In this investigation we study a family of networks, called spiders, which covers a range of networks going from chains to complete graphs. These spiders are characterized by three parameters: the number of nodes in the core, the number of legs at each core node, and the length of these legs. Keeping two of the three parameters constant we investigate if spiders are small worlds in the sense recently defined by Egghe.

This paper presents the development of an adaptive intelligent spider robot. With the incorporation of sensors, the four-legged spider robot is able to monitor the environment wirelessly. A new auto-station adaptation National Instrument (NI) controller in the application for an intelligent robot is proposed. The research work will solve the weak adaptive ability of conventional existing robot. The proposed project proposes a self-adaptive smart spider robot that functions without human interfacing. The proposed design utilizes the control scheme with National Instruments (NI) LabVIEW to produce a smart portable system. Furthermore, the adaptive intelligent spider robot easily adapts to new situations when facing obstacles. The design is carried out using feedback loop schematic LabVIEW interfacing with the smart controller and incorporation of GH-311 Ultrasonic Sensor to detect any obstacle in front of the robot, GH-312 Smoke Sensor which use to detect smoke in the particular area and LM35 Temperature sensor to get the temperature for the surround. The proposed module was designed and implemented using movable wireless Router Module TP-Link TL-MR3420 Router transceiver for device communication. The robot was tested and analyzed showing the system efficiency of above 95%, which is competent in robotic applications

It has been known for more than 300 years that the shape of an inelastic hanging cable, chain, or rope of uniform linear mass density is the graph of the hyperbolic cosine, up to scaling and shifting coordinates. But given two points at which the ends of the cable are attached, how exactly should we scale and shift the coordinates? Many otherwise excellent expositions of the problem are a little vague about that. They might for instance give the answer in terms of the tension at the lowest point, but without explaining how to compute that tension. Here we discuss how to obtain all necessary parameters. To obtain the tension at the lowest point, one has to solve a nonlinear equation numerically. When the two ends of the cable are attached at different heights, a second nonlinear equation must be solved to determine the location of the lowest point. When the cable is elastic, think of a thread in a spider's web for instance, the two equations can no longer be decoupled, but they can be solved using two-dimensional Newton iteration.

A tensor category is multiplicity-free if for any objects $A,B,CA,B,C$ we have that $\mathrm{H}\mathrm{o}\mathrm{m}(A\otimes B\otimes C,\mathbb{C})\backslash mathrm\{Hom\}(A\backslash otimes\; B\backslash otimes\; C,\backslash mathbb\{C\})$ is either $00$ or $11$ dimensional. It is known that $Re{p}^{uni}(U_q(\mathfrak{s}\mathfrak{p}(4)))Rep^\{uni\}(U\_q(\backslash mathfrak\{sp\}(4)))$ is not multiplicty-free. We find a full subcategory of $Re{p}^{uni}(U_q(\mathfrak{s}\mathfrak{p}(4)))Rep^\{uni\}(U\_q(\backslash mathfrak\{sp\}(4)))$ which is multiplicty-free. A description of the dimension of these $\mathrm{H}\mathrm{o}\mathrm{m}\backslash mathrm\{Hom\}$ spaces is given for this subcategory, including when $qq$ is a root of unity. The methods used arise from the description, given by Kuperberg, of $Re{p}^{uni}(U_q(\mathfrak{s}\mathfrak{p}(4)))Rep^\{uni\}(U\_q(\backslash mathfrak\{sp\}(4)))$ as a spider. The main tool is the recursive definition of clasps given by Kim. In particular, we provide an appropriate notion of admissibility when looking at the $\mathrm{S}\mathrm{p}(4{)}_k\backslash mathrm\{Sp\}(4)\_k$ ribbon graph invariants with restricted edge labels.

Language availability, translation quality, and interface usability are distinct outcomes, yet comparisons of widely supported and underrepresented languages can collapse them into a single ranking. This paper critically reviews eleven selected sources relevant to Amharic, Afaan Oromo, low-resource translation, dataset quality, and human evaluation. The synthesis finds direct research on both languages, evidence of language-specific resource construction, and reasons to question the transfer of prose benchmarks to interface tasks. It also identifies reporting inconsistencies that make unqualified numerical rankings inappropriate for one examined English-Amharic study. The paper contributes a coverage-and-quality decomposition, an account of cross-language comparability, and criteria for interpreting a software-domain language gap. No current provider-support audit, new translation benchmark, or estimate of a gap against European languages is reported. The central conclusion is that an interpretable language-gap claim requires aligned tasks and transparent coverage, together with qualified language-specific evaluation.

