We consider the fundamental tradeoff between the storage cost and the download cost in private information retrieval (PIR) systems, without any explicit structural restrictions on the storage codes, ...such as maximum distance separable codes or uncoded storage. Our focus in this work is on the two extreme points: the point when the storage cost is minimal, and the point when the download cost is minimal. Two novel outer bounds are provided, which have the following implications at these two extreme points. When the messages are stored without any redundancy across the databases, the optimal PIR strategy is to download all the messages; on the other hand, for PIR capacity-achieving codes, each database can reduce the storage cost, from storing all the messages, by no more than one message on average. To better understand the second extreme point, we then focus on the two-message two-database case, and show that a stronger outer bound can be derived through a novel pseudo-message technique. This stronger outer bound suggests that a precise characterization of the storage-download tradeoff may require more sophisticated bounding techniques.
Exact-repair regenerating codes are considered for the case (n,k,d) = (4,3,3), for which a complete characterization of the rate region is provided. This characterization answers in the affirmative ...the open question whether there exists a non-vanishing gap between the optimal bandwidth-storage tradeoff of the functional-repair regenerating codes (i.e., the cut-set bound) and that of the exact-repair regenerating codes. To obtain an explicit information theoretic converse, a computer-aided proof (CAP) approach based on primal and dual relation is developed. This CAP approach extends Yeung's linear programming (LP) method, which was previously only used on information theoretic problems with a few random variables due to the exponential growth of the number of variables in the corresponding LP problem. The symmetry in the exact-repair regenerating code problem allows an effective reduction of the number of variables, and together with several other problem-specific reductions, the LP problem is reduced to a manageable scale. For the achievability, only one non-trivial corner point of the rate region needs to be addressed in this case, for which an explicit binary code construction is given.
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually ...seen in the information theory literature. The linear programming (LP) outer bound of the entropy space serves as the starting point of this approach; however, our effort goes significantly beyond using it to prove information inequalities. We first identify and formalize the symmetry structure in the problem, which enables us to show the existence of optimal symmetric solutions. A symmetry-reduced linear program is then used to identify the boundary of the memory-transmission-rate tradeoff for several small cases, for which we obtain a set of tight outer bounds. General hypotheses on the optimal tradeoff region are formed from these computed data, which are then analytically proven. This leads to a complete characterization of the optimal tradeoff for systems with only two users, and certain partial characterization for systems with only two files. Next, we show that by carefully analyzing the joint entropy structure of the outer bounds for certain cases, a novel code construction can be reverse-engineered, which eventually leads to a general class of codes. Finally, we show that outer bounds can be computed through strategically relaxing the LP in different ways, which can be used to explore the problem computationally. This allows us firstly to deduce generic characteristic of the converse proof, and secondly to compute outer bounds for larger problem cases, despite the seemingly impossible computation scale.
This report aims to analyze the experimental monkey shortage generated by the COVID‐19 lockdown. The supply capability of the monkey breeding farms is insufficient to meet demand, and the sales ...prices have skyrocketed since 2018. The contradiction will be further aggravated with import prohibition although the countermeasures suggested.
In order to characterize the fundamental limit of the tradeoff between the amount of cache memory and the delivery transmission rate of multiuser caching systems, various coding schemes have been ...proposed in the literature. These schemes can largely be categorized into two classes, namely uncoded prefetching schemes and coded prefetching schemes. While uncoded prefetching schemes in general offer order-wise optimal performance, coded prefetching schemes often have better performance at the low cache memory regime. The significant differences in the coding components between the two classes may leave the impression that they are largely unrelated. In this paper, we provide a connection between the uncoded prefetching scheme proposed by Maddah Ali and Niesen (and its improved version by Yu et al. ) and the coded prefetching scheme proposed by Tian and Chen. A critical observation is made, where a coding component in the Tian-Chen scheme can be replaced by a binary code, which enables us to view the two schemes as the extremes of a more general scheme. An explicit example is given to show that the intermediate operating points of this general scheme can provide new memory-rate tradeoff points previously not known to be achievable in the literature. This new general coding scheme is then presented and analyzed rigorously, which yields a new inner bound to the memory-rate tradeoff for the caching problem.
The ability to slow down wave propagation in materials has attracted significant research interest. A successful solution will give rise to manageable enhanced wave-matter interaction, freewheeling ...phase engineering and spatial compression of wave signals. The existing methods are typically associated with constructing dispersive materials or structures with local resonators, thus resulting in unavoidable distortion of waveforms. Here we show that, with helical-structured acoustic metamaterials, it is now possible to implement dispersion-free sound deceleration. The helical-structured metamaterials present a non-dispersive high effective refractive index that is tunable through adjusting the helicity of structures, while the wavefront revolution plays a dominant role in reducing the group velocity. Finally, we numerically and experimentally demonstrate that the helical-structured metamaterials with designed inhomogeneous unit cells can turn a normally incident plane wave into a self-accelerating beam on the prescribed parabolic trajectory. The helical-structured metamaterials will have profound impact to applications in explorations of slow wave physics.
