contract “myofilaments” enabling the artificial muscle to mimic the architecture of muscle such as parallel, fusiform, convergent, and pennation and beyond the performance of skeletal muscle. The reported actuators excel in various aspects compared with skeletal muscle including actuation stress (0.41–0.9 MPa), strain (50%), optimal length, velocity‐independence output, power density (10.94 kW kg−1), and efficiency (69.11%). With its own adjustable pennation architecture, it achieves variable actuation stress up to 0.9 MPa meanwhile maintaining high efficiency. Furthermore, ExoMuscle highly conforms to the anatomical complexity of the human body to cooperate with skeletal muscles closely opening the door for bio‐robotics, especially wearable robots

Analysis of the relationship between the response after the First-line chemotherapy and the survival in the advanced non-small cell lung cancer

Background and objective Most patients with advanced non-small cell lung cancer (NSCLC) treated with first-line chemotherapy consisted of the third generation new drug got the disease in control (CR+PR+SD).In this study, we retrospectively reviewed our data to investigate the difference of survival between patients of disease control and progression (PD), and disease response (CR+PR) and stable (SD), to identify the prognosis factor correlated with survival. Methods In our retrospective study, 118 patients with stage IIIB (with malignancy pleural fluid) and IV NSCLC were identified who received the third generation new drug-based platinum or non-platinum regimens, the response of first-line chemotherapy were complete response (CR), partial response (PR), stable disease (SD) and progression disease (PD) according to RECIST criteria based on the records on the imaging reports papers. Results After first-line chemotherapy, 86 (72.9%) patients [CR2 (1.7%), PR47 (39.8%), SD37 (31.4%)) had disease control and 33 (27.1%) patients had progression disease. The median survival time of CR+PR+SD arm was significantly longer than PD arm (17.8 months vs 8.4 months, P=0.001), but there was no significant difference between CR+PR arm and SD arm (18.1 months vs 15.5 months, P=0.917), the PFS between two arms were no significantly different too (7.1 months vs 6.9 months, P=0.622). The Cox regression analysis shows that stage (IIIB or IV), chemotherapy lines (less than three lines or more than four lines) and disease control or not after first-line chemotherapy were independently prognosis factor of overall survival. Conclusion Our data shows that the survival of response and stable disease patients are better than that of patient with progression disease, the survival benefit of patients with stable disease and responses are no significantly difference