Spider silk is a remarkable example of bio-material with superior mechanical characteristics. Its multilevel structural organization of dragline and viscid silk leads to unusual and tunable properties, extensively studied from a quasi-static point of view. In this study, inspired by the Nephila spider orb web architecture, we propose a novel design for mechanical metamaterials based on its periodic repetition. We demonstrate that spider-web metamaterial structure plays an important role in the dynamic response and wave attenuation mechanisms. The capability of the resulting structure to inhibit elastic wave propagation in sub-wavelength frequency ranges is assessed and parametric studies are performed to derive optimal configurations and constituent mechanical properties. The results show promise for the design of innovative lightweight structures for tunable vibration damping and impact protection, or the protection of large scale infrastructure such as suspended bridges.

Spider walks are systems of interacting particles. The particles move independently as long as their movement do not violate some given rules describing the relative position of the particles; moves that violate the rules are not realized. The goal of this paper is to study qualitative properties, as recurrence, transience, ergodicity, and positive rate of escape of these Markov processes.

This project investigates the potential of computers to solve complex tasks such as games. The paper proves that the complexity of a generalized version of spider solitaire is NP-Complete and uses much of structure of the proof that FreeCell is NP-Hard in the paper Helmert, M. "Complexity Results for Standard Benchmark Domains in Planning." Artificial Intelligence 143.2 (2003): 219-62. Print. A given decision problem falls in to the class NP-Complete if it is proven to be both in NP and in NP-Hard. To prove that this is the case the paper shows that, not only do the kinds of possible moves that can be reversed prove this, but it is also shown that no spider solitaire game of size n will take more than a polynomial number of moves to complete if such a completion is possible. The paper reduces 3-SAT to SpiderSolitaire (the name used throughout the proof when referring to the generalized version of popular solitaire variant "Spider Solitaire") by showing that any 3-SAT instance can be replicated using an appropriately arranged initial tableau. The example provided reinforces the proof of NP-Hardness and helps to make the proof easier to understand, but the definitive proof lies in the equations providing instruction on how to set up any 3-SAT instance of clause size C as a instance of SpiderSolitaire.

Learning dexterous and agile policy for humanoid and dexterous hand control requires large-scale demonstrations, but collecting robot-specific data is prohibitively expensive. In contrast, abundant human motion data is readily available from motion capture, videos, and virtual reality, which could help address the data scarcity problem. However, due to the embodiment gap and missing dynamic information like force and torque, these demonstrations cannot be directly executed on robots. To bridge this gap, we propose Scalable Physics-Informed DExterous Retargeting (SPIDER), a physics-based retargeting framework to transform and augment kinematic-only human demonstrations to dynamically feasible robot trajectories at scale. Our key insight is that human demonstrations should provide global task structure and objective, while large-scale physics-based sampling with curriculum-style virtual contact guidance should refine trajectories to ensure dynamical feasibility and correct contact sequences. SPIDER scales across diverse 9 humanoid/dexterous hand embodiments and 6 datasets, improving success rates by 18% compared to standard sampling, while being 10X faster than reinforcement learning (RL) baselines, and enabling the generation of a 2.4M frames dynamic-feasible robot dataset for policy learning. As a universal physics-based retargeting method, SPIDER can work with diverse quality data and generate diverse and high-quality data to enable efficient policy learning with methods like RL.

Translation usage charges alone cannot determine the cost of releasing and maintaining a localized application. This paper reviews selected localization and post-editing evidence and derives an analytical comparison of hand-managed resources, API-based workflows, and localization platforms. Eight core sources and two accounting frameworks inform the distinction between translation productivity, application integration, and acceptable release quality. The resulting model includes common internationalization work, workflow-specific setup, recurring language-dependent labor, and external charges. It derives a break-even condition for recurring releases and shows algebraically why a reduction in generation price can be outweighed by additional review effort. The contribution is a quality-constrained accounting model, not a measured Next.js case study. No vendor prices, observed engineering hours, original cost savings, or Linguana performance figures are reported. The analysis identifies the conditions under which an economic comparison is interpretable and the measurements needed to instantiate it.

We prove a conjecture of L^{e} and Sikora by providing a comparison between various existing $S{L}_{n}SL\_n$ skein theories. While doing so, we show that the full subcategory of the spider category, $\mathcal{S}p(S{L}_n)\backslash mathcal\{S\}p(SL\_n)$, defined by Cautis-Kamnitzer-Morrison, whose objects are monoidally generated by the standard representation and its dual, is equivalent as a spherical braided category to Sikora's quotient category. This also answers a question from Morrison's Ph.D. thesis. Finally, we show that the skein modules associated to the CKM and Sikora's webs are isomorphic.