Standard phase-shifting interferometry (PSI) generally requires collecting at least three phase-shifted interferograms to extract the physical quantity being measured. Here, we propose the ...application of a simple two-frame PSI for the testing of a range of optical surfaces, including flats, spheres, and aspheres. The two-frame PSI extracts modulated phase from two randomly phase-shifted interferograms using a Gram-Schmidt algorithm, and can work in either null testing or non-null testing modes. Since only two interferograms are used for phase demodulation and the phase shift amount can be random, requirements on environmental conditions and phase shifter calibration are greatly relaxed. Experimental results of three different mirrors suggest that the two-frame PSI can achieve comparable measurement precision with conventional multi-frame PSI, but has faster data acquisition speed and less stringent hardware requirements. The proposed two-frame PSI expands the flexibility of PSI and holds great potential in many applications.
Inflammasomes are a class of cytosolic protein complexes. They act as cytosolic innate immune signal receptors to sense pathogens and initiate inflammatory responses under physiological and ...pathological conditions. The NLR-family pyrin domain-containing protein 3 (NLRP3) inflammasome is the most characteristic multimeric protein complex. Its activation triggers the cleavage of pro-interleukin (IL)-1β and pro-IL-18, which are mediated by caspase-1, and secretes mature forms of these mediators from cells to promote the further inflammatory process and oxidative stress. Simultaneously, cells undergo pro-inflammatory programmed cell death, termed pyroptosis. The danger signals for activating NLRP3 inflammasome are very extensive, especially reactive oxygen species (ROS), which act as an intermediate trigger to activate NLRP3 inflammasome, exacerbating subsequent inflammatory cascades and cell damage. Vascular endothelium at the site of inflammation is actively involved in the regulation of inflammation progression with important implications for cardiovascular homeostasis as a dynamically adaptable interface. Endothelial dysfunction is a hallmark and predictor for cardiovascular ailments or adverse cardiovascular events, such as coronary artery disease, diabetes mellitus, hypertension, and hypercholesterolemia. The loss of proper endothelial function may lead to tissue swelling, chronic inflammation, and the formation of thrombi. As such, elimination of endothelial cell inflammation or activation is of clinical relevance. In this review, we provided a comprehensive perspective on the pivotal role of NLRP3 inflammasome activation in aggravating oxidative stress and endothelial dysfunction and the possible underlying mechanisms. Furthermore, we highlighted the contribution of noncoding RNAs to NLRP3 inflammasome activation-associated endothelial dysfunction, and outlined potential clinical drugs targeting NLRP3 inflammasome involved in endothelial dysfunction. Collectively, this summary provides recent developments and perspectives on how NLRP3 inflammasome interferes with endothelial dysfunction and the potential research value of NLRP3 inflammasome as a potential mediator of endothelial dysfunction.
Talar fractures often require osteotomy during surgery to achieve reduction and screw fixation of the fractured fragments due to limited visualization and operating space of the talar articular ...surface. The objective of this study was to evaluate the horizontal approach to the medial malleolus facet by maximizing exposure through dorsiflexion and plantarflexion positions.
In dorsiflexion, plantarflexion, and functional foot positions, we respectively obtained the anterior and posterior edge lines of the projection of the medial malleolus on the medial malleolar facet. The talar model from Mimics was imported into Geomagic software for image refinement. Then Solidworks software was used to segment the medial surface of the talus and extend the edge lines from the three positions to project them onto the "semicircular" base for 2D projection. The exposed area in different positions, the percentage of total area it represents, and the anatomic location of the insertion point at the groove between the anteroposternal protrusions of the medial malleolus were calculated.
The mean total area of the "semicircular" region on the medial malleolus surface of the talus was 542.10 ± 80.05 mm2. In the functional position, the exposed mean area of the medial malleolar facet around the medial malleolus both anteriorly and posteriorly was 141.22 ± 24.34 mm2, 167.58 ± 22.36mm2, respectively. In dorsiflexion, the mean area of the posterior aspect of the medial malleolar facet was 366.28 ± 48.12 mm2. In plantarflexion, the mean of the anterior aspect of the medial malleolar facet was 222.70 ± 35.32 mm2. The mean overlap area of unexposed area in both dorsiflexion and plantarflexion was 23.32 ± 5.94 mm2. The mean percentage of the increased exposure area in dorsiflexion and plantarflexion were 36.71 ± 3.25% and 15.13 ± 2.83%. The mean distance from the insertion point to the top of the talar dome was 10.69 ± 1.24 mm, to the medial malleolus facet border of the talar trochlea was 5.61 ± 0.96 mm, and to the tuberosity of the posterior tibiotalar portion of the deltoid ligament complex was 4.53 ± 0.64 mm.
Within the 3D model, we measured the exposed area of the medial malleolus facet in different positions and the anatomic location of the insertion point at the medial malleolus groove. When the foot is in plantarflexion or dorsiflexion, a sufficiently large area and operating space can be exposed during surgery. The data regarding the exposed visualization area and virtual screws need to be combined with clinical experience for safer reduction and fixation of fracture fragments. Further validation of its intraoperative feasibility will require additional clinical research.
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