The population of millisecond pulsars (MSPs) has been expanded considerably in the last decade. Not only is their number increasing, but also various classes of them have been revealed. Among different classes of MSPs, the behaviour of black widows and redbacks are particularly interesting. These systems consist of an MSP and a low-mass companion star in compact binaries with an orbital period of less than a day. In this article, we give an overview of the high energy nature of these two classes of MSPs. Updated catalogues of black widows and redbacks are presented and their X ray/$\gamma \backslash gamma$-ray properties are reviewed. Besides the overview, using the most updated eight-year Fermi Large Area Telescope point source catalog, we have compared the $\gamma \backslash gamma$-ray properties of these two MSP classes. The results suggest that the X-rays and $\gamma \backslash gamma$-rays observed from these MSPs originate from different mechanisms. Lastly, we will also mention the future prospects of studying these spider pulsars with the novel methodologies as well as upcoming observing facilities.

Martian araneiform terrain, located in the Southern polar regions, consists of features with central pits and radial troughs which are thought to be associated with the solid state greenhouse effect under a CO${}_2\_\{2\}$ ice sheet. Sublimation at the base of this ice leads to gas buildup, fracturing of the ice and the flow of gas and entrained regolith out of vents and onto the surface. There are two possible pathways for the gas: through the gap between the ice slab and the underlying regolith, as proposed by Kieffer et al (2007), or through the pores of a permeable regolith layer, which would imply that regolith properties can control the spacing between adjacent spiders, as suggested by Hao et al. We test this hypothesis quantitatively in order to place constraints on the regolith properties. Based on previously estimated flow rates and thermophysical arguments, we suggest that there is insufficient depth of porous regolith to support the full gas flow through the regolith. By contrast, free gas flow through a regolith--ice gap is capable of supplying the likely flow rates for gap sizes on the order of a centimetre. This size of gap can be opened in the centre of a spider feature by gas pressure bending the overlying ice slab upwards, or by levitating it entirely as suggested in the original Kieffer et al (2007) model. Our calculations therefore support at least some of the gas flowing through a gap opened between the regolith and ice. Regolith properties most likely still play a role in the evolution of spider morphology, by regolith cohesion controlling the erosion of the central pit and troughs, for example.

Modern software design practice implies widespread use in the development of ready-made components, usually designed as external libraries. The undoubted advantages of reusing third-party code can be offset by integration errors that appear in the developed software. The reason for the appearance of such errors is mainly due to misunderstanding or incomplete understanding by the programmer of the details of external libraries such as an internal structure and the subtleties of functioning. The documentation provided with the libraries is often very sparse and describes only the main intended scenarios for the interaction of the program and the library. In this paper, we propose the approach based on the use of formal library specifications, which allows detecting integration errors using static analysis methods. To do this, the external library is described using the LibSL specification language, the resulting description is translated into the internal data structures of the KEX analyzer. The execution of the incorrect scenarios of library usage, such as the incorrect sequence of method calls or the violation of the API function contract, is marked in the program model with special built-in functions of the KEX analyzer. Later, when analyzing the program, KEX becomes able to detect integration errors, since incorrect library usage scenarios are diagnosed as calling marked functions. The proposed approach is implemented as SPIDER (SPecification-based Integration Defect Revealer), which is an extension of the Kex analyzer and has proven its efficiency by detecting integration errors of different classes on several special-made projects, as well as on several projects taken from open repositories.

Translation quality in a web application includes more than the linguistic quality of resource text. Messages interact with parsers, runtime values, locale-dependent selection, document direction, and constrained components. This paper synthesizes ten core research and authoritative technical sources plus a versioned MQM specification to derive a layered account of translation correctness for React applications. It distinguishes resource validity, message semantics, rendering behavior, and task meaning, then organizes failures by both observable symptom and attributable cause. The analytical result is a release-readiness model in which linguistic adequacy cannot compensate for broken technical contracts, and technical validity cannot establish correct meaning. The paper also identifies denominator and attribution choices that affect reported failure rates. The taxonomy is proposed for application and validation; no React translation benchmark, prevalence estimate, or product comparison is reported.

Context is often proposed as a remedy for ambiguous interface translations, but evidence about document translation does not automatically establish an effect on web-application strings. This paper critically reviews thirteen selected research sources spanning software localization, contextual neural translation, document adaptation, and evaluation. The review distinguishes information supplied during inference from changes to training or architecture, and separates translation context from the context available to evaluators. The synthesis identifies evidence that contextual systems can improve particular discourse phenomena, counterevidence concerning the source of aggregate gains, and substantial limits on transfer to interface tasks. The paper's contribution is an evidence-transfer framework and a factorial estimand for separating local context, terminology instructions, and their interaction. The reviewed findings support targeted evaluation of context rather than a universal quality claim. No new translation experiment, system ranking, or estimate of Linguana performance is reported.